Individual Response Modes to Pre-trip Information in Congestible Networks: Laboratory Experiment

Abstract

To better capture typical individual response modes under strategic uncertainty in congestible networks, we conducted laboratory experiments in a network with two-parallel routes under within-subject design. Sixty-four undergraduates were assigned into four sessions to make recurrent route-choice decisions under Condition partial-information (PI) first, and then under Condition full-information (FI). Individuals whose response modes are featured by a series of conditional probabilities regarding switching behaviour naturally cluster into three and four groups under Condition PI and FI, respectively. An in-depth analysis of behavioural bases of each type was discussed. In Condition FI, the proportion of highly responsive players (holding Direct-response-like and Contrary-response-like patterns) and Highly-risk-averse players drop, whereas the Status-quo-maintenance category players stand out. More feedback information was disclosed for the purpose of reducing uncertainty but turned out to reduce the proportion of people who were highly responsive to the new information and who firmly commit themselves to a unique route.

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Transportmetrica A: Transport Science
ISSN: 2324-9935 (Print) 2324-9943 (Online) Journal homepage: http://www.tandfonline.com/loi/ttra21
Individual response modes to pre-trip information
in congestible networks: laboratory experiment
Hang Qi, Shoufeng Ma, Ning Jia & Guangchao Wang
To cite this article: Hang Qi, Shoufeng Ma, Ning Jia & Guangchao Wang (2018): Individual
response modes to pre-trip information in congestible networks: laboratory experiment,
Transportmetrica A: Transport Science, DOI: 10.1080/23249935.2018.1485061
To link to this article: https://doi.org/10.1080/23249935.2018.1485061
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TRANSPORTMETRICA A: TRANSPORT SCIENCE
https://doi.org/10.1080/23249935.2018.1485061
Individual response modes to pre-trip information in
congestible networks: laboratory experiment
Hang Qia, Shoufeng Maa, Ning Jiaaand Guangchao Wangb
aInstitute of Systems Engineering, College of Management and Economics, Tianjin University, Tianjin,
People’s Republic of China; bSchool of Information Management, Central China Normal University, Wuhan,
People’s Republic of China
ABSTRACT
To better capture typical individual response modes under strate-
gic uncertainty in congestible networks, we conducted laboratory
experiments in a network with two parallel routes under within-
subject design. Sixty-four undergraduates were assigned into four
sessions to make recurrent route-choice decisions under Condi-
tion partial-information (PI) first, and then under Condition full-
information (FI). Individuals whose response modes are featured by
a series of conditional probabilities regarding switching behaviour
naturally cluster into three and four groups under Conditions PI and
FI, respectively. An in-depth analysis of behavioural bases of each
type was discussed. In Condition FI, the proportion of highly respon-
sive players (holding Direct-response-like and Contrary-response-
like patterns) and Highly-risk-averse players drops, whereas the
Status-quo-maintenance category players stand out. More feedback
information was disclosed for the purpose of reducing uncertainty
but turned out to reduce the proportion of people who were highly
responsive to the new information and who firmly commit them-
selves to a unique route.
ARTICLE HISTORY
Received 15 August 2016
Accepted 2 June 2018
KEYWORDS
Route choice; experimental
economics; inertia;
risk-aversion; clustering
1. Introduction
Every commuter makes route choices in an uncertain environment. An increasing number
of experimental and empirical studies aim to test the premise underlying the develop-
ment of advanced traveller information systems (ATIS) – that pre-trip travel information
regarding travel time empowers commuters to choose efficiently by reducing uncertain-
ties. The literature could be regarded as two branches concerning different uncertainty
sources, that is, environmental uncertainty (such as accidental network disruptions due to
bad weather and special events) and strategic uncertainty (such as negative externalities of
individual choices in a congestible network). See Schreckenberg and Selten (2013), Ben-Elia
and Avineri (2015), and Rapoport and Mak (2017) for review.
CONTACT Ning Jia jia_ning@tju.edu.cn Institute of Systems Engineering, College of Management and
Economics, Tianjin University, 300072 Tianjin, People’s Republic of China
Supplemental data for this article can be accessed here. https://doi.org/10.1080/23249935.2018.1485061
© 2018 Hong Kong Society for Transportation Studies Limited

2H. QI ET AL.
In the latter branch, travel time on roads is determined endogenously by the total num-
ber of players traversing the same routes, rather than modelled by probability distributions
that are assumed to be fixed over iterations of the trip and not affected by the travellers’
previous choices as in the former stream (like Ma and Di Pace 2017). Thus, individual route-
choice decisions under strategic uncertainty may be influenced by others’ choices and
the previous states of network flow distribution. In other words, this stream allows for
strategic thinking of commuters during recurrent interactions on congestible networks.
Therefore, how pre-trip information influences individual route choice and thereby impacts
the aggregated dynamics counts as a complicated problem and still in its infancy.
A brief summary of congestion experiments on pre-trip information effects is displayed
in Table 1, see more details in the review by Dixit et al. (2017). Mixed results have been
reported. Positive effects include significant reductions in the frequency of route switches
(Selten et al. 2007), resulting in a faster convergence towards equilibrium predictions (Iida,
Akiyama, and Uchida 1992). However, most of the others do not observe significant dif-
ferences in network flow distribution between two conditions (with or without foregone
payoffs (FPs) information) (Gisches and Rapoport 2012; Knorr, Chmura, and Schrecken-
Tab le 1 . A summary of representative laboratory experiments on pre-trip information effects in con-
gestion games under strategic uncertainty.
Experiment design
Author(s) and Year
Treatment of
information
Rounds of
games
Information effec ts
on traffic distribution
Behavioural
model
Iida,Akiyama,and
Uchida (1992)
Between-subject 50 The traffic gets much closer
to equilibrium with more
information about the history of
play
Regression functions
regarding predicted
time and accumulated
experience
Selten et al. (2007) Between-subject 200 Mean route choice frequencies
approach the equilibrium, with
persisting fluctuations until the
end of the sessions.
Simulations based
on a payoff-sum
reinforcement learning
model to update
propensities of four
strategies: Main road,
Side road, Direct and
Contrary response
Gisches and Rapoport
(2012)
Between-subject 80 Support for equilibrium behaviour
on the aggregate, but not
individual, level is obtained.
An individual-level
reinforcement learning
model
Knorr, Chmura, and
Schreckenberg (2014)
Between-subject 50 •The mean route choices
approached the equilib-
rium solution, but not
steadily achieved it.
•The overall number of
switches slowly decreased
over iterations but persisted
to the end of the session.
•Providing identical informa-
tion to all the participants
did not result in significant
benefits.
Rapoport et al. (2014) Within-subject 80 •Equilibrium predicted well for
both information regimes.
•Information paradox: when
capacities of routes vary inde-
pendently, total expected
travel cost decrease with
pre-trip information.
EWA learning model

