On Being Unpredictable and Winning

Abstract

In theory, it can be strategically advantageous for competitors to make themselves unpredictable to their opponents, for example, by variably mixing hostility and friendliness. Empirically, it remains open whether and how competitors make themselves unpredictable, why they do so, and how this conditions conflict dynamics and outcomes. We examine these questions in interactive attacker–defender contests, in which attackers invest to capture resources held and defended by their opponent. Study 1, a reanalysis of nine (un)published experiments (total N = 650), reveals significant cross-trial variability especially in proactive attacks and less in reactive defense. Study 2 (N = 200) shows that greater variability makes both attacker’s and defender’s next move more difficult to predict, especially when variability is due to occasional rather than (in)frequent extreme investments in conflict. Studies 3 (N = 27) and 4 (N = 106) show that precontest testosterone, a hormone associated with risk-taking and status competition, drives variability during attack which, in turn, increases sympathetic arousal in defenders and defender variability (Study 4). Rather than being motivated by wealth maximization, being unpredictable in conflict and competition emerges in function of the attacker’s desire to win “no matter what” and comes with significant welfare cost to both victor and victim.

Full text

On Being Unpredictable and Winning
Carsten K. W. De Dreu
1
,Jörg Gross
2
, Andrea Arciniegas
1
, Laura C. Hoenig
1
,
Michael Rojek-Giffin
1
, and Daan T. Scheepers
1, 3
1
Institute of Psychology, Leiden University
2
Institute of Psychology, University of Zurich
3
Organizational Behavior, Utrecht University
In theory, it can be strategically advantageous for competitors to make themselves unpredictable to their
opponents, for example, by variably mixing hostility and friendliness. Empirically, it remains open whether
and how competitors make themselves unpredictable, why they do so, and how this conditions conflict
dynamics and outcomes. We examine these questions in interactive attacker–defender contests, in which
attackers invest to capture resources held and defended by their opponent. Study 1, a reanalysis of nine
(un)published experiments (total N=650), reveals significant cross-trial variability especially in proactive
attacks and less in reactive defense. Study 2 (N=200) shows that greater variability makes both attacker’s
and defender’s next move more difficult to predict, especially when variability is due to occasional rather
than (in)frequent extreme investments in conflict. Studies 3 (N=27) and 4 (N=106) show that precontest
testosterone, a hormone associated with risk-taking and status competition, drives variability during attack
which, in turn, increases sympathetic arousal in defenders and defender variability (Study 4). Rather than
being motivated by wealth maximization, being unpredictable in conflict and competition emerges in
function of the attacker’s desire to win “no matter what”and comes with significant welfare cost to both
victor and victim.
Keywords: behavioral game theory, predator–prey dynamics, testosterone, sympathetic arousal
In the aftermath of a civil war marked by ethnic cleansing and
genocide, former diplomat Richard Holbrooke mediated a peace
settlement between the leaders of Serbia and Bosnia-Herzegovina.
His memoires recount that, at some point, the Serbian army general
Ratko Mladic “suddenly …erupted [into] a long, emotional
diatribe. …I did not know if his rage was real or feigned, but this
was the genuine Mladic, the one who could unleash a murderous
rampage”(Holbrooke, 1999; p. 150). Mladic’s unexpected eruption
reminds of former U.S. president Nixon who, at the height of the
Vietnam War, pondered:
I want the North Vietnamese to believe I’ve reached the point where I
might do anything to stop the war. We’ll just slip the word to them
that …he has his hand on the nuclear button and Ho Chi Minh himself
will be …begging for peace. (Haldeman, 1978, p. 83)
And it reminds of Donald Trump’sfirst foreign policy speech:
I have a simple message for [ISIS]. Their days are numbered. I won’t tell
them where and I won’t tell them how. We must, we must as a nation be
more unpredictable. We are totally predictable. We tell everything.
We’re sending troops …have a news conference. We have to …be
unpredictable starting now. (New York Times, 2016)
In both international conflict and interpersonal competition,
individuals sometimes erratically switch between hostile and friendly
behavior, or between moving against and moving away (Hilty &
Carnevale, 1993;Sinaceur et al., 2013). Such variability in conflict
behavior may render one unpredictable to outsiders and some
have suggested that it can be functional: “Sometimes [it] can be
wise to simulate madness”(Machiavelli, 1531/2013, p. 68) and
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Carsten K. W. De Dreu https://orcid.org/0000-0003-3692-4611
Jörg Gross https://orcid.org/0000-0002-5403-9475
This project has received funding from the European Research Council
under the European Union’s Horizon 2020 research and innovation
programme, AdG agreement n° 785635 awarded to Carsten K. W. De
Dreu. The authors thank Zsombor Meder for supporting the game-theoretic
analysis of the attacker–defender contest. The authors have no conflicts of
interest to disclose.
The authors report how the authors determined the authors’sample size, all
data exclusions, all manipulations, and all measures in the study. All data,
analysis code, and background materials are available at https://doi.org/
10.34894/WUTY3N. Study design and analyses were not preregistered.
Carsten K. W. De Dreu played a lead role in conceptualization, data
curation, formal analysis, funding acquisition, investigation, project
administration, supervision, and writing–original draft and an equal role
in methodology, validation, visualization, and writing–review and editing.
Jörg Gross played a supporting role in writing–review and editing and an
equal role in data curation, formal analysis, investigation, and methodology.
Andrea Arciniegas played a supporting role in data curation, methodology,
and software. Laura C. Hoenig played a supporting role in data curation,
investigation, methodology, visualization, and writing–review and editing.
Michael Rojek-Giffin played a supporting role in data curation, investigation,
visualization, and writing–review and editing. Daan T. Scheepers played a
supporting role in investigation, methodology, supervision, and writing–
review and editing and an equal role in data curation and validation.
Correspondence concerning this article should be addressed to
Carsten K. W. De Dreu, Institute of Psychology, Leiden University,
Wassenaarseweg 52, 2300 RA, Leiden, The Netherlands. Email:
c.k.w.de.dreu@fsw.leidenuniv.nl
Journal of Personality and Social Psychology:
Attitudes and Social Cognition
© 2024 American Psychological Association 2024, Vol. 126, No. 3, 369–389
ISSN: 0022-3514 https://doi.org/10.1037/pspa0000378
369

strategically advantageous to be unpredictable (Schelling, 1960). Yet
four issues remain open that we aim to address. First, there is limited
evidence that competitors are variable in their conflict behavior.
Second, work in cognitive science calls into doubt whether variable
mixing of actions during conflict makes competitors irreducible
unpredictable to their opponents (Burns & Vollmeyer, 1998;Cooper,
2016;Sanderson, 2018;Wagenaar, 1972;Warren et al., 2018;Wong
et al., 2021). Third, the biological and psychological mechanisms
producing unpredictability remain poorly understood. Finally, we do
not know how being (unpredictably) variable in one’s behavior
conditions conflict dynamics, individual payoffs, and the likelihood
of winning.
Unpredictability in Conflict and Competition
The idea that being unpredictable can be strategically advanta-
geous is at the heart of the conceptualization of conflict as a game of
strategy (Camerer, 2003;Kimbrough et al., 2020;Schelling, 1960).
In its simplest form, a game of strategy involves two agents each
with two actions to choose from. Agents are assumed to be rational
and risk neutral and expected payoff maximizing (viz., homo
economicus), and conflict emerges when the outcome that one agent
prefers is at odds with the outcome preferred by the other agent
(De Dreu, 2010;Pruitt, 1998;Pruitt & Kimmel, 1977;Rusbult &
Van Lange, 2003;Schelling, 1960). A prime example is the
prisoner’s dilemma game in which agents can choose between
“cooperate”and “defect.”All else equal, to maximize personal
payoffs, agents in the prisoner’s dilemma game should defect
regardless of whether they expect the other to cooperate, or to defect
as well (Camerer, 2003;Halevy & Chou, 2014;McClintock &
Liebrand, 1988;van Dijk & De Dreu, 2021).
In games of strategy like the prisoner’s dilemma, randomly
switching between actions has no clear advantages, and agents do
not need to care about their counterpart being able to predict their
next move (Axelrod & Hamilton, 1981;Camerer, 2003;Sheldon,
1999). This is different in games of strategy with its equilibrium in
mixed strategies, such as hide-and-seek games (Bar-Hillel, 2015;
Lahat-Rania & Kareev, 2023), best-shot-weakest link games (Clark
& Konrad, 2007), inspection games (Nosenzo et al., 2016), and
colonel-blotto and attacker–defender contest games (Chowdhury et
al., 2021;Chowdhury & Topolyan, 2016;De Dreu & Gross, 2019b;
Hunt & Zhuang, 2023;Roberson, 2006). In hide-and-seek games,
for example, hiders want to be where seekers are not looking, yet
seekers want to look where hiders are hidden. Accordingly, when
hiders expect that seekers search location x, they want to hide in
location y, but seekers realizing this may search location y and this
makes hiding in location x most attractive. In inspection games,
likewise, managers want to not inspect workers who comply,
because inspection is costly. But workers will not comply when not
inspected, because compliance is costly. Accordingly, what is in the
worker’s best interest (e.g., comply or shirk) fully depends on what
the manager decides (e.g., inspect or not inspect), and vice versa.
As these examples show, agents personally benefit from
mismatching their opponent’s action in conflict games that have
their equilibrium in mixed strategies. In attacker–defender contests,
for example, attackers benefit from investing in conflict when their
defenders do not, akin to nonhuman predators wanting to attack
when their prey is expecting it the least (Dugatkin & Godin, 1992),
revisionist states wanting to invade when their neighbors are poorly
defended (Jordana et al., 2009), and terrorists wanting to avoid areas
where security forces are expecting them (Arce et al., 2011; also see
Bar-Hillel, 2015). And precisely for these reasons, it is each agent’s
best interest to vary their conflict behavior nonsystematically so that
opponents cannot predict one’s next move—switching where to
hide and seek, inspecting targets at random points in time, and
erratically alternating between laying low and lashing out when
attacking opponents (e.g., De Dreu & Gross, 2019b;Emara et al.,
2017;Erev & Roth, 1998;Schelling, 1960).
Whereas conflict with its equilibrium in mixed strategies
motivates to be unpredictable, and individuals can be expected
to nonsystematically vary whether and how much they invest in
conflict, earlier work returned mixed evidence, with some showing
that participants mix strategies quite well and others rejecting such
claims (for reviews and discussions, see e.g., Chiappori et al., 2002;
Erev & Roth, 1998;Misirlisoy & Haggard, 2014). In contrast to
stylized agents assumed to be motivated and capable to rationally
maximize expected payoffs, people may be limited in the degree to
which they vary actions both with the same or with different
opponents. For example, people may want to avoid the risk of losing
and therefore, compared to “homo economicus”agents, reduce the
amount they invest in attack and increase the amount they invest in
defense (Chowdhury et al., 2018;Meder et al., 2023;Sheremeta,
2013;Yang et al., 2020). In both cases, the range of possible actions
is reduced, and with that variability in conflict behavior may be
reduced as well. Relatedly, survival threat can make people rigid in
their thinking (Porcelli & Delgado, 2017;Pratto & John, 1991;Staw
& Ross, 1989) and lead them to rely on a “better-safe-than-sorry”
heuristic by excluding the option to not defend at all (Halevy,
2017;Jervis, 1978;Simunovic et al., 2013;Walker et al., 2018;
Zou et al., 2020). Acting on a “better-safe-than-sorry”heuristic
(viz., “minimax”strategy; Erev & Roth, 1998;Von Neumann &
Morgenstern, 1944) would, for example, increase overall expendi-
ture on defense and make defenders less variable in their actions.
The other way around, attackers may be motivated not only to
maximize earnings but also, or exclusively so, to win the conflict
(Cason et al., 2020;Thaler, 1988;van den Bos et al., 2008). This
could increase both the number and intensity of attacks beyond strict
randomization.
Apart from current evidence being limited, it is presently unknown
whether and how mixing actions across trials and opponents makes
competitors unpredictable to the degree that opponents have diffi-
culty anticipating their next move. In general, being variable not
necessarily means that one is irreducibly unpredictable. For example,
an aggressor who systematically alternates between minimum and
maximum investment in attack would be highly variable yet also is,
at least after some time, quite predictable—the same level of
variability can be achieved by varying conflict expenditures more or
less systematically, and any systematicity can make one behaviorally
variable but predictable at the same time. Because people have
difficulty generating randomness (Baddeley et al., 1998;Lahat-Rania
& Kareev, 2023;Sanderson, 2018;Wagenaar, 1972), it may well be
that people mix conflict actions in sucha nonrandom, systematic way
that they are variable but also predictable.
Given that we presently have limited insight into whether
and how (unpredictably) variable people are in conflicts with its
equilibrium in mixed strategies, we also poorly understand whether
and how being (unpredictably) variable in one’s conflict invest-
ments shapes interaction dynamics and conflict outcomes. We lack
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370 DE DREU ET AL.

