Warlord Competition

Abstract

Warlords compete for turf that provides them with rents and 'taxable' resources, but they can also offer a semblance of security within their respective territories. This article first examines two economic models of warlord competition. Because such competition takes place through the use of force or the threat of the use of force, more competition typically leads to lower material welfare as resources are wasted on unproductive arming and fighting. This is in contrast to ordinary economic models, in which typically greater competition leads to higher material welfare. Furthermore, rents from oil, diamonds, and even foreign aid crowd out production. In extreme cases, this crowding out of ordinary production can be complete, whereby all economic resources can be devoted to the unproductive competition for rents. The article then reviews factors that lead either to actual war or to peace in the shadow of war. Because war is destructive, human beings are typically risk averse, and there exist numerous complementarities in production and consumption, we can expect peace in the shadow of war to be most often preferable by all parties. Actual war can take place because of incomplete information about the preferences and capabilities of the adversaries but also, somewhat surprisingly, when the shadow of the future is sufficiently long.

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Copyright ã UNU/WIDER 2001
* Department of Economics, University of California, Irvine.
This study has been prepared within the UNU/WIDER project on Why Some Countries Avoid Conflict
While Others Fail, which is co-directed by Dr Tony Addison and Dr Mansoob Murshed.
Discussion Paper No. 2001/54
Warlord Competition
Stergios Skaperdas*
August 2001
Abstract
Warlords compete for turf that provides them with rents and ‘taxable’ resources but they
can also offer a semblance of security within their respective territories. This article first
examines two economic models of warlord competition. Because such competition
takes place through the use of force or the threat of the use of force, more competition
typically leads to lower material welfare as resources are wasted on unproductive
arming and fighting. This is in contrast to ordinary economic models, in which typically
greater competition leads to higher material welfare. Furthermore, rents from oil,
diamonds, and even foreign aid crowd out production. In extreme cases this crowding
out of ordinary production can be complete, whereby all economic resources can be
devoted to the unproductive competition for rents. The article then reviews factors that
lead either to actual war or to peace in the shadow of war. Because war is destrucrive,
human beings are typically risk averse, and there exist numerous complementarities in
production and consumption, we can expect peace in the shadow of war to be most
often preferable by all parties. Actual war can take place because of incomplete
information about the preferences and capabilities of the adversaries but also, somewhat
surprisingly, when the shadow of the future is long.
Keywords: warlord competition, conflict, cooperative and non-cooperative behaviour
JEL classification: C71, C72, O17

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Warlord Competition*
STERGIOS SKAPERDAS
Department of Economics, University of California, Irvine
Abstract: Warlords compete for turf that provides them with rents and
’taxable’ resources but they can also o¤er a semblance of security within
their respective territories. This article …rst examines two economic models
of warlord competition. Because such competition takes place through the
use of force or the threat of the use of force, more competition typically leads
to lower material welfare as resources are wastedon unproductive arming and
…ghting. This is in contrast to ordinary economic models, in which typically
greater competition leads to higher material welfare. Furthermore, rents
from oil, diamonds, and even foreign aid crowd out production. In extreme
cases this crowding out of ordinary production can be complete, whereby all
economic resources can be devoted tothe unproductive competition for rents.
The article then reviews factors that lead either to actual war or to peace in
the shadow of war. Because war is destrucrive, human beings are typically
risk averse, and there exist numerous complementarities in production and
consumption, we can expect peace in the shadow of war to be most often
preferable by all parties. Actual war can take place because of incomplete
information about the preferences andcapabilities of the adversaries but also,
somewhat surprisingly, when the shadow of the future is long.
*Presented at the workshop on ’why some countries avoid con‡ict while
others fail;’ held at, and sponsored by, the World Institute for Development
Economics Research (WIDER), United Nations University, Helsinki, 20-21
October, 2000. I would like to thank Halvor Mehlum, Mansoob Murshed,
other workshop participants, and three referees for their helpful comments.
1