TRANSPORTMETRICA A: TRANSPORT SCIENCE 3
berg 2014; Rapoport et al. 2014). It would seem that a major reason for the discrepancy
is common knowledge of the cost function of all routes, which exists in part of these exper-
iments but not the others. Further experiments might contribute to our understanding of
the impact of information about the route conditions and the impact of game parameters.
Therefore, there is merit in conducting additional research experiments.
More importantly, we believe a key issue to better understand aggregate dynamics is to
explore how the individuals respond to such information (Bogers, Viti, and Hoogendoorn
2005; Smith et al. 2014). After all, aggregates do not switch routes; individual commuters do.
Therefore, the major purpose of this paper is to depict the effects pre-trip information on
individual response modes, following necessary statistical analysis of effects on aggregated
dynamics. In speaking of individual response mode, we refer to the process through which
an agent shifts his/her own strategy to respond to perceived information and adapt to the
changing environment involving opponents. Information, as a description of the current
environment state generated by all agents’ choices, incorporating with personal experi-
ence, stimulates adaptive agents to form believes and expectations regarding what would
others do most likely, and to translate all this into an update of their strategy or choices
(Bogers, Viti, and Hoogendoorn 2005).
Researchers have applied various theories embedding boundedly rationality to depict
individual response modes under strategic uncertainty. See Di and Liu (2016) for a review.
Sun et al. (2017) apply reinforcement learning and Fermi learning models; Zhao and Huang
(2014) introduce Quantal Response Equilibrium theory into route-choice modelling and
network equilibrium analysis; Alibabai and Mahmassani (2016) consider two types of com-
muters as first-level thinkers (termed by sheep) and second-level thinkers (termed by foxes),
inspired by level-ktheory and Cognitive Hierarchy theory (Camerer, Ho, and Chong 2004)
that describes the individual heterogenicity in the depth of strategic thinking. Besides, Mah-
massani and Chang (1987) and Zhang and Yang (2015) introduce the concept of inertia
or habit to capture unresponsive agents and their routine-like behaviour that commuters
are stuck to their usual driving routes and do not necessarily minimize travel time. Other
non-expected utility theories have been applied including Prospect theory (Avineri and
Prashker 2006), Regret theory (Chorus 2012a), Reinforcement Learning theory (Macy and
Flache 2002; Roth and Erev 1995) and Experience-Weighted Attractions (EWA) learning
(Gisches and Rapoport 2012).
To capture typical individual response modes from experimental data, two pioneering
works are by Selten et al. (2007) and Helbing et al. (2005). The former proposes a route-
choice game under two information policies on directed networks with two parallel routes
connecting a common origin and a common destination. The two conditions with dif-
ferent information policies are, respectively, Condition PI (partial-information) where only
travel time on chosen routes is disclosed, and Condition FI (full-information) where addi-
tional information regarding foregone payoffs (FPs for short) on the other route would
be disclosed as well. With the index of Yule coefficient, they successfully identify half of
the patterns that participants behave as direct- and contrary-response modes, whereas
the other half was left undefined. In addition, Helbing et al. (2005) revise Yule coefficient
into S-coefficient to describe individual tendency towards direct or contrarian responses,
and introduce the supplemental Z-coefficient to describe the likelihood for an individual
to switch away when travel time on two routes are the same in the last round which is
commonly known as user equilibrium among all players.

4H. QI ET AL.
To our best knowledge, the above studies, including a study by Avineri and Prashker
(2006), artificially classified subjects into different types according to man-made criteria.
However, heterogenous individual profiles of route switches defy simple classification (Gis-
ches and Rapoport 2012; Zhao and Huang 2016). Promisingly, clustering methods (like
k-mean clustering analysis; Hartigan and Wong 1979) have advantages to address multi-
dimensional data without leading to a rapidly increasing number of subgroups, and they
comply with the natural aggregation or distribution of data objects. It thus has potential
to identify the entire gamut of objects based on multiple dimensions and allows for in-
depth analysis on how individual response modes changes with more pre-trip information
available.
The present study has two main purposes. The major purpose is to depict the changes
on individual response modes between with/without pre-trip information conditions. The
minor motivation is to conduct additional experiment to support either side of mixed
results regarding pre-trip information effects on aggregated dynamics. Also, we sought to
discuss results at the aggregated level by the individual response modes captured from
data at the individual level under two information scenarios.
For both purposes, we conducted laboratory experiments similar to the classical route-
choice experiment by Selten et al. (2007), except for the implementation of a within-subject
design and some minor differences (details in Section 3.1). Sixty-four undergraduates were
assigned into four sessions to make recurrent route-choice decisions under Condition
PI first, and then under Condition FI. We opted for within-subject than between-subject
design mostly for its advantages in controlling individual differences in personality across
different information regimes. That design facilitated us to go deeper to identify the entire
gamut of response modes through clustering analysis, and to explore the differences that
pre-trip information induces to individual response modes.
The rest of the paper is organized as follows. Section 2 introduces of the route-choice
experiment with the two information regimes; Section 3 presents statistical analysis of the
equilibrium prediction and information effects on aggregate dynamics. In Section 4, we
identify clusters of individuals who behaved similarly. Section 5 provides a discussion and
conclusion.
2. Methods
2.1. Subjects
The participants were undergraduates at Tianjin University, who volunteered to take part
in a decision-making task in return for money payoff, contingent on their performance dur-
ing experiments. A total of 64 subjects (randomly assigned to one of four groups as four
sessions), in roughly equal proportions of males and females, participated in computer-
controlled route-choice experiments between October 2014 and January 2015. The sub-
jects were paid 30 for a show-up fee, and additional monetary reward contingent on their
performance in the game. On average, participants earned 98, with the maximum of 130
and a minimum of 85.
The individual payoff (defined as, P, for points) for each round was calculated by sub-
tracting the travel cost (defined as, T) from a fixed reward for completing a trip (defined
as, R=40). A conversion rate of 40 points =1 was used. The additional rewards were