insight in whether and how individuals across repeated interactions
respond, in thinking and doing, to their opponent’s (unpredictably)
variable behavior. And to the best of our knowledge, there is no
empirical evidence to support the theoretical proposition that being
unpredictable can be strategically advantageous (Machiavelli, 1531/
2013;Schelling, 1960) either when contestants interact once or
repeatedly across a series of contest trials.
Overview of the Present Research
The present research addressed the three open issues identified
above: (a) Do people in conflict (with a unique mixed-strategy
equilibrium) variably mix whether and how much they invest
in conflict; (b) does such variable mixing render competitors
unpredictable to their counterpart; and (c) how does being
(unpredictably) variable influence conflict dynamics and outcomes?
We examined these issues in the realm of the attacker–defender
contest, a conflict game with a discrete rather than binary action
space—parties could invest nothing, something, or a lot in conflict
either to win and exploit the counterpart (viz., “greed”or appetitive
competition in attackers) or to minimize loss and protect against
exploitation (viz., “fear”or aversive competition in defenders;
Coombs, 1973;De Dreu & Gross, 2019b;Messick & McClintock,
1968;Ten Velden et al., 2009). Thus, in addition to the three open
issues that motivated the present study, we explored (d) whether and
how the psychological underpinnings of attack and defense shape
variable mixing and unpredictability during conflict.
To answer our research questions, we proceeded in three steps.
First, to detect (differences in) variable mixing during attack and
defense, we combined and reanalyzed the data of seven published and
two unpublished attacker–defender contest experiments (Study 1). To
examine whether and how mixing actions rendered individuals
unpredictable to their counterpart, we performed Study 2. To shed
light on the neuropsychological underpinnings of variable mixing
during attack and defense, we examined how variability in conflict
behavior related to individual differences in basal testosterone and
sympatheticarousal (Studies 3 and 4). All data and code can be found
at De Dreu (2023).
Properties of Attacker–Defender Contests
In its most basic form, the attacker–defender contest involves an
Attacker A and Defender D each with an endowment efrom which
they can invest xin the contest (with 0 ≤x≤e), simultaneously
and without communication. Investments are nonrecoverable, akin
to resources wasted on conflict. Yet when x
A
>x
D
, A(ttacker) wins
the contest and earns the noninvested resources from D(efender)
(e
D
−x
D
). These “spoils of war”are added to the attacker’s
noninvested resources, yielding an earning of r
A
=2e−(x
A
+x
D
).
In this scenario, the defender earns r
D
=0. When x
A
≤x
D
,both
attacker and defender earn their noninvested resources (e−x
A
,x
D
).
As such, the game is formally equivalent to a contest with as contest
success function f=x
A
m
/(x
A
m
+x
D
m
), where fis the probability that
the attacker wins, m→∞for x
A
≠x
D
and f=0ifx
D
=x
A
(De Dreu
et al., 2015;Meder et al., 2023).
For e=10 per trial (as used in the experiments reported herein),
and assuming that participants are risk neutral and invest to maximize
personal earnings, the contest has a unique Nash equilibrium in mixed
strategies. Specifically, the probability pof investing xin attack is
p(x=1) =2/45, p(x)=p(x−1)[(12 −x)/(10 −x)] for 2 ≤x≤6, and
p(x)=0forx≥7. For defense, the probability pof investing y
in defense is p(y)=1/(10 −y) for 0 ≤y≤5, p(y=6) =1−[p(y=0) +
…+p(y=5)] =0.15, and p(y)=0fory≥7(De Dreu et al., 2015,
2021;Meder et al., 2023). This implies that participants should invest,
on average, x
A
=2.62 in attack and x
D
=3.38 in defense and that
across trials, investments should vary with variance v
A
=6.12 for
attack and v
D
=3.68 for defense. We note that such cross-round
variability is assumed tobe nonsystematic; yet, whether this indeed is
the case for humans remains an empirical question.
In attacker–defender contests with e=10, payoff-maximizing
contestants should never invest more than six; investments 7 ≤x≤
10 are out-of-equilibrium and reminiscent of extreme actions like
“brinkmanship”(Frank, 1988;Schelling, 1960) and “pondering the
nuclear option”(viz., Mutual Assured Destruction; Jervis, 1978).
For example, while an attacker may win the conflict by investing all
their 10 endowment points, they can maximally earn 10 points back
by doing so and only in the unlikely case that the defeated defender
did not invest anything in defense. In this case, they could have
guaranteed earnings of 10 by not investing anything into conflict in
the first place. In game-theoretic terms, an investment of x
A
=10 is
(weakly) dominated by x
A
=0. Because such extreme behaviors are
considered irrational from a strict payoff-maximizing perspective,
they should not be played according to game theory (De Dreu et al.,
2021;Meder et al., 2023). At the same time, extreme risk aversion
among defenders may lead them to invest out-of-equilibrium
(e.g., “better to live poor than to die rich”) and being motivated to
“win-at-all-cost”may lead attackers to perform such extreme actions
(Dechenaux et al., 2015;Loewenstein, 1996;Malhotra, 2010;Zou
et al., 2014). Importantly, performing such extreme actions extends
the space of viable actions, thereby allowing to increase the
possible variability in behavior, making players comparatively more
unpredictable to their opponents and helping defenders survive
and attacker to win. If people are simply motivated to win whatever
it takes, they may consider playing dominated, out-of-equilibrium
actions.
Study 1
Method
Identifying Eligible Studies for Reanalysis
In a first step performed in January 2022, we combined and
integrated nine experiments from our own research laboratory,
including Study 4 here below, that (a) used the attacker–defender
contest, (b) had at least five consecutive investments in attack and
defense so that cross-round variability in investment could be
assessed, and (c) provided in between trials full feedback on the
trial outcomes so that participants could predict, in theory, their
counterpart’s next move. In June 2022 we searched Google Scholar
and Web of Science for additional studiesfor possible inclusion in the
reanalysis. Search terms included (variations on) “attack–defense,”
“attacker–defender,”and “asymmetric contest.”We also searched
all citations to published work on attacker–defender contests. No
additional experiments were found that could be included in the
reanalysis. This is not surprising given our restrictive inclusion
criteria and because the attacker–defender contest is a recent advance
in the behavioral game literature (De Dreu & Gross, 2019b)withmost
work being theoretical rather than experimental (for a review, see
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COMPETITION AND CONFLICT 371

Hunt & Zhuang, 2023). In short, to our knowledge, all studies
available for our research questions are included in the reanalyses
(i.e., there is no file drawer).
Study Designs and Main Features
All experiments were performed in behavioral laboratories, were
fully incentivized, void of deception, and with methods and
procedures largely like those in Studies 3 and 4 reported below
(for an example of instructions for a random-matching protocol
experiment, see De Dreu et al., 2019). Five experiments used a
random-partner matching protocol with attackers and defenders
being randomly rematched on each new round of the contest (with
either 30 or 60 rounds; total N=276). The other four experiments
used fixed-partner matching protocols with attackers and defenders
nested in dyads for repeated interaction (with between 20 and
90 rounds in total; total N=374; see Tables 1–2).
In theory, the experimental protocol should not matter for
investment or variability. However, being unpredictable may be more
important during repeated interactions as it prohibits being exploited
by the other party. In addition, during repeated play, participants may
adapt conflict investments to their competitor’s previous investments,
and this may escalate the conflict. For example, a defender paired to
an attacker who occasionally invests out-of-equilibrium may be
forced to invest out-of-equilibrium themselves as well. Conversely,
defenders may occasionally initiate out-of-equilibrium investments to
signal toughness and to discourage their attackers.
Measures
For each experiment, we extracted the per round conflict
investment in attack or defense (range between 0 and 10) and
computed (sample size weighted) average investment in attack and
defense, the average earning for attacker (range between 0 and 19)
and defender (range between 0 and 10), and the number of contest
rounds where attackers (defenders) successfully defeated (defended
against) the defender (attacker; Tables 1–2).
Our main variable of interest was cross-round variability in
conflict investment. As noted above, the attacker–defender contest
has its equilibrium in mixed strategies, and we have precise
probability estimates for each investment level x(0 ≤x≤e)
(De Dreu et al., 2015,2021;Meder et al., 2023). We operationalized
cross-round variability in two complementary ways. First, we
identified the relative frequency with which participants chose each
possible investment level across rounds. This empirical distribution
can be compared to the game-theoretic probability distribution that
is expected under rational play (see Figure 1A and 1B). Second, we
computed for each participant in each of the nine experiments the
variability vas the deviation between investment xfrom the mean
investment macross all rounds t:v=Σ(x−m)/t(Figure 1C).
Parameter vthus provides a point estimate that can be related to
contest outcomes without having to control for for example, mean
investments and without having to make assumptions about the
(differences in probability distributions in) actual investments made
during attack and defense. Parameter vserves to identify to what
degree competitors can make themselves unpredictable to their
opponents in further analyses (see Study 2 in particular).
Results
Analysis of average conflict expenditures confirmed that mean
investment in attack is below to that in defense (M
A
=4.404 vs.
M
D
=5.236; Cohen’sd±SE
g
=0.60 ± 0.135, 95% CI [0.332,
0.860], z=4.425, p<.001; based on N=382). Furthermore, and in
line with game theory and the mixed-strategy equilibrium properties
of the attacker–defender contest, investments in attack and defense
are variable across trials (Figure 1A and 1B). Cross-trial variability v
in investment for both attack and defense closely match game-
theoretic equilibrium predictions (v
A
=6.12 for attack and v
D
=3.68
for defense) for one-shot conflict interactions, and there is greater
variability in attack than in defense (Cohen’sd=0.438, 95% CI
[0.29, 0.58], z=5.948, p<.001; Table 3). In repeated interactions,
variability exceeds equilibrium predictions for both attack and
defense (Figure 1C).
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Table 1
Study Characteristics of the Experiments Included in the Meta-Analysis and Their Descriptive Statistics for Cross-Round Variability (VAR)
and Proportion of Out-of-Equilibrium (O-E) Investments for Attack and Defense
Study
a
N(no. trials) VAR attack; defense (SD)ttest
b
O-E attack; defense (SD)ttest
b
One-shot
De Dreu et al. (2019; Exp. 1a) 27
a
(60) 4.885 (3.149); 2.998 (2.677) 2.32** 0.217 (0.227); 0.089 (0.901) 3.03**
De Dreu et al. (2019; Exp. 1b) 58
a
(30) 6.897 (5.377); 4.741 (3.888) 3.10** 0.376 (0.289); 0.493 (0.264) −2.95**
De Dreu et al. (2019; Exp. 2a) 80
c
(30) 5.535 (4.770); 3.605 (2.432) 2.29*0.499 (0.217); 0.300 (0.267) 3.66**
De Dreu et al. (2019; Exp. 2b) 84
c
(60) 5.594 (4.139); 3.780 (1.977) 2.52*0.275 (0.277); 0.184 (0.119) 1.93
^
Rojek-Giffin et al. (2020)27
a
(60) 3.639 (2.951); 2.467 (2.335) 2.69** 0.171 (0.253); 0.553 (0.242) −6.38**
Repeated
De Dreu et al. (2016) 40
d
(20) 7.224 (5.631); 4.068 (2.977) 2.91** 0.238 (0.250); 0.392 (0.308) −2.95**
De Dreu (2019) 116
d
(30) 5.689 (4.196); 4.146 (2.628) 2.77** 0.347 (0.295); 0.364 (0.295) −1.01
Reddmann et al. (2021) 112
d
(60) 8.073 (4.678); 5.270 (2.938) 1.56 0.309 (0.313); 0.330 (0.299) −1.09
Present Study 4 106
d
(90) 6.806 (2.355); 6.170 (2.303) 5.74** 0.297 (0.228); 0.377 (0.294) −3.60**
Note. Exp. =experiment.
a
Within-subjects design with participants investing in one block of trials as attacker and in another block of trials as defender, each trial with a
new opponent.
b
Test statistics are based on paired-sample ttests for within-subjects and dyadic designs and independent sample ttests for between-
subjects designs.
c
Between-subjects design with participants investing as attacker or as defender, on each trial with a new opponent.
d
Repeated-
interaction design in which participants are paired in dyads and one invests as attacker the other as defender.
^
p≤.10. *p≤.05. ** p≤.01.
372 DE DREU ET AL.