1 Introduction
From the earliest recorded wars in history to the present, con‡ict has been
taking place between hierarchically organized groups with emperors, kings,
lords or generals at the top and common foot soldiers at the bottom. Nowa-
days, in many countries from Colombia, to Somalia, to the northern parts
of Afghanistan broad swaths of territory are outside the e¤ective control of
central governments - if those exist at all - and contested by rival groups, typ-
ically headed by what we could fairly characterize as warlords. By linguistic
convention, such con‡ict constitutes competition, and that competition has
at least some economic objectives. Evaluating con‡ict as competition from
an economic perspective is not a simple matter, however, for we cannot
blindly apply the received economic models without running into problems.
Is a greater number of competitors, for example, a good thing when there
is con‡ict as it is taken to be in the case of ordinary competing business
…rms? With more competitors we would expect more …ghting and resource
waste, less predictability, and greater di¢culties in communication, negoti-
ation, and settlement. Therefore, intuitively at least, it appears that the
answer to the question just posed above cannot be ’yes’ – more competition
can be expected to lead to a worse outcome.
To make sense of this and other related peculiarities of what we call
in this paper ”warlord competition”, we need a model di¤erent from the
model of ordinary …rms competing on priceandpossibly onother dimensions.
Warlords instead compete over rents - oil, diamonds, drugs, foreign aid - as
well as over ’taxation’ of their subjects by being su¢ciently strong to deter
and, if necessarily, …ght their competitors. We …rst examine two types of
competition, one which is localized and another which is more generalized.
We…ndthatrents, byincreasingtheintensityofcompetitionamong warlords,
’crowd out’ some of the production under both types of competition. The
crowding-out e¤ect though is higher under generalized competition and in
some circumstances it can be nearly complete. There are even cases under
which all the productive resources and population are diverted toward the
unproductive competition for rents.
We then examine the incentives warlords face for going to war compared
to those for engaging in ’armed peace’, whereby they negotiate and settle
under the threat of going to war. Factors that favor armed peace include the
degree to which war is destructive, the risk aversion of the warlords, and how
complementaryorinterdependentisthe contestedsurplus withothergoodsor
2

services. War can be induced by thefactors thathave beenwidelynoted - like
misperceptions, misunderstandings, absence of communication channels - as
well as by characteristic that is normally considered to promote cooperation,
not con‡ict: a long value attached to the future by the adversaries.
2 Two Kinds of Competition
Consider an area - district, country, or even more than one country - in
which the state is weak or non-existent. In the face of rampant insecurity,
individual producers are’protected’ by warlords. Inreturn, warlords receive a
…xed share ® 2 (0;1) of each producer’s output, which for simplicity we take
to be equal to unity. For brevity and analytical convenience we do not model
explicitly here how warlords protect producers from individuals robbers or
bandits. The interested reader is instead referred to Konrad and Skaperdas
(1999) or Skaperdas (2001) in which a is derived from the maximizing choices
of producers and warlords – brie‡y, producers take costly actions to reduce
the size of that share, whereas warlords also devote resources to increase the
same share. We denote the number of producers by P. Therefore, the total
output received by warlords from producers is aP:
In addition to producers, the area under consideration has additional
rents that can have di¤erent sources: natural resources like oil, gas, timber,
or diamonds as well as cash, loans, and in-kind contributions from foreign
governments, international organizations, NGOs, or foreign diasporas.
1
Let
the net size of these rents available to warlords be T.
The L warlords compete for these rents and the surplus extracted from
producers through force or the threat of the use of force. Force is determined
by the number of warriors hired by each warlord at a resource cost ¯ 2 (0;1).
Competition is modeled as a contest (e.g., Tullock, 1980; Dixit, 1987) as it
also has been done in models of con‡ict (e.g., Hirshleifer; 1988; Grossman,
1991; Skaperdas, 1992). With more than two warlords, though, there is
not a single way of modeling competition between them. We shall therefore
examine two di¤erent types of competition: one that is more localized and
the other one being closer to free-for-all.
1
These outside forces could also directly subsidize the cost of …ghting and therefore
in‡uence warlord competition in other ways. The role of diasporas has been emphasized
by Collier & Hoe-er (2001).
3