TRANSPORTMETRICA A: TRANSPORT SCIENCE 5
calculated separately according to player performance under the two conditions. At the
end of each session, the participants were paid their winnings by cash individually and
dismissed.
2.2. Scenarios
Subjects were presented with the network game displayed in Figure 1that can traced back
to the classical papers by Pigou (1920) and Knight (1924). The game was designed as a situ-
ation where a fixed number of commuters living in the same community (the origin) must
choose each one of the two possible routes (either M, for main road or S, for a side road)
every morning to a common workplace (the destination) (see Figure 1).
Each route was designed to be susceptible to congestion; the participants were
instructed to ‘arrive at your workplace as quickly as possible’. The travel time (in minutes)
on a given route, tMand tS, is assumed as linear functions of the route flow (i.e. the numbers
nMand nS). Under both information conditions, the cost functions were defined as follows:
tM=6+2nM,
tS=12 +3ns.(1)
This situation is modelled as a non-cooperative n-person iterated game with a specific type
of information provision regime. All the pure-strategy Nash equilibrium in this game under
any of the two conditions can be characterized by nM=11 and nS=5. The social optimum
is featured by nM=10.2 and nS=5.8.
The subjects were instructed that travel time might vary from round to round depending
on multiple factors in reality, but only two factors mattered in the experiment: (1) the more
subjects choosing the same route, the longer time it takes to travel this route; and (2) the
travel time on road Mis shorter than on road Sif the traffic load is the same for both of them
(that is, the same number of subjects choosing them).
Two information conditions were conducted in a within-subject design. Subjects were
arranged to participate in Condition PI first and then Condition FI. At the beginning of each
round, the following information was displayed (see the interface screens in Appendix A).
Figure 1. Participants had to choose between a side road [S] and a main road [M].

6H. QI ET AL.
•The travel time on the player’s chosen route during the last round;
•The travel time on the player’s non-chosen route in the preceding period (only under
Condition FI);
•The last-chosen route and the payoff in the last round;
•The cumulative payoff in RMB;
•The number of the current period and
•All the previous route choices and the corresponding travel time.
Indeed, some research applied complex non-linear cost function in virtual experiments
like Ye, Xiao, and Yang (2017) and Jin and Barberillo (2012). However, we have chosen lin-
ear cost functions mostly for experimental purposes like previous experimental studies (like
Gisches and Rapoport 2012; Knorr, Chmura, and Schreckenberg 2014). Despite their simplic-
ity, linear cost functions capture the most important aspects of the relationship between
travel time and traffic flow loaded on routes described above. Besides, from the partici-
pants’ perspective, the relation between travel time and traffic flow was consistent with
their own travel experiences.
2.3. Procedure
The four sessions, each including 16 subjects, were conducted in a computerized laboratory
with multiple terminals located in separate cubicles. Visual contact among subjects was
impossible, and communication among the subjects was prohibited. Subjects were handed
the instructions that they read at their own pace. The instructions described the network
game, the procedures for choosing among the routes, and the computation of payoff. Each
session lasted between 90 and 120 minutes, beginning with a presentation of instruction
and a warming-up practice part (about 10 rounds), consisting of formal experiments under
Condition PI and then FI, and ending with a post-experiment interview.
Totally, we have four different groups of subjects as four sessions. Each of these groups
of people participated into Condition PI first and then Condition FI. Each condition con-
sists of a few repetitions (regarded as ‘rounds’) of the route-choice game (called a stage
game). Note that if we run sessions where full-information condition was played first, to
counterbalance the order of conditions, some subjects could learn the comparison rela-
tionship between actual travel time and alternative travel time on their unchosen route in
Condition FI and then apply what they learned to predict FPs which are not disclosed in the
following Condition PI. Therefore, the regular method of conducting reverse condition in
order to counterbalance the possible carryover effect does not work.
To minimize carryover effects resulting from the within-subject design, we applied three
key settings in this experiment. First, participants were only handed the instructions for
condition PI at the beginning of the session. After reading these instructions, they took a
10-minute break and received a second round of instructions before a Condition FI began
(Lu et al. 2014). Second, the performance-contingent monetary rewards for an individual’s
performance was calculated separately for the two conditions and were kept secret until
the end of all sessions; a player wishing to maximize her rewards could not be sure whether
her strategy was the best, when a new condition began.
Third, we applied ‘stochastic ending point’ (e.g. Dal Bó and Fréchette 2011;Qietal.2015)
to avoid an end game effect (Östling et al. 2011) and to simulate the transport reality that