The variability vshown in Figure 1C not necessarily reflects that
individuals mix conflict investment unpredictably (Figure 1A and
1B)—the same variability vcan be achieved through different means
and indeed, average investment in attack and in defense was
(substantially) above the mean expected in equilibrium (x
A
=2.62
and x
D
=3.38). Human competitors waste 46.2% of their collective
resources on conflict, 16% more than what is predicted under the
assumptions of rational selfish play. This is because, as can be seen
in Figure 1A and 1B, individuals frequently chose out-of-
equilibrium investments in both attack and defense (i.e., x>6),
with the proportion for out-of-equilibrium defense expenditures
exceeding that for attack in repeated but not one-shot conflict
interactions (Figure 2A, and Table 3). The variability in attack and
defense investment appears partially achieved by extreme conflict
investments that are irrational from a strict pay off-maximizing
perspective (further see Study 2 here below).
Fitting the observation that individuals occasionally invest
out-of-equilibrium, variability in defense investments was nega-
tively associated with postcontest wealth in both defenders and
attackers (Figure 2B and Table 4). Increased variability was costly
and wasteful. And whereas defense variability did not relate
to defender survival, both out-of-equilibrium investments and
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Table 2
Study Characteristics of the Experiments Included in the Meta-Analysis, and the Associations Between Variability (VAR) and Out-of-
Equilibrium (O-E) Investments in Attack and Defense and Conflict Success (Victory/Survival) and Wealth (Earnings)
Study
r
VAR, success
Attack (defense)
r
VAR, wealth
Attack (defense)
r
O-E, VAR
Attack (defense)
r
O-E, success
Attack (defense)
One-shot
De Dreu et al. (2019; Exp. 1a) 0.15 (−0.593**)−0.084 (−0.756**) 0.119 (0.445**) 0.885*** (0.147)
De Dreu et al. (2019; Exp. 1b) 0.239
^
(−0.437**) 0.026 (0.213) 0.048 (−0.405**) 0.878*** (0.457**)
De Dreu et al. (2019; Exp. 2a) 0.463** (−0.505**)−0.272
^
(−0.094) −0.311*(−0.048) 0.919*** (0.708**)
De Dreu et al. (2019; Exp. 2b) 0.314*(−0.041) −0.318*(−0.180) 0.099 (0.479**) 0.865*** (0.425**)
Rojek-Giffin et al. (2020)0.299 (−0.660***)−0.089 (−0.070) 0.120 (−0.028) 0.828*** (0.366*)
Repeated
De Dreu et al. (2016) 0.126 (−0.113) −0.232 (−0.041) 0.314*(−0.126) 0.062 (−0.150)
De Dreu (2019) 0.310*(−0.006) −0.105 (0.044) 0.273*(−0.002) 0.566** (0.450**)
Reddmann et al. (2021) 0.630** (−0.495**) 0.087 (−0.257*) 0.085 (−0.061) 0.516*** (0.311**)
Study 4 0.404** (−0.299*)−0.011 (−0.063) 0.353** (0.121) 0.638** (0.240
^
)
Note. Cell entries are zero-order correlations between variables of interest. Exp. =experiment.
^
p≤.10. *p≤.05. ** p≤.01. *** p<.001.
Figure 1
Variability in Investment in Attack and Defense
0.0
0.1
0.2
0.3
0.4
0.5
012345678910
Probability
Attack Investment
(A)
0.0
0.1
0.2
0.3
0.4
0.5
012345678910
Probability
Defense Investment
(B)
0
2
4
6
8
10
Variability
(C)
Note. (A) Occurrence of possible investment levels in attack as expected by rational choice actors (mixed-strategy
equilibrium, open bars), in one-shot interactions (observed, solid bars; N=172) and in repeated interactions (observed, dashed
bars; N=192). (B) Occurrence of possible investment levels in defense as expected by rational choice actors (mixed-strategy
equilibrium, open bars), in one-shot interactions (observed, solid bars; N=168) and in repeated interactions (observed, dashed
bars; N=192). (C) Observed variability in attack exceeds that in defense in one-shot interactions (solid bars) and, in repeated
interaction, both attackers and defenders (dashed bars) exceed game-theoretic equilibrium predictions (open bars). See the
online article for the color version of this figure.
COMPETITION AND CONFLICT 373

variability in attack increased the likelihood that attackers emerged
victorious and defeated their defenders (Figure 2B). Variability
in attack reduced wealth but increased the likelihood of winning
the contest.
Study 2
The reanalysis of past experiments in Study 1 showed clear
evidence that participants in attacker–defender contests are variable
in their behavior across rounds, both with different opponents
and when paired to the same opponent for multiple trials. What the
reanalysis cannot show, however, is that such cross-round variability
makes competitors unpredictable to their opponents. Therefore,
we approached this question in two complementary ways. First,
we examined whether participants in Study 1 made investments in
identifiable ways. We collapsed data from each experiment and
created unique blocks of five consecutive investments. Sequences of
five trials were chosen for three reasons. First, there is some evidence
that people can detect systematicity after ∼5 sequential actions and
predict the next action above-chance level (Erev & Roth, 1998).
Second, and relatedly, we have recently shown that people learn their
opponent’s acceptance levels in ultimatum bargaining games after
approximately five interactions (Rojek-Giffinetal.,2023). Third,
with discrete option space, five consecutive trials is the lowest number
to identify deviations from four “systematic”strategies: stationary
(t
0
=t
1
=t
2
=…=t
5
); ascending (t
0
≤t
1
∧t
0
<t
2
=…≤t
5
∧t
3
<t
5
);
descending (t
0
≥t
1
∧t
0
>t
2
=…≥t
5
∧t
3
>t
5
); and alternating (t
0
>
t
1
∧t
1
<t
2
∧t
2
>t
3
…or t
0
<t
1
∧t
1
>t
2
∧t
2
<t
3
…). We coded each
of the five-trial sequences in terms of these four strategies. Out of
the 1,032 (1,008) attack (defense) sequences, only 29% (27%)
fell into one of these four “systematic”sequences (Figure 3A).
This suggests that in the experiments in Study 1, both attackers’and
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Table 3
Effect Size Estimates (Cohen’s d) and 95% Confidence Intervals for Investment Variability
(VAR) and Out-of-Equilibrium Investments (O-E) in Attack Versus Defense
Effect size (attack vs. defense) VAR Proportion O-E
One-shot game
Effect size [95% CI: LL,UL] 0.457 [0.255, 0.658] 0.007 [−0.198, 0.213]
Q(w) 0.287 48.036***
Repeated game
Effect size [95% CI: LL,UL]0.419 [0.212, 0.583] −0.183 [−0.327, −0.039]
Q(w) 1.681 4.938
Overall
Effect size [95% CI: LL,UL]0.440 [0.29, 0.58] −0.121 [−0.238, +0.003]
Q(w) 2.035 55.186***
Note. Effect sizes (Cohen’sd). 95% CI =95% confidence intervals; LL =lower limit; UL =upper
limit; Q(w)=effect size heterogeneity across studies.
*** p≤.01.
Figure 2
Consequences of Variability in Attack and Defense
0
0.2
0.4
0.6
0.8
1
Out-of-Equilibtrium (O-E)
(A)
100%
80%
60%
40%
20%
0%
0
7
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
(B)
Aack variability, wealth
Defense variability, survive
Defense O-E, variability
Aack O-E, variability
Defense O-E, survival
Aack O-E, victory
Aack variability, victory
Defense variability, wealth
Note. (A) Sample-size weighted mean proportion ± SE of “out-of-equilibrium”(O-E) investment in
attack and defense for one-shot (solid bars; N=194) and repeated interactions (dashed bars; N=188);
(B) Sample-size weighted mean correlation between cross-round variability, out-of-equilibrium
investment (O-E), and postconflict wealth and contest success for attack (red font) and defense
(blue font; shown Cohen’sdand 95% confidence intervals). Effect sizes with whiskers not including
0 (vertical dotted line) are statistically significant at p<.05 (based on k=9 studies with N=650).
SE =standard error. See the online article for the color version of this figure.
374 DE DREU ET AL.