2.1 Localized Competition
Because of geography, transportation di¢culties, and communication costs,
warlords possibly could extend their range and pose challenges to those in
their immediate vicinity only. To capture that characteristic of limited range,
suppose the warlords are equally spaced around a circle. The neighbors of
warlord l = 2;:::;L ¡ 1 are warlords l ¡ 1 and l + 1; warlords 1 and L have
one another as neighbors as well as, respectively, 2 and L ¡ 1.
The rents and other output are evenly distributed around the circle and
there is thus a surplus of size
T+®P
L
available for distribution among any
particular pair of warlords. Each warlord can contest the surplus to either of
his sides and can hire warriors who are dedicated to guarding either the left
or right ’border’. That is, warlord l can hire w
l
l¡1
warriors to contest the
surplus on the side of warlord l ¡1 and w
l
l+1
warriors on the side of warlord
l + 1. The share of the surplus goes to warlord l when challenging warlord
l ¡ 1 is determined by a ’contest success function’ that equals:
2
w
l
l¡1
w
l
l¡1
+ w
l¡1
l
(1)
All warlords are risk neutral and theirpayo¤ functions canthus be de…ned
as follows:
V
l
¸
=
w
l
l¡1
w
l
l¡1
+ w
l¡1
l
T + ®P
L
¡¯w
l
l¡1
+
w
l
l+1
w
l
l+1
+ w
l+1
l
T + ®P
L
¡¯w
l
l+1
= (
w
l
l¡1
w
l
l¡1
+ w
l¡1
l
+
w
l
l+1
w
l
l+1
+ w
l+1
l
)
T + ®P
L
¡ ¯(w
l
l¡1
+ w
l
l+1
) (2)
Because of risk neutrality and the absence of other complications, there
is no di¤erence between assuming that
w
l
l¡1
w
l
l¡1
+w
l¡1
l
represents the share of the
local surplus received by warlord l in competition with warlord l ¡ 1 or the
probability of winning the same surplus. Later we shall discuss instances in
which settling under the threat of going to war leads to di¤erent outcomes
2
This is the functional form employed by Tullock (1980) for rent-seeking contests.
Hirshleifer (1989) hasdiscussed itsproperties andSkaperdas(1996)has providedaxiomatic
derivation of this and other functional forms.
4

than the one in which actual war takes place and, importantly, why actual
war or settlement under its threat would take place.
All warlords choose the number of warriors they allocate to each of their
two borders non-cooperatively, so that these choices form a Nash equilib-
rium. It can be shown that a symmetric equilibrium exists, whereby every
warlord chooses to deploy the following number of warriors against each of
his neighbors:
w
¸
=
T + ®P
4¯L
(3)
Consistently with intuition, the number of warriors deployed is positively
– actually, linearly – related to the surplus available between neighboring
warlords,
T+®P
L
; and negatively related to the cost of hiring warriors (¯). By
substituting w
¸
into the warlord’s payo¤ function, we obtain the equilibrium
pro…t of a warlord:
V
¸
=
T + ®P
2L
(4)
Even though this pro…t decreases as the number of warlords increases,
the total pro…t by summing up over all warlords equals LV
¸
=
T+®P
2
and is
therefore independent of the number of warlords. Given, then, the functional
forms we have assumed, half of the total surplus is taken as pro…t by warlords
whereas the remainder becomes dissipated in the hiring of warriors.
3
The warriors and warlords do not add anything to production - they both
play a parasitic role in the economy by competing for the appropriation of
the surplus. Whereas in the short-run production is given, in the long-run
we could expect it to respond to the level of appropriation. A major way in
which production is determined in our context is simply by the number of
individuals who decide to become producers. The other option is to become
a warrior. (For simplicity, we ignore the possibility of warlords coming from
the same population). Let N denote the total number of individuals in the
3
Of course, there is no signi…cance to having the surplus exactly split between warlords
and warriors. This property is a consequence of our speci…c assumption on the contest
success function, and other functional forms would yield di¤erent splits, which would have
a similar qualitatitive interpretation.
5

area under consideration and W the total number of warriors. The producers
and warriors exhaust the population so that:
N = P + W (5)
For individuals who reside in the area to choose to become warriors, they
wouldlike to have anincomeat least ashigh as thatof producers, whichas we
have seen equals 1 ¡®. Therefore, the cost of hiring warriors from the area,
¯, must equal or be higher than 1 ¡®. By (3), the total number of warriors
under localized competition is W
¸
= 2Lw
¸
=
T+®P
2¯
. By substituting this
quantity in (5), we can …nd the induced number of producers under localized
competition:
P
¸
=
2¯
2¯ + ®
N ¡
1
2¯ + ®
T (6)
Total production, by the choice of units we have made, also equals P
¸
:
Note how the presence of higher rents, T, induces lower production. This oc-
curs because higher rents induce a greater level of appropriative competition
which in turn induces the hiring of a greater number of warriors that have
to come from the ranks of producers.
The total ’income’ of the area, however, should include the rents and
would equal:
T + P
¸
=
2¯
2¯ + ®
N +
2¯ + ® ¡1
2¯ + ®
T (7)
Income increases as rents increase, but less than the increase in rents
because of the reduction in production induced by the higher rents.
2.2 Generalized Competition
The model we have just examined has many idealized properties. Rents and
production are not typically uniformly distributed across areas. Mineral
wealth is often concentrated in one area and much economic activity is to be
found agglomerated in geographically small areas. This characteristic and
the ease of communication and movement make plausible that those who, in
6