TRANSPORTMETRICA A: TRANSPORT SCIENCE 7
commuters travelling between the same origin and the same destination interact with each
other day after day without a commonly known ending of interactions. The server com-
puter randomly selected the total number of rounds in the range [70, 120] (see Table A.1
in Appendix A). As for the setting of this range, we referred to most previous experiments
(like 200 rounds in Selten et al. (2007), 100 rounds in Chmura (2011), 40 rounds in Rapoport
et al. (2009) represented in Table 1).
3. Aggregate results
Given that most previous experiments using between-subject design reported non-
significant influence of full-feedback information (referring to Table 1). Within-subject fea-
ture makes it easier to find evidence in support of equilibrium because of potential learning
effects. Nevertheless, if significant difference is not observed as well using within-subject –
as in the present experiment – then the finding should prove more convincing. That is,
traffic flow distribution among a group of commuters may not achieve Nash equilibrium
steadily even with full-feedback information regarding travel time.
3.1. Equilibrium prediction
A prior analysis should be conducted to test the differences among the four sessions in
Condition PI and also among the four sessions in Condition FI. If no significant differences
are observed, the data from four sessions in the same condition can be amalgamated here-
after. For this purpose, the following three statistics concern system variables in different
perspectives, were computed for each of the four sessions in both conditions. That is, the
observed mean value and standard variance of choice frequencies of route S,andtheaver-
ageofsystemcost.Table2shows that the means of each session are very closed to each
other. For instance, the observed mean number of players on route Sin Condition FI was
5.41 (1.90) ranging between 5.33 and 5.53; and 5.32 (1.78) ranging between 5.24 and 5.38
in Condition PI, respectively. Also, F-tests support that observation (p>.05 for all the three
statistics for both conditions). Thus, hereinafter, we pooled all the four sessions in each
condition.
The dynamics of the traffic flow on route Sunder both conditions in four sessions are
exhibited in Figure 2. The results are displayed in blocks of five rounds each, with a ref-
erence line (black dashed line) indicating the pure-strategy Nash equilibrium prediction. A
visual inspection of Figure 2suggests three findings: (1) the route flow on Soscillates around
Tab le 2 . The observed mean and standard deviation of the number of players on the side road S, and
the system average travel time under both conditions among four sessions.
Mean choices of SroadaStandard variation of Sroad Mean system travel cost
Session PI condition FI condition PI condition FI condition PI condition FI condition
1 5.38 (5.21) 5.40 (5.69) 1.89 1.79 28.65 28.53
2 5.36 (5.28) 5.53 (5.45) 1.73 2.01 28.49 28.78
3 5.24 (5.33) 5.33 (5.50) 1.72 2.18 28.51 29.04
4 5.29 (5.00) 5.36 (5.05) 1.78 1.64 28.56 28.39
Average value 5.32 (5.21) 5.41(5.32) 1.78 1.90 28.55 28.68
aThe average value of final 20 rounds are shown in parentheses.

8H. QI ET AL.
Figure 2. Route-choice with pre-trip information (laboratory experiment results): the number of route
S choices, presented in blocks of 5 periods each, for both conditions (with and without FP information),
from Session 1 to Session 4, corresponding to (a), (b), (c) and (d), respectively.
the equilibrium value of 5 until the end of the sessions; (2) the equilibrium solution seems
perform better in accounting for the aggregate route choices in the final stage (around last
20 rounds) of each session than there in the initial stage, with an exception of Session 1;
and (3) the two information conditions do not differ significantly from each other.
Then, we conducted statistical analysis to further test against equilibrium prediction,
measured by the choice frequency of Sroute. Firstly, we conduced t-test on the session
averages of choice frequencies of route S(shown in Table 2) as independent data points,
and found significantly deviation from equilibrium prediction with 5 players on S(p<.05
for both conditions). Secondly, considering the potential learning process in the initial part
of experiment in each condition, as reported by many previous studies, one may wonder
that whether there is a long-term decreasing trend of the evolution of choice frequencies
of route Swith the increasing of round number. To this end, we picked a non-parametric
method known as Daniels’ test on moving averages (Meneguzzer and Olivieri 2013). For
each condition, a new series of choice frequency on Swas generated, where each item is the
average value of frequency in the same round across four sessions. We found that, in both
conditions, the negative values of ρwere statistically significant from zero, when the mov-
ing average was computed over 9 or larger time-step (Condition PI: ρ=−0.208, p=.040;
Condition FI: ρ=−0.206, p=.041). It means that the average preference of Sroad tends to
decrease over time, which suggests the possibility that equilibrium conditions might have
been approached over an appropriately extended time horizon. Thirdly, it is therefore worth
comparing the traffic flow distribution in final stage (20 rounds) of each session with equi-
librium predictions. We found that, in both Conditions PI and FI, choice frequencies of Sin

TRANSPORTMETRICA A: TRANSPORT SCIENCE 9
the final 20 rounds were no longer significantly different from the equilibrium predictions
at p<.05 (Condition PI: t(3) =2.781, p=.088; Condition FI: t(3) =2.4, p=.286).
In a word, in both conditions, although the session averages of traffic flow on route S
were significantly larger than equilibrium prediction, the values decreased over time to
approach to pure-strategy equilibrium state in the final stage approximately. However, the
day-to-day dynamics has not settled down until the end of the games.
3.2. Dierences between conditions
With the group as the statistic unit of analysis, we tested the null hypotheses that the
full pre-trip information does not affect the aggregated traffic flow distribution. Since
the same group of subjects participated in both the information regimes (i.e. repeated
measurements), the two samples of observations are not independent. Thus, we resorted
to non-parametric statistical hypothesis test method (Wilcoxon-signed-rank test) to com-
pare dependent samples and applied bootstrap method to expand the sample size. The
Wilcoxon-signed-rank test cannot reject the null hypothesis concerning mean choice of
route S(p>.9, two-tailed test); and the observed and predicted means in the two con-
ditions are not statistically different. The same result (confidence interval containing zero)
was obtained when the two conditions were compared to each other by Bootstrapping
with 10,000 samples drawn from all choices in each condition.
Although non-significant difference was observed, one may argue that players have
learned from their experience in the first Condition PI that diminishes the value of the infor-
mation. When subjects with an 80-round experience start to play games in the following
Condition FI, they are more likely to learn faster than people attending between-subject
design experiments without any prior experience about this network. Hence, it is supposed
to be easier to observe subjects approaching to equilibrium in the next condition. Recall
that subjects have already learned the equilibrium in the final stage of the first-played
Condition PI. If either of the above effects exists, the system variables in the first stage of
Condition FI are supposed to be very similar to those in the final stage of Condition PI.
However, significant differences between the ‘continued’ stages across different conditions
were observed (paired t-test, p<.05); thus, it seems to be a renewed learning process when
the second condition began.
Taken together, the findings regarding aggregated dynamics are as follows. Firstly, with
the existence of learning effects detected by a decreasing trend of choice frequency of S
route over time, the equilibrium solution seems perform better in accounting for the aggre-
gate route choices in the final stage of each session than there in the initial stage. Secondly,
however, the high degree of volatility persists until the end of games. Thirdly, the provision
of more feedback information regarding FPs seems to cause no significant differences in
traffic flow distribution and system cost at the aggregate level.
4. Individual response modes
The last section of this study was to test the pre-trip information effects on aggregated
dynamics using the pure-strategy equilibrium solution as a benchmark. Moreover, indi-
vidual response patterns to information provision are also critical for understanding the
group dynamics, since after all information processing and learning takes place on the