defenders’consecutive behavior could not be captured by simple
sequences, like continuously increasing or decreasing investments or
simply alternating between high and low investments, sequences that
arguably are easy to predict.
That investments across trials vary in a seemingly nonsystematic
manner not necessarily means that the individual’s next investment
is not thought through or conditional. For example, individuals may
adapt their investment contingent on whether previous rounds were
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Table 4
Effect Size Estimates (Cohen’s d) and 95% Confidence Intervals for the Correlations Between Variability (VAR) and Out-of-Equilibrium
(O-E) Investment and Success (Victory) and Wealth (Earnings) for Attack, Defense, and Their Difference
Effect size r
VAR, success
r
VAR, wealth
r
O-E, VAR
r
O-E, success
One-shot game
Attack [95% CI: LL,UL] 0.601 [0.397, 0.805] −0.282 [−0.483, −0.081] 0.004 [−0.191, 0.209] 3.581 [3.258, 3.904]
Q(w) 3.867 7.820 10.348
^
9.236
Defense [95% CI: LL,UL]−0.927 [−1.14, −0.714] −0.213 [−0.419, −0.008] 0.062 [−0.144, 0.268] 0.993 [0.779, 1.207]
Q(w) 24.621** 46.409** 52.437*** 20.172**
Q(b) 103.176*** 0.221 0.128 171.542***
Repeated game
Attack [95% CI: LL,UL]0.907 [0.691, 1.122] −0.067 [−0.270, 0.136] 0.497 [0.291, 0.704] 1.216 [0.993, 1.439]
Q(w) 16.505*3.717 4.815 15.937**
Defense [95% CI: LL,UL]−0.513 [−0.721, −0.304] −0.170 [−0.374, 0.033] 0.005 [−0.199, 0.208] 0.625 [0.416, 0.834]
Q(w) 17.444** 5.454 2.514 8.297
^
Q(b) 86.176*** 0.495 11.121*** 14.354***
Overall
Attack [95% CI: LL,UL] 0.746 [0.598, 0.894] −0.176 [−0.312, −0.033] 0.246 [0.102, 0.389] 1.979 [1.796, 2.163]
Q(w) 24.455** 13.714 26.211*164.735***
Defense [95% CI: LL,UL]−0.715 [−0.86, −0.57] −0.192 [−0.337, −0.047] 0.033 [−0.112, 0.177] 0.805 [0.655, 0.954]
Q(w) 49.492*** 51.948*** 55.101*** 34.302**
Q(b) 185.929*** 2.285 4.198*94.647***
Note. Effect sizes (Cohen’sd). 95% CI =95% confidence intervals; LL =lower limit; UL =upper limit; Q(w)=effect size heterogeneity across studies;
Q(b)=effect size heterogeneity across groups of studies (akin to a planned comparison).
^
p≤.10. *p≤.05. ** p≤.01. *** p<.001.
Figure 3
Variability in Attack and Defense Investments Render the Individual Unpredictable
0
2
4
6
8
10
12345
Investment
Contest Round
0
2
4
6
8
10
12345
Investment
Contest Round
0
2
4
6
8
10
12345
Investment
Contest Round
0
2
4
6
8
10
12345
Investment
Contest Round
0
0.2
0.4
0.6
0.8
1
Proportion
5-Trial Sequence
Attack One-Shot
Attack Repeated
Defense One-Shot
Defense Repeated
(A) (B) ab
cd
Note. (A) Proportion of attack and defense strategies that are simple and systematic (stationary, descending, ascending,
or alternating) or more nonsystematic across five consecutive trials (one-shot interaction: solid bars; repeated interactions:
dashed bars); based on the unique 1,008 five-trial sequences from the experiments incorporated in Study 1. (B) Examples
of materials used in Study 2, where participants estimated what attacker (red player) and defender (blue player) would
invest on Round 6. Panels vary from lower (a) to higher (d) variability in attack. Participants saw the 5-round sequence for
the attacker and defender player and had to guess the 6th round investments for each player, respectively. See the online
article for the color version of this figure.
COMPETITION AND CONFLICT 375

won or lost (e.g., a win-stay/loose-shift strategy; Messick &
Liebrand, 1995;Vlaev & Chater, 2006) or they may adapt their
investment contingent on their opponent’s previous move (viz.,
k-level reasoning; Rojek-Giffin et al., 2020). What matters more
here, however, is whether and to which degree counterparts, with
some knowledge about the history of play, can predict the
individual’s next move with above-chance accuracy. If the
empirically observed cross-round variability in the studies included
in the meta-analyses provides (more or less hidden) clues to what
attackers and defenders do next, we should see above-chance
prediction accuracy. If, however, cross-trial variability creates
unpredictable competitors, we should see prediction accuracy to be
low and at, or close to, chance level.
Method
Research Ethics and Sample Size
Study 2 was performed online through the Prolific platform with
N=200 (48% female, 1% not indicated; mean age 29.18 years).
The study received ethics approval (Leiden Psychology Ethics
Board 2021-11-12-Author-V1-3542). Participants provided written
informed consent and were debriefed afterward. They received a
participation fee of 3.15 Great British Pound and an additional 0–4
Great British Pound depending on their performance during the
experiment. The experiment did not use deception.
Upon providing informed consent, participants read a brief
description of the attacker–defender contest and were told that they
would observe a series of investments of a red (attacker) and blue
(defender) player. It was made clear that series shown were from
individuals who had actually engaged in the contest and that action–
reaction patterns were real. Participants answered three questions to
probe their comprehension and when having answered all three
correctly were shown five decision rounds between the red and the
blue player in graphic form (see Figure 3B for examples). Their task
was to predict what red and blue players invested on the 6th decision
round. Participants were reminded that red and blue could both
invest anywhere between 0 and 10, and that they could enter their
prediction for the sixth decision round by entering a number
between 0 and 10 for the red player and for the blue player. Correct
estimates would earn the participant 1 Great British Pound.
In total, participants were shown 20 graphs of varying variability
in attacker investments. The 20 graphs shown were drawn from
725 diagrams showing the five consecutive investments of an
attacker and their defender in the 130 blocks from the repeated-
interaction experiments included in the meta-analysis. To ensure
that the full range of variability was presented to each participant,
we first divided up the 725 diagrams into four quartiles of
variability—wherein Quartile 1 contained all five-trial chunks
whose variance was between the 0th and 25th percentile of attacker
variance (Figure 3B, Panel a), Quartile 2 contained all five-trial
chunks whose variance was between the 25th and 50th percentile of
attacker variance (Figure 3B, Panel b), and so on (Figure 3B, Panels
c and d). We opted to base this division on attacker variance because
in repeated interactions (a) attacker and defender variance tend to
mirror one another and (b) defender behavior follows attacker
behavior more than vice versa (De Dreu & Gross, 2019b; also see
Study 4 here below).
Each participant was shown five unique graphs from each
quartile, thus ensuring that the entire range of variability was
adequately represented. For each diagram participants predicted the
attacker and defender investment on the next, sixth trial. As we knew
what the actual investment on the sixth trial was, we could assess to
what extent individuals are able to predict attack and defender
investments under various levels of cross-round variability. Upon
completing the final graph with their predictions for the red and blue
players, participants received a short debriefing statement that
concluded the experiment.
Results
In total, participants were shown 20 series and made 20 ×2
(attacker/defender) estimates. Estimates were compared to the actual
Round-6 investments made by the attacker and defender, giving us
both an accuracy score (1 =correct; 0 =incorrect) and a prediction
error (actual investment −predicted investment). Analyses showed
that when predicting the sixth investment in attack and defense,
predictions were incorrect in 75% and 77% of the cases for attack
and defense, respectively (Figure 4A).
The five-round sequences shown to participants were, for each
participant, a random selection from the actual five-round sequences
observed in the repeated-interaction experiments included in Study
1. Recall that we observed in Study 1 not only significant variability
but also nontrivial amounts of out-of-equilibrium investment in both
attack and defense. As a result, also in the stimuli used in Study 2,
both attacker and defender invested out-of-equilibrium. Figure 4B
shows, as can be expected, that scenarios with intermediate numbers
of out-of-equilibrium investment in attack and defense also had
greater cross-round variability than scenarios in which attacker or
defender always or never invested out-of-equilibrium.
This emerging property of our stimulus materials allowed to
explore how out-of-equilibrium investments contribute to unpre-
dictability. We built multilevel regression models with as dependent
variable absolute prediction errors (|predicted −actual investment|),
and expected investment in conflict. Role, cross-round variability,
number of out-of-equilibrium investments, and their interactions
served as predictor variables. To examine whether occasional rather
than (in)frequent out-of-equilibrium investment not only adds
to cross-round variability, as shown in Figure 4B, but also to
unpredictability, we added the squared number of out-of equilibrium
investments as a final predictor.
Results are summarized in Table 5. Overall, participants expected
higher investment in conflict than were actually made (actual −
predicted investment: M=−0.367, t=−8.773, p<.001).
Participants also expected lower investment in attack than in
defense, mimicking the actual behavior of attackers and defenders in
Study 1 (b=−0.690, t=−5.634, p<.001). Higher investments in
conflict were expected when players were less variable (b=−0.051,
t=−4.516, p<.001), and invested more often out-of-equilibrium
(b=1.167, t=11.416, p<.001), the latter especially for investment
in attack (Role ×Out-of-Equilibrium, b=0.841, t=5.202, p<
.001). Finally, participants predicted higher investment when
attackers occasionally rather than (in)frequently invested out-of-
equilibrium (main effect b=−0.066, t=−3.142, p=.002;
interaction with role: b=−0.141, t=−4.172, p<.001).
Table 5 also summarizes results for absolute prediction errors.
Prediction was less accurate for next-round attack than defense
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376 DE DREU ET AL.

(b=0.527, t=4.860, p<.001), and the more variable cross-trial
investment was (b=0.085, t=8.534, p<.001). Over and beyond
these main effects, we also found that prediction accuracy scaled to
out-of-equilibrium investments in an inverted U-shape manner (b=
−0.098, t=−5.268, p<.001). As shown in Figure 4C, absolute
prediction errors were larger when out-of-equilibrium investment in
conflict occurred occasionally rather than (in)frequently.
Study 3
Findings thus far show that individuals can be variable in their
conflict investments both across contests with different partners and
across repeated interactions with the same partner. This variability
appeared mainly nonsystematic (or at least not captured by a simple
functional form such as strictly increasing or decreasing investments
over consecutive rounds) and to some degree due to occasional out-
of-equilibrium investment in conflict. Both variability and out-of-
equilibrium investments made competitors difficult to predict,
yet also reduced rather than increased individual payoffs. Rather,
variability increased the likelihood of victory among attackers
(and of defeat among defenders).
One possible explanation for the pattern of results from Studies 1
and 2 is that (unpredictable) variability is produced by the competitive
desire to win the conflict “no matter what”(Dechenaux et al., 2015;
Malhotra, 2010). Such motivation may lead to occasional out-of-
equilibrium investments in attack that render competitors unpredict-
ably variable and likely to win at significant welfare cost. If true, we
should see variability alongside nontrivial frequency of extreme, out-
of-equilibrium investment in attack especially in individuals that are
biologically and psychologically predisposed to such “winning-at-all-
cost”motivation. Studies 3 and 4 focused on this possibility, building
on extant work showing that competitive motivation and a desire to
“come out ahead”associates with endogenous levels of the steroid
hormone testosterone.
In humans, testosterone is secreted in the adrenal cortex, the
testicles of males and, to a lesser extent, the ovaries of females (Mazur
&Booth,1998). Testosterone has a well-known and important role in
the development of secondary sexual attributes such as increased
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Table 5
Absolute Prediction Errors and Expected Investment in Conflict as
a Function of Observed Variability and Number of Out-of-
Equilibrium Investments for Attack and Defense (Study 2)
Predictor
Absolute
prediction error
Expected
investment
BSEBSE
Role 0.527*** 0.108 −0.690*** 0.123
Variability 0.085*** 0.010 −0.051*** 0.011
Out-of equilibrium 0.607*** 0.090 1.167*** 0.102
Role ×Variability 0.026*0.012 −0.021 0.014
Role ×Out-of-Equilibrium −0.367** 0.143 0.843*** 0.162
Out-of-equilibrium (squared) −0.098*** 0.019 −0.066** 0.021
Role ×Out-of-Equilibrium
(squared)
0.064*0.030 −0.141*** 0.034
Note. Role is dummy coded with 1 =attacker; 0 =defender; Estimates
based on multilevel regressions with 8,000 observations nested in 200
participants and 2 ×20 decisions (random intercepts for participant and
decision blocks not shown). SE =standard error.
*p<.05. ** p<.01. *** p<.001.
Figure 4
Predicting Next-Round Investment in Attack and Defense
(A) (B)
25 23
34 33
41 44
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Attack Defend
Prediction
Overestimate
Underestimate
Correct
(C)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
012345
Absolute Prediction Error
Out-of-Equilibrium Investments
Attacker
Defender
0
4
8
12
16
20
012345
Cross-round Variability
Out-of-Equilibrium Investments
Note. (A) Proportion of (in)accurate prediction of 6th round investments by attacker and defender, shown are total ratio
of all participant decisions that were correct (lowest), underestimated (middle), or overestimated (highest). (B) Cross-round
variability is larger with occasional rather than (in)frequent out-of-equilibrium investment in attack (red bars) and defense
(blue bars). (C) Prediction inaccuracy increases when out-of-equilibrium investment in attack and defense emerge
occasionally rather than (in)frequent (lines show best-fitting curvilinear regression). See the online article for the color
version of this figure.
COMPETITION AND CONFLICT 377

muscle and bone mass and shapes conflict and competition in a
bidirectional manner (Coates et al., 2010;Eisenegger et al., 2011). On
the one hand, engaging in competitions for status and resources can
release testosterone in both males and females (for reviews, see e.g.,
Carré& Olmstead, 2015;Casto & Edwards, 2016). On the other
hand, elevated levels of testosterone cause individuals to take risks
(Apicella et al., 2008;Coates & Herbert, 2008;Stanton et al., 2011)
and to more aggressively engage in competitions and status contests
(Eisenegger et al., 2011;Geniole et al., 2020;Mehta et al., 2008). For
example, participants treated with testosterone (vs. placebo) more
aggressively respond to provocation (Dreher et al., 2016), are more
distrusting (Boksem et al., 2013;Bos et al., 2010), and have stronger
status-seeking motivation (Vermeer et al., 2020). We expected that
individuals with higher levels of testosterone more likely exhibit
a winning-at-all-cost motivation and therefore make extreme and
variable investments in conflict.
To test the possibility that precontest testosterone predicts vari-
ability and extremity in conflict, and attack in particular, participants
drooled saliva prior to engaging in the contest. From their saliva
samples we extracted endogenous testosterone levels and, addition-
ally, cortisol—a glucocorticoid hormone produced in and released
by the adrenal glands especially following exposure to stressors
(McEwen, 1998). There is some evidence that cortisol buffers the
effects of testosterone on aggressive competition and status seeking
(viz., dual-hormone hypothesis; e.g., Casto & Edwards, 2016;Knight
et al., 2022;Mehta & Josephs, 2010;seeGrebe et al., 2019 for a
critical assessment of this literature). For example, a recent meta-
analysis revealed a small but significant interaction between test-
osterone and cortisol on status-relevant behavior (r=−.061, p=.026;
Dekkers et al., 2019). We thus explored whether testosterone predicts
attacker variability and out-of-equilibrium investment especially
when individuals have lower rather than higher levels of baseline
cortisol.
Method
Sample and Ethics
With an expected medium effect size ( f=0.40) for overall
investment in attack versus defense, 28 subjects were needed to
achieve a power of 1 −β=0.80 (with α=.05), a number fitting
earlier studies on the relationship between testosterone and social
decision making (e.g., Mehta & Josephs, 2010). We thus recruited
28 healthy males (age range 18–43) for an experiment that consisted
of two sessions with 7–10 days apart. In Session 1, participants
invested as attacker (or defender) and in Session 2 invested as
defender (or attacker). One participant failed to show up for the
second session, leaving a final sample size of N=27 males.
The study was fully incentivized, did not involve deception, was
approved by the (WOP-2015-4311) and adhered to the Helsinki
Protocols for research with humans. We only included participants
who indicated they had no current or past neurological or psychiatric
diseases and had not taken (prescribed) psychotropic drugs within
the past 2 weeks. All experimental sessions were performed between
9:30 and 11:30 in the morning.
Experimental Procedures
Upon arrival in the laboratory, participants were seated in an
individual cubicle equipped with a network-connected computer
and, after they provided written informed consent, asked to relax and
fill out a series of surveys about neutral topics and their lifestyle
(survey responses were stored but not analyzed). After 20 min of
habituation, the experimenter handed participants a 25 ml sterile
polypropylene tube and asked them to swallow all saliva in their
mouths and then allow saliva to collect for 3 min, spitting once a
minute, for a total of >3 ml of saliva. Collected samples were put
on ice immediately and within an hour stored at −18 °C, until
transported and analyzed at the Medical Center of the University of
Utrecht.
Upon collection of the saliva samples the experimenter unlocked
the computer to present participants with the instructions for
the attacker–defender contest and a short comprehension test.
Participants read that they would make decisions involving
themselves and, on each decision trial, an unknown other player
that was randomly selected from a pool of other participants.
Unbeknown to participants, this pool of decisions consisted of 120
participants making 60 decisions as attacker and 60 as defender
in the exact same setup as used here (i.e., 7,200 incentivized
investments in attack and 7,200 investments in defense), and
dynamically changed as the decisions of the current participants
were added to the pool. Thus, each trial was with a new counterpart
and trial outcomes were based on real decisions by both attackers
and defenders. In Session 1, half of the participants decided in the
role of attacker (labeled Role A) and paired on each trial to a new
partner in the role of defender (labeled Role B). The other half
decided in the role of defender (labeled Role B) and on each trial
paired to a new partner in the role of attacker (labeled Role A). Thus,
participants made sixty “one-shot”contest decisions. Roles reversed
in Session 2, which started with a summary of the attacker–defender
contest, and then proceeded with decision making. For 25 out of the
27 participants, we were able to schedule their second session on the
same weekday and timeslot as their first session.
In each session, participants made 60 investment decisions as
attacker or as defender. On each trial, subjects decided how much to
invest (out of €10 endowment) by clicking on numbers between 0
and 10 displayed in a clocklike circle on their computer screen. After
each trial, the subject was shown how much the other person for that
trial had invested, and their earnings for that trial. If the attacker
invested more than its defender, the attacker earned what the
defender had not invested and this was added to the attacker’s own
leftover; if the attacker invested equal or less than its defender,
both attacker and defender earned their leftover. The task took
approximately 30 min to complete.
Measures
From the 60 investments, we derived the average overall
investment (range 0–10), and the cross-round variability (v)in
investments, and the proportion of out-of-equilibrium investments.
From the saliva collected at the start and ending of each session,
testosterone and cortisol were extracted at the endocrinology
laboratory at Utrecht University Medical Center, with analysts being
blind to the study goals and hypotheses.
Precontest cortisol averaged at M±SE =10.722 ± 0.748 nmol/L
for sessions in which participant invested as attacker and 10.593 ±
0.686 nmol/L for sessions in which they acted as defenders and
neither differed between roles or time of measurement (all F<1).
Precontest testosterone averaged at M±SE =290.33 ± 14.974 pmol/L
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378 DE DREU ET AL.

during attack and 302.148 ± 12.606 pmol/L during defense. Role and
time of measurement did not influence testosterone levels (all F<1).
For our analyses and to interpret statistical interaction effects, we
standardized log-transformed values of cortisol and testosterone.
Exploratory analyses detected no statistical outliers (at 3 SD ±M) and
all data were used in the final analyses.
Results
Replicating our earlier findings, variability across trials was
greater during attack than defense, t(26) =2.321, p=.028, η
2
=
0.172; and individuals more often made out-of-equilibrium
investments in attack than in defense, t(26) =3.031, p=.005,
η
2
=0.261. Also, as predicted, individuals invested less in attack
than defense but this effect was not significant (n.s.), t(26) =1.797,
p=.084, η
2
=0.110.
To relate contest behavior to precontest testosterone, we built
regression models separately for attack and defense using a three-
step procedure. In Model 1 (or Step 1), we included (standardized)
testosterone. Model 2 (or Step 2) included both testosterone
and cortisol as predictors, and Model 3 (or Step 3) added the
Testosterone ×Cortisol interaction. Model 1 is thus directly aimed
at testing our main hypothesis that especially attackers with higher
levels of testosterone would show more variable mixing of conflict
investment. Models 2 and 3 were included to explore the dual-
hormone hypothesis that effects of testosterone emerge especially at
lower levels of precontest cortisol.
Table 6 summarizes results. Focusing on Model 1 results, we see
that testosterone is unrelated to overall investment in attack and
negatively related to overall investment in defense. For variability
in investment, we see that precontest testosterone associated with
greater variability in attack, but not with variability in defense. This
pattern of results remains when including cortisol (Model 2) and the
Testosterone ×Cortisol interaction (Model 3). The same applies to
out-of-equilibrium investments. Precontest testosterone is positively
associated with extreme investments during attack, but not defense
(Model 1 in Table 6).
Results for Models 2 and 3 additionally showed that cortisol
negatively associated with extreme investment in defense, and for
attacker variability and out-of-equilibrium investment, we observed
significant Testosterone ×Cortisol effects (Model 3 in Table 6).
Testosterone effects were stronger when cortisol was higher (rather
than weaker, as predicted under the dual-hormone hypothesis; we
return to this after having reported Study 4).
Study 4
Results from Study 3 resonate with earlier work showing that
higher levels of testosterone associate with aggressiveness during
resource and status competitions (Boksem et al., 2013;Bos et al.,
2010;Dreher et al., 2016;Eisenegger et al., 2011;Geniole et al.,
2020;Mehta et al., 2008;Vermeer et al., 2020). To this literature,
we add that precontest testosterone also predicts more variability
and out-of-equilibrium investment in attack, but not in defense. This
fits our hypothesis that attacker unpredictability resides in a
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Table 6
Conflict as a Function of (Standardized) Precontest Cortisol, Testosterone, and Their Interaction for Attack and
Defense (Study 3)
Predictor
Model 1 Model 2 Model 3
BSEBSEBSE
Attacker conflict investment
Testosterone (T) −0.160 0.408 −0.112 0.505 −0.182 0.516
Cortisol (C) −0.083 0.505 −0.074 0.569
T×C0.105 0.369
Defender conflict investment
Testosterone (T) −0.289** 0.131 −0.166 0.170 −0.646 0.757
Cortisol (C) −0.191 0.170 −0.141 0.188
T×C0.207 0.318
Attacker conflict variability
Testosterone (T) 1.414** 0.562 1.330*0.694 0.424 0.645
Cortisol (C) 0.149 0.694 0.267 0.585
T×C1.382** 0.419
Defender conflict variability
Testosterone (T) 0.272 0.533 0.578 0.702 3.266 3.108
Cortisol (C) −0.476 0.702 −0.756 0.772
T×C−1.161 1.307
Attacker out-of-equilibrium
Testosterone (T) 0.777** 0.282 0.799** 0.349 0.290 0.304
Cortisol (C) −0.040 0.394 0.027 0.276
T×C0.778** 0.197
Defender out-of-equilibrium
Testosterone (T) −0.018 0.028 0.040 0.033 −0.051 0.148
Cortisol (C) −0.09** 0.030 −0.080** 0.037
T×C0.039 0.062
Note. Cortisol and testosterone are standardized with M=0 and SD =1.0. SE =standard error.
*p<.05. ** p<.025 (with N=27).
COMPETITION AND CONFLICT 379