10 H. QI ET AL.
individual rather than aggregate level. In addition, potential response modes could not be
directly observed from experimental data but could be probed by mapping pre-trip infor-
mation provided to route switches explicitly observed. Thus, our major emphasis changes
to individual route-switching behaviour hereinafter.
This section begins with the analysis of sequential dependence (Section 4.1) to support
that both the last choice and last outcomes influence individual propensity to switch routes.
Based on this observation in Section 4.1, we design the measurement to capture the indi-
vidual differences in switching as a response to different previous outcomes in Section 4.2
and discuss behavioural basis of the typical response modes captured in Section 4.3. In the
end of this section, we revisit the comparison between two information conditions.
4.1. Sequential dependencies
Sequential dependencies arise in psychological experiments where individuals perform
a task repeatedly or need to take a series of tasks and one task trial may influence their
behaviour on subsequent trials (Mozer, Kinoshita, and Shettel 2007). In such a recur-
rent route-choice game like this study, it is reasonable to assume that last choices may
influence the route-switching propensity of this individual, along with last outcome her
encountered.
To test this assumption, firstly we calculated the proportions of players who switch from
Mto Sand the opposite separately in every round under each condition (around 80 rounds
per session ×4 sessions). Then, we divided all the data points regarding the switching pro-
portions from Mto Sinto several subgroups by the actual travel cost of route Min last round;
also, divided the ratio data points from StoMby the last travel cost on route S. According
to laws of large numbers, only the subgroups with more than 20 data points count in the
following analysis. Sequentially, we calculate the average value of each subgroup. Figure 3
plots the two trends of switching ratios with the increase of actual travel time on previous
routes, with a black dashed line indicating travel time in pure-strategy Nash equilibrium
state (28 minutes on route S).
Two major observations from Figure 3warrant mentioning. Firstly, for both trends, there
is an obviously increasing trend with the growth of the actual travel time during the last
round. On average, the higher travel cost they experiences in last round, the more propor-
tion of players switch away. In other words, under both conditions, there is at least 40%
possibility to hold their last choices regardless the realized travel time in last round. Sec-
ondly and interestingly, the switching proportions on route Mare consistently larger than
those on route S(paired t-test, p<.05) after subjects experiencing the same travel time on
the two routes. According to the cost functions of this experiment (Equation 1), since the
marginal cost of the change in traffic flow on route Sis one and a half times as that of route
M, it is easy to prove that the standard deviation of travel time on route Sshould theoret-
ically be one and a half times as that of route M. In fact, we did observe this relationship
in data. Thus, one of the possible reasons for the lower response strength on route Mmay
be that players might sense that the travel time on route Mvaries in a narrower range than
that on route Sby experience, as shown in Figure 4.
Taken together, under both conditions, the fraction of switches from Sto Mis more dra-
matic, than that of the other direction, after experiencing the same travel time on their
chosen route. Thus, the results support our assumption that both the last choice and last

TRANSPORTMETRICA A: TRANSPORT SCIENCE 11
Figure 3. The rate of route switches (two directions) from round tto round t+1 versus actual travel
time by information condition.
Figure 4. The frequency distribution diagram of travel time on both routes.
outcomes did influence individual response modes that manifested by switching behaviour
in this study.
4.2. Clustering analysis
Based on the observation that both last choice and last outcomes may influence individual
choices, we applied conditional probability to describe the propensity of an individual lto
select an alternative strategy, r’, given the actual payoff of her last strategy, r,andtheFPof