“winning-at-all-cost”motivation, a motivation presumably stronger
in individuals with higher levels of testosterone.
In Study 4, we again examined the relation between precontest
testosterone (and cortisol) and variability and extremity in attacker–
defender conflict behavior. Whereas Study 3 used a random-partner
matching protocol and an all-male sample, Study 4 included both
male and female participants and had dyads fixed in a 90-round
attack–defense contest. This allowed us to examine in detail and
over time the action–reaction dynamics at both the neurocognitive
and behavioral level. Earlier work already showed that average
investment in defense tracks attacker investment more than the other
way around (De Dreu & Gross, 2019b). This fits the idea that attack
is more instrumental and proactive and defense more reactive
and “impulsive”(Nelson & Trainor, 2007;Wrangham, 2018). In
essence, defenders follow and react more to what attackers do, while
attackers have greater initiative. At the behavioral level, we would
thus expect that variability in defense follows variability in attack
more than vice versa.
A similar asymmetry can be expected at the neurocognitive level,
and in particular for sympathetic arousal. Sympathetic arousal refers
to the release of the neurohormone norepinephrine and subsequent
physiological changes including accelerated heart rate and restricted
preejection period (PEP; McEwen, 1998; also see Blascovich et al.,
2004;Jonas et al., 2014;Mendes et al., 2007). PEP is the most direct
cardiovascular measure of sympathetic arousal, while heart rate is
under the influence of both the sympathetic and parasympathetic
nervous system (Brownley et al., 2000). Combined, these
physiological changes mobilize the brain and body for a fight-or-
flight response to stress and perceived threat (Chida & Hamer, 2008;
Lorber, 2004;Murray-Close et al., 2017; also see Kelsey, 2012;
Richter et al., 2016). There is some evidence that predatory attack in
nonhuman animals is purposeful and goal-directed, whereas reactive
and defensive aggression is more “impulsive”and more strongly
conditioned by sympathetic arousal (Nelson & Trainor, 2007;
Potegal & Nordman, 2023;Weinshenker & Siegel, 2002;
Wrangham, 2018). Possibly, variability in conflict investment is
less strongly related to sympathetic arousal in attackers than in
defenders. Furthermore, unpredictable attackers may be more
threatening and arousing than unpredictable defenders. If true, we
should see attacker variability to increase sympathetic arousal in
defenders more than the other way around.
Method
Research Ethics and Sample Size
The experiment was fully incentivized, did not involve deception
and received ethics approval from Leiden University (CEP17-1026/
362). Participants were treated in accordance with the Helsinki
Protocols for research with humans. Participants indicated that they
had no current or past neurological or psychiatric diseases and had
not taken (prescribed) psychotropic drugs within the past 2 weeks.
To control diurnal fluctuations in hormone secretion, all experi-
mental sessions were performed between 9:30 and 11:30 a.m., and
each session lasted approximately 90 min. In addition, participants
were instructed and reminded that in the 2 hr before the experimental
session, they should not eat (except a light snack), not consume
caffeine or alcohol, and not smoke.
Participants gave written informed consent and were debriefed.
They received a €6.50 show up fee and the outcome of five
randomly selected rounds of decision making (range €1–€14.5; M=
€7.40). Sample size was determined at n=55 attacker–defender
dyads, based on a power analysis for a multivariate within-dyad
repeated measures (90 contests) design with f=0.2, α=.05 and 1 −
β=0.90. We recruited 112 participants (79.5% female; age M=21,
SD =3.05, range 18–35 years), resulting in 56 attacker–defender
dyads. Data files of three dyads were corrupted, leaving N=53
dyads for final analyses.
Experimental Procedures and Measures
An experimental session consisted of two participants unknown
to each other and scheduled to arrive 10 min apart. Participants were
seated in individual cubicles, prohibiting them from seeing each
other. Participants first filled in their personal information after
which physiological electrodes were applied to the body of the
participants (Figure 4; also see Blascovich et al., 2011). To ensure
that participants’physiological responses were not influenced by
unrelated activities performed before the experiment, they had to
wait at least 30 min in the lab before recording cardiovascular
activity. During this habituation period, participants read instruc-
tions for the attacker–defender contest, followed by comprehension
questions that ensured their understanding of the task. To fill the
remaining time, participants filled out several surveys (data not
analyzed).
After the 30-min habituation period, participants were shown
peaceful underwater nature scenes for 5 min while baseline cardio-
vascular responses were recorded. Then participants were given a
25 ml sterile polypropylene tube and asked to swallow all saliva in
their mouths and allow saliva to be collected for 3 min, spitting once
a minute, for a total of >3 ml of saliva. Tubes were collected
immediately and stored on dry ice during the remainder of the session,
after which they were placed in a storage freezer at −18° Celsius.
Upon collection of the saliva samples, the experimenter unlocked
the participants’computers and participants were presented with
the instructions for the attacker–defender contest and a short
comprehension test. Participants read that they would make
decisions involving themselves and, on each decision trial, the
other player currently present with whom they were paired. Within
each dyad, one participant was randomly assigned to the role of
“attacker”(labeled as Role A) while the other participant was
assigned the role of a “defender”(labeled as Role B). On each trial,
participants had to decide how much to invest (out of their €10
endowment). After each trial, the participants were shown how
much the other person for that trial had invested and their earnings
for that trial. If the attacker invested more than its defender, the
attacker earned what the defender had not invested and this was
added to the attacker’s own left over (the defender earned 0,
respectively); if the attacker invested equal or less than its defender,
both attacker and defender earned their left over.
The contest involved 90 rounds of decision making, and to
accommodate physiological measurement, each decision round
lasted exactly 12 s (Figure 5). Specifically, participants were first
presented with a screen that prompted them to prepare their decision.
After 3 s, participants were shown the investment screen and were
given 5 s to select their investment by clicking on one of 10 buttons
shown in a row on the screen numbered from 0 to 10. Making a
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380 DE DREU ET AL.

selection would register their investment and take them to the
feedback screen. If the participant failed to choose an investment
within 5 s, the computer would generate a random investment for
them, but they would earn 0 on that round. This happened in 1.78%
of the trials, and we removed these trials from the analyses. The
investment was followed by a feedback screen that lasted a variable
amount of time to ensure that each trial took a total of 12 s
(specifically, 9 s minus participant’s time to make investment).
Upon completion of the contest, participants filled out several
surveys to complete a lapse of 30 min after the first saliva sample.
Participants filled a second tube with >3 ml of saliva and received a
written debriefing.
Measures and Data Preprocessing
Saliva samples were assayed for testosterone and cortisol at the
neuroendocrinology laboratory at the Free University Amsterdam.
Cortisol and testosterone were standardized within genders (Stanton
et al., 2021). The level of (log-transformed) cortisol detected at
baseline was lower post contest (M
change
=−0.284, 95% CI
[−0.337, −0.232]); the within-genders standardized level of
testosterone detected at baseline was about the same as post contest
(M
change
=0.041; 95% CI [−0.054, 0.137]). At baseline, cortisol and
testosterone were not correlated, r(53) =0.233, p=.109 for
attackers and r(53) =0.145, p=.302 for defenders; post contest,
these correlations were r=0.149 ( p=.288) and r=0.153 ( p=
.275), respectively. Exploratory analyses detected no statistical
outliers (at 3 SD ±M) in our data. Twenty-eight percent of the
females indicated they used hormonal contraception, yet this
variable did not affect the detected level of precontest testosterone or
cortisol detected (t<1). In addition, among our female participants,
we found no correlations between precontest testosterone and
cortisol on the one hand, and self-reported days since last
menstruation (all r<0.20, ps>.15). Both variables are further
ignored, and for all analyses involving hormonal indicators we only
controlled for participant age and gender (Stanton et al., 2021).
To obtain measures of sympathetic arousal, we continuously
measured electrocardiography and impedance cardiography (see
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Figure 5
Experimental Timeline and Measurements
99
101
103
105
107
109
baseline 3 6 9 12 15 18
Pre-ejection Period
Contest Block (5 trials, 60 seconds)
Note. After application of physiological sensors, a baseline physiology measure, and a saliva sample,
participants engaged in the attacker–defender contest game (ADCG, top panel); placement of electrodes (left
middle panel): For electrocardiography (ECG), we used two spot electrodes: on the manubrium (1) and on the
left lower costal margin (2; left). For impedance cardiography (ICG), we used four spot electrodes: five
centimeters higher than the base of the neck (1), at the base of the neck (2), 30 centimeters below the base of the
neck (3), and 33 centimeters below the base of the neck (4; right). Electrodes 1 and 4 emitted a high-frequency
alternating current of 400 μA and Electrodes 2 and 3 detected the voltage flowing through the thorax; examples
of ECG and ICG waveforms are shown in the left bottom. The interval between the Q-point and the B-point
marks the preejection period (PEP, and LVET, left ventricular ejection time). Right middle panel shows the
timeline of one contest round; right lower panel shows the average preejection period at baseline and for each
five-trial contest block participants engaged in. See the online article for the color version of this figure.
COMPETITION AND CONFLICT 381

Figure 5) using a Biopac MP150 system. Electrocardiography and
impedance cardiography data were stored used Acqknowledge
software (Biopac Systems Inc., Goleta, California, USA) and scored
with the PhysioData Toolbox software (Sjak-Shie, 2019). Segments
of movement artifacts were removed, and the impedance cardio-
graphy and electrocardiography signals were ensemble-averaged
across 1-min epochs yielding one epoch for baseline and 18 epochs
for the contest blocks for each participant. The Q-point (Berntson
et al., 2004), C-Point, X-point, and B-point (Sherwood et al., 1990)
were automatically scored by the software (yielding one PEP value
per epoch) and then manually checked. A 2 (role: attacker vs.
defender) ×19 (block: baseline vs. Block 1 vs. …Block 18) mixed-
model analysis of variance with role within-dyads and block as a
within-subjects repeated measure only revealed a main effect for
block, F(1, 52) =6.970, p=.011. Effects for role and Role ×Block
were not significant, F<1. For both attacker and defender, engaging
in the contest was initially arousing, with PEP reducing between
baseline and the first contest block for defenders from M=106.887
to M=101.613; t(52) =4.388, p<.001, and for attackers from M=
103.283 to M=99.915, t(52) =2.219, p=.031 (recall that lower
values for PEP indicate higher sympathetic arousal). As can be seen
in Figure 5 (bottom right panel), however, by the fourth block
sympathetic arousal was back to precontest baselines and remained
relatively stable thereafter.
Finally, from the investment decisions, we derived the overall
investment (range 0–10) and the cross-round variability in invest-
ments. We also computed earnings and the percentage of attacker
victories. To relate behavior to sympathetic arousal, we binned
investment and variability across the five trials in each block for
which we had a measure of sympathetic arousal.
Results
As in Study 1 (Tables 1 and 2), participants in Study 4 invested
less in attack than in defense (t=21.673, p<.001) and were more
variable in their investments during attack than defense (t=5.74,
p<.01). Extreme, out-of-equilibrium investments were frequently
seen during both attack and defense (proportion out of 90 trials:
0.297 and 0.377, respectively), with no difference between them
(t<1, not significant). We already showed in Table 2 that attacker
variability is associated with attacker victory (r=0.404, p<.001).
In addition, although not significant, the more variable defenders
were, the more often they were defeated by their attackers, r(53) =
0.229, p=.099. Finally, the more variable defenders were, the more
their attackers earned, r(53) =0.337, p=.014.
Moderation by Testosterone
To examine conflict behavior as a function of precontest
testosterone, we computed regression models separately for attack
and defense, with precontest testosterone, cortisol, and their
interaction as predictors. Participant age and gender were entered
as control variables. To account for the interdependency in the
dyadic data we partialled out defender behavior when examining
attackers, and vice versa (e.g., when estimating attacker invest-
ments, we included defender investment as a covariate). As in Study
3, and for each criterion (average conflict investment, variability,
and out-of-equilibrium investment), we estimated three models.
Model 1 included standardized precontest testosterone, Model 2
added standardized precontest cortisol, and Model 3 further
included the Testosterone ×Cortisol interaction. As in Study 3,
Model 1 was our main focus.
Results are summarized in Table 7. Replicating Study 3, neither
average investment in attack nor in defense was conditioned by
precontest testosterone (or cortisol; top panel in Table 7). Also as
in Study 3, and in all three models, higher levels of precontest
testosterone were associated with more variability in attack but not in
defense (Figure 6A). Again, neither cortisol nor the Testosterone ×
Cortisol interaction reached significance (middle panels in Table 7).
Finally, in contrast to Study 3, we find no evidence for a link between
testosterone and extreme (out-of-equilibrium) investment in attack
and defense (bottom panel in Table 7).
Sympathetic Arousal and Conflict Behavior
To explore how conflict dynamics shape and are shaped by
sympathetic arousal, we built lagged-panel regression models with
PEP as a marker of sympathetic arousal. As before, to account for
the interdependency in the dyadic data, we partialled out defender
behavior when examining attackers, and vice versa (e.g., when
estimating attacker investments, we included defender investment as
a covariate). Regression models and results are summarized in
Table 8.
We first estimated attacker (defender) arousal as a function of their
previous block investments in conflict. Specifically, we regressed
attacker’s (defender’s) PEP in block
(x)
onto their PEP in block
(x−1)
,
their own attacker (defender) investment and variability therein in
block
(x−1)
, and their defender’s (attacker’s) investment and
variability in block
(x−1)
. For attackers, the overall regression model
was significant, F(6, 45) =3.147, p=.012. Attacker arousal was
higher when their defender displayed more variability in their
investment in the previous block, b=−3.016, t=−3.014, p=.004
(Table 8). Conversely, we do not find this effect for defender arousal.
The overall regression model is not significant, F(6, 45) =1.709, p=
.141, and neither attacker nor defender behavior associated with PEP.
Second, we estimated attacker’s (defender’s) conflict invest-
ment as a function of their previous block sympathetic arousal.
Specifically, we regressed attacker’s (defender’s) investment in
block
(x)
onto their PEP, attacker (defender) own investment and
variability, and their opponent’s (defender’s or attacker’s) invest-
ment and variability in block
(x−1)
. For attacker’s investment in
conflict, the overall regression model was not significant, F(7, 44) =
1.930, p=.087. Attacker’s investments were nonsignificantly
higher the more they invested in the previous block, b=0.378, t=
1.756, p=.086, and significantly lower the more their defenders
invested in the previous block, b=−0.623, t=−2.643, p=.011.
For defender investment in conflict, the overall regression was
significant, F(7, 44) =2.379, p=.037, yet no single predictor
emerged as significant (Table 8).
Finally, we estimated attacker (defender) conflict variability as a
function of attacker’s (defender’s) sympathetic arousal. Specifically,
we regressed attacker’s (defender’s) variability in block
(x)
onto
their PEP, attacker (defender) own investment and variability, and
their opponent’s (defender’s or attacker’s) investment and
variability in block
(x−1)
. For attackers, the overall regression model
was not significant, F(7, 44) =0.321, p=.940, nor was any single
predictor. For defenders, however, the overall regression was
significant, F(7, 44) =2.842, p=.016: Defender variability was a
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382 DE DREU ET AL.

function of both their own and their attacker’s sympathetic arousal in
the previous block, b=−0.65, t=−2.392, p=.021, and b=
−0.078, t=−3.301, p=.002 (Figure 6C, and Table 8). Put
differently, the more sympathetic arousal attackers and defenders
had in the previous block, the more variable defense investments
were subsequently.
Discussion
Results of Study 4 combined suggest that (a) attackers are
more variable when their precontest testosterone levels are higher
(Figure 6A and Table 7), and (b) the more variable attacker
investments are, the more variable defenders are in their response
(Figure 6B, and Table 7). More variable attacker behavior (c)
increases sympathetic arousal in defenders (Figure 6C, and Table 8)
which, in turn, (d) associates with increased variability in defense
(Table 8). Variability in defenders thus emerges as a function of their
sympathetic arousal in response to attacker’s variability. Finally, (e)
the more variable defenders were, the more often they were defeated
by their attackers and the more their attackers earned. This suggests
that the arousal-induced variability in defenders helps attackers to
settle conflict in their favor.
Together these results from Study 4 add three insights to our
earlier studies. First, we replicated that precontest testosterone
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Table 7
Regression of Testosterone and Cortisol on Variability in Attacker and Defender Conflict Investment (Top),
Variability in Investment (Middle), and Out-of-Equilibrium Investment (Bottom; Study 4)
Predictor
Model 1 Model 2 Model 3
B SE B SE B SE
Attacker investment
Gender 0.010 0.414 0.199 0.435 0.117 0.439
Age 0.101 0.063 0.111 0.063 0.107 0.063
Defender investment 0.862*** 0.100 0.846*** 0.099 0.839*** 0.099
Testosterone −0.144 0.222 −0.209 0.225 −0.097 0.244
Cortisol 0.231 0.173 0.140 0.190
Testosterone ×Cortisol −0.327 0.284
Defender investment
Gender 0.762** 0.336 0.819** 0.342 0.786** 0.347
Age 0.021 0.042 0.023 0.042 0.020 0.042
Attacker investment 0.702*** 0.083 0.688*** 0.085 0.693*** 0.085
Testosterone −0.182 0.192 −0.215 0.195 −0.207 0.197
Cortisol 0.139 0.149 0.100 0.159
Testosterone ×Cortisol 0.114 0.163
Attacker variability
Gender −1.411 1.189 −2.069 1.270 −2.172 1.301
Age −0.325 0.184 −0.375*0.186 −0.382*0.188
Defender variability 1.010*** 0.162 0.969*** 0.164 0.960*** 0.166
Testosterone 1.794*** 0.649 1.977*** 0.656 2.103*** 0.719
Cortisol −0.705 0.508 −0.817 0.570
Testosterone ×Cortisol −0.377 0.841
Defender variability
Gender 0.244 0.789 0.085 0.813 −0.075 0.805
Age −0.022 0.094 −0.026 0.095 −0.042 0.094
Attacker variability 0.396*** 0.072 0.408*** 0.073 0.407*** 0.072
Testosterone 0.336 0.418 0.378 0.422 0.398 0.415
Cortisol −0.284 0.337 −0.471 0.350
Testosterone ×Cortisol 0.583 0.358
Attacker O-E
Gender −0.019 0.056 0.007 0.059 −0.013 0.059
Age 0.012 0.009 0.013 0.009 0.012 0.008
Defender O-E 0.753*** 0.095 0.750*** 0.094 0.730*** 0.093
Testosterone −0.007 0.029 −0.016 0.030 0.008 0.032
Cortisol 0.030 0.023 0.011 0.024
Testosterone ×Cortisol −0.069 0.037
Defender O-E
Gender 0.103** 0.051 0.105 0.052 0.101 0.053
Age 0.002 0.006 0.002 0.006 0.001 0.006
Attacker O-E 0.775*** 0.097 0.772*** 0.100 0.774*** 0.101
Testosterone −0.010 0.029 −0.011 0.029 −0.010 0.030
Cortisol 0.003 0.023 −0.001 0.024
Testosterone ×Cortisol 0.012 0.025
Note. Gender is dummy coded with 0 =male, 1 =female; Cortisol and testosterone are standardized with M=0 and
SD =1.0. SE =standard error; O-E =out-of-equilibrium.
*p<.010. ** p<.05. *** p<.01 (with N=53).
COMPETITION AND CONFLICT 383