12 H. QI ET AL.
the alternative strategy, r’. Under both conditions, each player, l, is described by six pairs of
probabilities (three payoff scenarios ×two routes) as follows.
•cp
r=relative frequency of a changed subsequent decision if the actual payoff was lower
than the FP (p=−), or approximately equal to the FP (p=0) or higher than FP (p=+);
and rrepresents his/her last route choice, so r=Mor S.
•sp
r=relative frequency to stay with the previous decision if the payoff was lower than
the FP (p=−), or approximately equal to the FP (p=0) or higher than the FP (p=+);
and rrepresents his/her last route choice, so r=Mor S.
Before conducting clustering analysis based on these multiple conditional probabilities,
we need to make two adjustments of this measurement. First, in Condition PI, since the FPs
are not disclosed to subjects, we assume the FP on road requals to the latest actual payoff
on this road, if it has been chosen during the last t−1 rounds; otherwise, FP equals to zero.
This idea could track back to Cournot dynamics, where players weight only the most recent
observation since they think new information is more useful in forecasting what others will
do. Also, as noted by Iida, Akiyama, and Uchida (1992), Chang and Mahmassani (1988)have
suggested that the more recent experience has a substantially greater effect on travel time
prediction. Second, it is reasonable to assume that people have rare motivation to change
decisions when the payoffs are approximately equal between binary options. In fact, the
pure-strategy Nash equilibrium state (where the payoff difference between two routes is
smaller than 2) did seldom happen during the whole game (around 5%). And thus, we
believe the two pairs of probabilities conditional on Nash equilibrium just happened in last
round may contribute little to capture individual response modes. Taken together, Table 3
displays the definition and notation of four pairs of switching probabilities. Furthermore,
four parameters from each of the four pairs of the probabilities could capture individual
response characteristics, i.e. c−
S,s+
M,c−
M,s+
S, since each pair of them sum up to 1.
According to this measurement, every individual owns a configuration of these four
parameters. Heterogeneous players are therefore expected to distribute in the four-
dimensional parameter space. Moreover, individuals holding a similar response mode
should aggregate closely to each other, while far away from other aggregations of differ-
ent response modes. One possibility to find typical response modes is to abstract these
naturally aggregated subgroups. Thus, we select the k-mean clustering method that has
advantage of finding kcentral vectors based on the natural dispersion of individual objects
and represent each cluster of objects assigned to their nearest centres by the kcentres
(Hartigan and Wong 1979; Teknomo 2006).
Tab le 3 . The 2 ×2 table for the definition of individual route-switching conditional probabilities
from tround to t+1round.
Last payoff contrasted situation
P (change or stay)
given the event
Condition PI Condition FI Last choice change stay
Actual payoff <the last actual payoff
on the unchosen choice
Actual payoff <FP on Mc
−
Ms−
M
on Sc
−
Ss−
S
Actual payoff >the last actual payoff
on the unchosen choice payoff
Actual payoff >FP on Mc
+
Ms+
M
on Sc
+
Ss+
S

TRANSPORTMETRICA A: TRANSPORT SCIENCE 13
Clustering analysis is conducted among 59 individuals in Condition PI and 58 individuals
in Condition FI, except for a small proportion of subjects who rarely choose Route Sor M
throughout the duration of an entire condition and thereby cannot be captured by valid
probabilities. After normalizing the data by the method suggested by Milligan and Cooper
(1988), we employ the iterative refinement approach by Caliński and Harabasz (1974)toget
the optimal clustering number, k. The stopping rule of the k-mean clustering is to minimize
the ratio of Intra-Cluster Distance (Milligan and Cooper 1985) to the Inter-Cluster Distances.
Hence, we get k=3 for Condition PI, k=4 for Condition FI, and then conduct k-mean
clustering in the four-dimensional parameter space using SPSS Statistics software.
The clustering results under the two information regimes were presented in Tables 4
and 5, respectively. Each cluster differs remarkably from each other in the four dimen-
sions while parameter configurations within a cluster are close to one another, therefore
implying that subjects from the same cluster share the similar response mode. Thus, the
average behaviour or the mean values of probabilities for each cluster generally represent
the response patterns of the entire cluster.
Note that this method to locate individuals in a four-parameter space has advantage of
embodying classic theories including direct and contrary response proposed by Selten et al.
(2007). For direct-response players, the worse the obtained payoff was, the more probably
a road change would happen, whereas the contrary-response ones behaved on the con-
trary. That means if an individual’s four probabilities are very close to (1, 1, 1, 1), it is very
Tab le 4 . Cluster analysis results using individual-level observations in Condition PI.
Mean characteristic observations (Std. Dev.)
M-dominant scenario S-dominant scenario
Type name Number of subjects Ratio of subjectsa(%) c−
Ss+
Mc−
Ms+
S
Type 1 24 37 0.55 0.68 0.58 0.72
(0.25) (0.21) (0.26) (0.17)
Type 2 9 22b0.33 0.35 0.37 0.18
(0.13) (0.22) (0.18) (0.13)
Type 3 26 41 0.75 0.83 0.29 0.34
(0.19) (0.10) (0.19) (0.24)
aNote that the ratio is the outcome of the number of a specific type divided by the total number 64 persons.
bThis ratio is the outcome of the sum of 9 and 5 then divided by 64.
Tab le 5 . Cluster analysis results using individual-level observations in Condition FI.
Mean characteristic observations (Std. Dev.)
M-dominant scenario S-dominant scenario
Type Name Number of subjects Ratio of subjectsac−
Ss+
Mc−
Ms+
S
Type 1 12 19% 0.63 0.86 0.65 0.85
(0.11) (0.06) (0.13) (0.17)
Type 2 12 28%b0.37 0.43 0.40 0.44
(0.15) (0.12) (0.13) (0.16)
Type 3 18 28% 0.67 0.79 0.21 0.20
(0.16) (0.10) (0.11) (0.18)
Type 4 16 25% 0.39 0.85 0.22 0.88
(0.19) (0.10) (0.15) (0.13)
aNote that the ratio is the outcome of the number of a specific type divided by the total number 64 persons.
bThis ratio is the outcome of the sum of 12 and 6 then divided by 64.