predicts how variable attackers but not defenders are. This finding
resonates with our hypothesis that an increased motivation to
“win-at-all-cost”underlies unpredictably variable behavior, partic-
ularly for attacks. We return to this in the General Conclusions and
Discussion. Note that in some earlier work, effects of testosterone
on aggression and competitiveness emerged especially under lower
levels of basal cortisol (viz., dual-hormone hypothesis; Casto &
Edwards, 2016;Mehta & Josephs, 2010). In our studies, we did not
observe this. In Study 3 we found, in some analyses, an interaction
between testosterone and cortisol but not in the form expected
under the dual-hormone hypothesis. In Study 4, we never observed
significant Testosterone ×Cortisol interactions. As such, current
results align and add to the conclusion from recent meta-analyses
that evidence for the dual-hormone hypothesis is limited to specific
cases (Dekkers et al., 2019) and potentially problematic (Grebe et
al., 2019). As our studies were not designed to test the dual-hormone
hypothesis in the context of attacker–defender contests, we refrain
from further interpretation of these null results.
Our second insight from Study 4 is that, in fixed-partner
protocols, defenders respond, both in their overall investment and in
their variability to their attacker’s initiatives—the more variable
attacker’s investments are, the more variable the defenders become.
Crucially, we obtained some evidence that attacker variability
increases sympathetic arousal in defenders, and that defender
arousal predicts how variable their investments subsequently are.
Because defender variability associates with a higher likelihood of
being defeated, these results point to a possible pathway from
attacker variability, through sympathetic arousal in their defenders,
to attacker successes in defeating their defenders.
Conclusions and General Discussion
Conflict theory anticipates that, in some situations, individuals
may be motivated to be unpredictable and can be expected to vary
whether and how much they invest in conflict. Our review of the
empirical literatures in experimental economics and psychological
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Figure 6
Testosterone and Sympathetic Arousal Shape and Are Shaped by Conflict Dynamics
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 4 8 121620
Pre-z
( e
noretsots
eT tsetno
c-scored)
Attacker Variability
(A) (B) (C)
0
4
8
12
16
20
0 4 8 121620
Variability Block (x-1)
Variability Block (x)
Linear (Attacker x-1 -> Defender x)
Linear (Defender x-1 -> Attacker x)
0
4
8
12
16
20
60 110 160
Variability Block (x-1)
Pre-Ejection Period Block (x)
Linear (Attacker x-1 -> Defender x)
Linear (Defender x-1 -> Attacker x)
Note. (A) Higher levels of precontest testosterone in attackers associate with more variability in conflict investment; (B)
attacker variability predicts subsequent variability in defense better than the other way around; (C) higher variability in
attackers predicts more sympathetic arousal (i.e., lower preejection periods) in defenders. Scatterplots show individual pairings
(red dots =attackers; blue diamonds =defenders) with best-fitting linear regression lines inserted (solid =attack predicting
defense; dashed =defense predicting attack). See the online article for the color version of this figure.
Table 8
Sympathetic Arousal and Conflict Dynamics (Study 4)
Predictor
Defender block
(x)
Attacker block
(x)
Arousal Investment Variability Arousal Investment Variability
B SE B SE B SE B SE B SE B SE
Gender 7.16** 4.776 −1.016
^
0.596 2.445** 0.874 12.752** 4.469 0.408 0.645 0.054 2.077
Att. inv.
(x−1)
0.885 1.534 0.194 0.203 0.271 0.298 −1.557 1.568 0.378
^
0.215 −0.576 0.692
Att. var.
(x−1)
0.076 0.505 −0.003 0.064 −0.034 0.094 0.718 0.506 −0.046 0.070 −0.018 0.226
Def inv.
(x−1)
−2.455 1.633 −0.342 0.223 −0.168 0.327 1.842 1.686 −0.623** 0.236 0.468 0.759
Def. var.
(x−1)
−1.018 0.965 0.190 0.127 0.143 0.186 −3.016** 1.001 0.208 0.139 −0.002 0.449
Att. arousal
(x−1)
NA NA 0.015 0.016 −0.065** 0.027 0.092 0.125 −0.001 0.018 −0.057 0.059
Def. arousal
(x−1)
−0.109 0.130 −0.031
^
0.018 −0.078** 0.024 NA NA −0.029 0.019 −0.062 0.062
Note. Gender is dummy coded with 1 (0) =female (male); arousal is proxied by preejection period, with lower scores indicating more sympathetic
arousal. SE =standard error; (x)(x−1) =measure in current (previous) block, with one block consisting of five investments rounds of 12 s each; Att.
(Def.) inv. =attacker (defender) investments averaged across the five trials in one block; Att. (Def.) var. =attacker (defender) variability in investment
across the five trials in one block; NA =not applicable (i.e., this predictor was not entered into the regression model for the specific criterion).
^
p<.10. ** p<.01 (with N=52) .
384 DE DREU ET AL.

science revealed three open issues: (a) do people in conflict with its
equilibrium in mixed strategies variably mix whether and how
much they invest in conflict; (b) does such variable mixing render
competitors unpredictable to their counterpart; and (c) how does
being (unpredictably) variable influence conflict dynamics and
outcomes. In four studies, we addressed these questions in the realm
of attacker–defender contests in which one individual invests, as
attacker, to win against and exploit an opponent who, in turn, invests
to defend against attacks and prevents being exploited.
Findings combined answer the open questions as follows.
First, attackers as well as defenders produce significant variation
in their conflict investments both when interacting with different
opponents and when repeatedly interacting with the same opponent.
Second, variability makes conflict parties’next move difficult to
predict—variability renders competitors unpredictable, and espe-
cially when variability is produced by occasional out-of-equilibrium
investment in conflict. Third, being unpredictably variable reduced
earnings especially for defenders, and increased the likelihood
that attackers successfullydefeated their defender. The reason for this
is that being unpredictable during attack partly resides in and
emerges from a motivation to “win-at-all-cost”and leads attackers
to occasionally lash out with extreme investments that are irrational
from a payoff-maximizing perspective.
Implications for Theory and Future Research
Findings have several implications for conflict theory. First, agents
are often assumed to be rational (expected) payoff maximizers (viz.,
homo economicus), which simplifies mathematical analyses, makes
very few assumptions (parsimony), and can sometimes approximate
human behavior well enough. Here, we identified that people may
also not only, or not at all, be motivated by earnings per se. Rather,
our results suggest that people during attack may be also, or
exclusively, motivated to win the contest and emerge victorious “no
matter what.”Attackers were, accordingly, occasionally investing
out-of-equilibrium and while this cannot be understood from a strict
payoff-maximizing perspective, such behavior does fit a winning-at-
all-cost motivation (Thaler, 1988;van den Bos et al., 2008).
Second, and relatedly, our findings subscribe to the general insight
that human preferences are heterogeneous and, possibly, malleable
(De Dreu & Gross, 2019a). In both Studies 3 and 4, we found that
the utility from winning appeared stronger among individuals with
higher levels of precontest testosterone, a steroid hormone associated
with risk tolerance, competition, and status seeking (e.g., Coates
et al., 2010;Eisenegger et al., 2011;Geniole et al., 2020;Mazur &
Booth, 1998). Third, and finally, findings specify Schelling’s
conjecture that being unpredictable can be strategically advantageous
in two ways. First, the advantage resides in attackers and not in the
defending party. Second, the advantage is in terms of the ability to
win and emerge victorious (viz., relative fitness), and not (only) in the
ability to maximize expected payoff (viz., absolute fitness).
Next to contributions to theory on conflict, findings contribute
to work on the neurobiology of human aggression. Attacking has
been linked to instrumental and proactive aggression that may
be premediated and “cool-headed.”Defending, in contrast, is a
more reactive form of aggression that may be more impulsive and
conditioned by sympathetic arousal (Nelson & Trainor, 2007;Potegal
& Nordman, 2023;Weinshenker & Siegel, 2002;Wrangham, 2018).
Elsewhere, we indeed observed attack decisions to take more time
(De Dreu et al., 2015,2019), and to involve more sophisticated
cognitive reasoning (Rojek-Giffin et al., 2020). Here, we can add,
from Study 4, that attacker behavior is not,and defender behavior is, a
function of (their own) sympathetic arousal. Accordingly, current
findings further support the possibility that attacker–defender contests
allow for a clean decomposition of instrumental and proactive versus
impulse and reactive aggression and help to shed further light on the
neurobiological and psychological underpinnings of these distinct
forms of human aggression (Sarkar & Wrangham, 2023).
Outside of the domain of conflict and aggression, cognitive science
has questioned whether humans can be unpredictable because they
have difficulty being random(Burns & Vollmeyer, 1998;Cooper,
2016;Sanderson, 2018;Wagenaar, 1972;Warren et al., 2018;Wong
et al., 2021). Our results speak to this issue in two ways. First, we
obtained some evidence that conflict strategies are less rather than
more systematic and that more variable strategies made competitors
difficult to predict. Possibly, at least in conflict and competition,
humans can be nonsystematic and unpredictable at least to a degree
to which other humans have difficulties predicting their next
move. Second, we obtained suggestive evidence that humans
can be unpredictably variable at least when this serves strategic
considerations—when conflict has its equilibriumin mixed strategies,
for example. It would be interesting to further pursue these possibi-
lities and test whether unpredictability is indeed observed more
when being unpredictable has fitness functionality rather than not.
In addition, our results cannot tell whether unpredictably variable
investments in conflict were cognitively controlled and deliberated
or instead uncontrolled and intuitive. If the latter would be the case,
being unpredictable or not may reflect an evolved capacity with
nontrivial fitness relevance.
Study Limitations
Our conclusions and implications need to be considered in light
of several limiting factors. First, we studied populations of well-
educated adults performing stylized economic contests. We have
shown elsewhere that competitive actions in these attacker–defender
contests are replicable across cultural contexts, and that investment
in attack and defense correlate with self-reported “willingness to
fight”from social value survey measures (Romano et al., 2022).
Nevertheless, future research is needed to examine to what extent
our findings replicate in other conflict games with their equilibrium
in mixed strategies such as hide-and-seek games (Bar-Hillel, 2015)
and best-shot-weakest link games (Clark & Konrad, 2007). Second,
in our studies, individuals only had their counterpart’s past behavior
to predict the future. Outside stylized games of conflict, however,
individuals often invest in obtaining information about their
counterpart and incorporate such information in their predictions.
For example, governments and private organizations invest in
intelligence and counterintelligence to identify targets for military
invasions and hostile takeover attempts and to assess the potential
aggression from nearby competitors. Ordinary citizens, likewise,
install cameras and silent alarms on their front entrance to survey
for and preemptively detect potential burglars; burglars in turn
investigate estates to identify its weak spots and possibilities
for entry and theft. Accordingly, individuals respond to each
other’s unpredictability in an “arms race”manner between being
deliberately unpredictable toward others and deliberately “undoing”
another’s unpredictability. There is some irony in this, as in the end
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COMPETITION AND CONFLICT 385

the investments in intelligence and counterintelligence do not solve
the profound advantages of being unpredictable in conflict with
mixed-strategy equilibria—when defenders reduce the attacker’s
ability to be unpredictable, attackers become motivated to improve
on their unpredictability, which motivates defenders to invest further
in intelligence, and so on.
Coda
High-ranking politicians and military leaders sometimes appear
irrational and irreducibly unpredictable. Here, we elucidated why
and when such erratic mixing between hostility and amity can be
functional in the context of attacker–defender conflicts. Human
participants, indeed, showed substantial variation in their behavior,
even considering extensively costly actions that allow them to be
more unpredictable and victorious at significant welfare cost to both
victor and victim. Being unpredictable sometimes serves to win no
matter what.
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Received March 28, 2023
Revision received November 21, 2023
Accepted November 28, 2023 ▪
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Correction to “What Limitations Are Reported in Short Articles in Social and
Personality Psychology”by Clarke et al. (2023)
The following article is being corrected: Clarke, B., Schiavone, S., & Vazire, S. (2023). What
limitations are reported in short articles in social and personality psychology. Journal of Personality
and Social Psychology: Personality Processes and Individual Differences, 125(4), 874–901. https://doi
.org/10.1037/pspp0000458. The percentages in the seventh sentence in the abstract now appear as 41%
and 20%, respectively. The online version of this article has been corrected.
https://doi.org/10.1037/pspp0000502
COMPETITION AND CONFLICT 389