14 H. QI ET AL.
Tab le 6 . Summaries the extreme examples of response mode categories
based on the four conditional probabilities.
When Mis dominant When Sis dominant
Response mode categories c−
Ss+
Mc−
Ms+
S
Direct response 1 1 1 1
Contrary response 0 0 0 0
Always stay on M1100
Always stay on S0011
Status-quo-maintenance 0 1 0 1
likely that this player hold the direct-response mode. In additions, if an individual tends
to be strongly preferring a specific route more than actively responding to new informa-
tion, the values of her first pair of probabilities are supposed to be much different from
the values of her second pair of probabilities. Moreover, this presentation method makes it
possible to distinguish whether an individual has strong inertia in maintaining status quo
(sticking on the previous route choice), by observing its distance from the benchmark point
(0, 1, 0, 1). In Table 6, we demonstrate the above special cases of response modes with their
corresponding probability configuration.
4.3. Interpretation of each type
To give the interpretations of these types in Tables 4and 5, we firstly assume the cluster
centres as their representations and then regard their closest special cases (in Table 6)that
have well-defined behavioural basis as the corresponding benchmarks. As for determining
which case could be served as the baseline model for a specific cluster, we pick the one
whose extreme point has smallest Euclidean distance from the cluster centre. This method
to put interpretations of clusters by comparing their centres to their closest special cases
in a multiple-dimension space derives from classic experimental studies like Ho, Wang, and
Camerer (2008).
Tables 4and 5show that the first three clusters in both conditions could be regarded as
response rules with a baseline model of Direct Response (all four parameters are equal to 1),
Contrary Response (all parameters are equal to 0) and Highly-Risk-Averse (always staying
with Route M), respectively. Therefore, these three clusters are termed as Direct-response-
like, Contrary-response-like and Highly-risk-averse-like patterns. In addition, another cluster
(closest to (0, 1, 0, 1)) only emerges in Condition FI, defined as the Status-quo-maintenance
Category.
The interpretation of each type is as follows. Note that we put interpretations of these
types based on their explicitly observed behavioural tendency, but we will discuss several
potential behavioural bases of each of them.
(1) Type 1 and 2: Highly responsive categories to new information
Type 1 subjects with Direct-response-like patterns seem to change her road after hav-
ing a bad payoff on last choice in order to travel where it is less crowded. The worse the
payoff was, the more probable is a road change. In contrast, for Contrary-response-like
Type 2 players, the better the payoff was on the last-chosen road, the more likely they
shifted from this road. They could be regarded as ‘forward-looking’ players holding a more

TRANSPORTMETRICA A: TRANSPORT SCIENCE 15
‘sophisticated’ strategy than the Type 1. Based on an anticipated belief that most others
may choose the currently dominant route after observing its higher payoffs and result in a
congestion on it, they are more likely to give up the currently higher-paid choice.
In terms of similarities between these two types, they were both actively responsive ones
to information regarding payoffs in last round, and did not show strong preferences on
a specific route. Two potential explanations for Type 1 players are Reinforcement Learn-
ing theory (Macy and Flache 2002; Roth and Erev 1995) and win-stay-lose-shift strategy
(Nowak and Sigmund 1993). Their own choices that led to satisfactory outcomes in the
past tend to be repeated in the future, while choices that led to unsatisfactory experiences
are avoided. Moreover, the existence of Type 2 players suggests this proportion of players
made decisions based on the reflections or predictions on others’ possible choices, which
generally verifies the validity of level-ktheory and Cognitive Hierarchy theory in such a
route-choice game.
(2) Type 3: Highly-risk-averse-like Category
The first two probabilities under the M-dominant scenario (both near 1) are dramatically
higher than the last two (close to 0) in the S-dominant scenario, therefore implying that
they formed a strong preference for Route M,comparedtoRouteS. Thus, we supplement
the very few players who chose Route Mall the time and were set aside before clustering
analysis (five players in Condition PI and six players in Condition FI) into this category. One
could also describe them as fast learners who rapidly formed a ‘habit’ and converge onto a
certain strategy, and then locked on to it as a long-term strategy, regardless of the changing
payoff levels.
We found very rare players preferring Road S, which may be reasonable, since the travel
time on Route Mhas lower variation and less extreme bad payoffs than that on the other
as shown in Figure 4. For Type 3 people, they may recognize this feature from experience
and information, so they occasionally depart from the preferred Route Mto occasionally
seek higher payoffs but return immediately after a switch, rarely sticking on Route Sfor a
few periods. Meanwhile, based on the above reason, we term it as Highly-risk-averse-like
players.
As for the potential behavioural mechanisms for this type, we separately analyse two
information conditions. In Condition PI, the ‘hot stove’ effect (Denrell and March 2001)may
offer an explanation of this type of response modes. Ben-Elia, Erev and Shiftan (2008)experi-
mental supports of this pattern, that is, when the feedback available to the decision makers
is limited to their obtained payoff, experience reduces the tendency to select risky (high
variance) alternatives. This pattern is a natural consequence of the inherent asymmetry
between the effect of good and bad experiences.
Under Condition FI, both actual payoffs and FPs of their non-chosen alternatives were
informed, which may trigger regret-based reasoning of part of subjects (Ben-Elia, Robert,
and Shiftan 2013;Chorus2012a,2012b). This type of subjects are more likely to minimize
their regret values but do not necessarily minimize travel time (Li and Huang 2017). Also,
anticipated regret is found to play an important role in those choices (e.g. Ben-Elia, Robert,
and Shiftan 2013; Mak, Gisches, and Rapoport 2015). On an anticipated belief that choosing
Route Swould be more probable to experience large level of regret than Road M,this
subgroup of people tend to remain with Route Malmost all the time.

16 H. QI ET AL.
(3) Type 4: Status-quo-maintenance Category
Interestingly, we have found strong support of the existence of the Status-quo-
maintenance Category of players but only under Condition FI. Like Type 3, these players
are seldom influenced by minor payoff differences between two routes in previous round;
however, unlike Type 3, they do not quickly form a strong preference/habit for a particular
route. More specifically, the Status-quo-maintenance players tend to stay with the alterna-
tive that they have previously chosen until another alternative provides sufficiently higher
utility to warrant a switch, and then they would stick on the new ‘status quo’ choice for
another stage. Once they make a choice, it seems to be not easy to change their mind. In
other words, while other types of players consider which route to choose, this type of player
would seem to think about when to change.
Interpretations for the motivations behind such behaviour pattern are multiple, as sum-
marised by Zhang and Yang (2015) and Xie and Liu (2014). It could because of a satisfaction
level being achieved, which could be quantified by the ‘indifference band’ (Hu and Mah-
massani 1997). It is also framed as the ‘effort-accuracy trade-offs’, reflecting the hope to
save energy in cognitive thinking (Chorus and Dellaert 2012). It may also result from strate-
gic thinking that they decide to stay on the same route no matter experiencing good or bad
payoffs on it, assuming that other people will switch in some way and lead my choice to be
less crowed.
4.4. Dierences between conditions
Next, we focus on how the behavioural types change with more feedback information avail-
able in Condition FI. Notice that we aim to abstract typical response patterns, rather than
classify ‘individuals’. More specifically, we compare how the proportion of each type change
under two conditions (Tables 4and 5), instead of tracking how every individual’s response
modes evolve.
Firstly, Direct-response-like and Contrary-response-like response modes account for less
proportion of all players (dropping from 59% to 47%), especially for the Direct-response-like
category (from 37% to 19%). Also, the proportion of players adopting the Highly-risk-
averse-like pattern shrinks by 13%. These imply that less people are highly responsive
to new information or form a routine choice during the games. More interestingly, the
Status-quo-maintenance category emerges and accounts for as more as a quarter of the
population in Condition FI. Thirdly, these two types of unresponsive players constitute
more than 50% of the population when full-feedback information available. Note that both
Highly-risk-averse-like and Status-quo-maintenance players could be regarded as inertia
players, who tend to be reluctant in adjustment of status quo, but with different degree of
this reluctance, according to the definition by Zhang and Yang (2015). They simply defined
route choice inertia in a transportation network as ‘decision maker repeatedly choosing
the same alternatives, sticking to unique or some fixed choices, having regular and stable
response patterns’.
It is interesting to observe status-quo-maintenance mode accounting for much larger
proportion in full-information condition than in Condition PI. One explanation is that with
little information, people have much higher need to switch between routes to gather more
information. Moreover, the existence of status-quo-maintenance mode, along with the

TRANSPORTMETRICA A: TRANSPORT SCIENCE 17
decreasing number of Highly-risk-averse-like pattern, could provide us with some insights
about the counterintuitive finding in Section 3.2. It was a common conviction that more
pre-trip information about route conditions is likely to reduce travel time uncertainty and
thereby speed up the learning process and induce the aggregated converging towards
equilibrium state. However, recent experiments including this work fail to find significant
difference that full-feedback information causes on aggregated dynamics, in terms of either
traffic flow distribution or average network cost. More information is provided to reduce
uncertainties regarding travel time, but it turns out to be less people responsive to the
prevailing conditions conveyed by new information or firmly committing themselves to
a unique route.
5. Conclusion and discussion
Inspired by Selten et al. (2007), we conducted a route-choice game with two parallel net-
works under strategic uncertainty but using within-subject design. Different from most
previous experiments focus on aggregated analysis, the main purpose of this paper is the
in-depth analysis on individual response modes under two information conditions. To this
end, we opted for a within- rather than between-subject design to exploit its advantages
by controlling individual differences in personality across different information regimes. A
total of 64 undergraduates participated in four groups of experiments, with each consisting
of 16 subjects interacting for more than 80 consecutive rounds. The same group of players
were exposed to PI regarding actual travel time in Condition PI, and then to full-feedback
information regarding actual and forgone payoffs in Condition FI.
To capture individual response modes from experiment data, we first observed two fac-
tors that may influence subjects’ switching behaviour, that is, both last payoffs and last
choices, which indicates the existence of sequential dependencies; then applied condi-
tional probability to distinguish the route-switching propensity of an individual given the
prevailing situations in last round. On basis of this measurement in four-parameter space,
we conducted clustering analysis to abstract the natural aggregations of individual data.
Almost 60 subjects were clustered into three and four subgroups under Condition PI and
Condition FI, respectively.
Results of clustering analysis show highly responsive and unresponsive individuals coex-
ist within a population under both conditions. Direct-response-like and Contrary-response-
like players pay attention to new feedback information regarding last outcomes, omit
forming a routine, and quickly adapt their behaviour to the prevailing conditions round
after round. However, Highly-risk-averse-like players quickly form a routine that stick on
Route Mwith the lower risky travel time level than the other, and Status-quo-maintenance
players tend to maintain their previous choice but fail to settle down on a routine choice till
the end of the games.
More provision of pre-trip information does change the distribution of individual
response types, although it seems to cause non-significant difference in aggregated
dynamics. With full-feedback information, the proportion of responsive players (adopting
Direct-response-like and Contrary-response-like modes) and Highly-risk-averse-like players
drops by 12% and 13%, respectively, while the Status-quo-maintenance Category emerges.
Put in another way, two types of unresponsive players constitute more than 50% of the pop-
ulation when full-feedback information available. It is believed that the provision of more

18 H. QI ET AL.
feedback information could boost learning process and thereby induce converge towards
equilibrium. However, it turns out to be less people highly responsive to the prevailing
conditions conveyed by new information or firmly committing themselves to a unique
route. The findings in response modes could offer an explanation of the counter-intuition
between common conviction and the observation at the aggregated level.
Our study is potentially valuable for capturing individual route-choice behaviour and
network traffic dynamics, which plays a critical role in transportation planning and further
developments of the ATIS. However, indeed, this study is the first step in a planned series
of work, and thus is concerned only with the simplest cases. A limitation of the current
study is the lack of direct data on the socio-demographic characteristic of subjects.Afur-
ther possibility is to carry out risk-attitude surveys at the beginning of each session. Another
limitation is that we did not put emphasis on the choice behaviour when equilibrium state
has been approximated achieved. The previous research by Bifulco, Di Pace, and Viti (2014)
just focused on that in equilibrium conditions and discussed the difference between infor-
mation compliance and concordance, which interested readers may refer to. In addition, an
investigation is warranted as to whether present research conclusions can be extended to
more complex traffic networks or combined uncertainty sources.
Acknowledgement
We wish to thank the participants in our experiments at Tianjin University.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
The research reported in this paper was supported by the National Natural Science Foundation of
China [grant numbers 71571132, 71431005 and 71701078] and National Science Foundation of the
Ministry of Education of China [grant number 17YJC630150].
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