the absence of su¢cient restraints, contest the rents and output of a given
area do so as a whole, and not just some small subset of it that is determined
by the accidents of geography. We will therefore examine now a model in
which all warlords compete for all the surplus that is available in a ’free-for-
all’. Whereas this type of competition is in some ways the other extreme of
the localized competition we have already analyzed, and is thus inevitably
unrealistic, our objective is to determine how our …ndings change with the
di¤erent assumptions. We can then be more con…dent for the results that
do not change and we will have good reason to attribute the results that do
change to the type of competition that takes place.
Each warlord, l; now chooses a number of warriors, w
l
, that is not aimed
against his neighbors but against all other lords. The share of the surplus
received by that warlord is determined by the higher dimensional analogue
to (1):
w
l
§
L
j=1
w
j
where L > 1 (8)
The payo¤ function of warlord l under generalized competition then be-
comes the following:
V
l
g
=
w
l
§
L
j=1
w
j
(T + ®P) ¡¯w
l
(9)
Again, as withthe case of localized competition, because of riskneutrality
and other assumptions,
w
l
§
L
j=1
w
j
can be interpreted as a share or as probability
of winning the total surplus. The Nash equilibrium choices of warriors and
the induced equilibrium payo¤ of a warlord are:
w
g
=
(L ¡1)(T + ®P)
¯L
2
(10)
V
g
=
T + ®P
L
2
(11)
Each warlord hires more warriors now, provided that L > 2: Note how
the payo¤ of a warlord is inversely related to the square of the number of
7

warlords. Thus, contrary to the case of localized competition, the total
pro…ts of warlords, LV
g
=
T+®P
L
, vary inversely with their number - the more
warlords there are, the more intense the competition among them becomes
and the lower the total pro…ts are.
To determine the number of producers we follow the same method we
employed in the case localized competition. The total number of warriors
under generalized competition is W
g
= Lw
g
=
(L¡1)(T+®P)
¯L
, and the substitu-
tion of this number in (5) and rearrangement yields the number of producers
(as well as of total output):
P
g
=
¯L
(® + ¯)L ¡®
N ¡
L¡1
(® + ¯)L ¡®
T (12)
In the absence of any rents (T = 0) and with more than two warlords,
it can be shown that the number of producers in (12) is lower than those
under localized competition in (6). As with localized competition, output is
decreasing in the size of the rents
_
T. However, contrary to that other case,
production depends on the number of warlords. For a large enough number
of lords (and, for example, when ¯ = 1 ¡ ®), the reduction in output as a
result of a given increase in rents is almost the same as the increase in rents
itself! Competition is more intense here and any increase in the rents induces
a considerably greater demand for warriors who have to come out of the ranks
of potential producers. Total ’income’ can be similarly calculated by adding
the value of the rents to the output in (12). The addition of even large rents
can have a negligible e¤ect on income by the aforementioned reduction in
output that they can induce.
4
Equation (12) has been derived on the assumption that the number of
producers is positive. In fact, when the rents are high enough it is possible
to have the whole population turn into warriors with no one becoming a
producer. When ¯ = 1 ¡ ®; that occurs when N <
L¡1
(1¡a)L
T: Hence, when
rents are high enough relative to the population, there may be no production.
Finally, it should be noted that the number of warlords should be en-
dogenous in the long-run. Whereas under localized competition that number
does not a¤ect production, under generalizedcompetition by (12) production
4
Parenthetically, the property we have just noted could provide the basis of an alterna-
tive explanation of the ’Dutch disease’, the commonly noted tendency of some countries
becoming poorer following the exploitation of a newly discovered resource like oil.
8

depends on the number of warlords.
5
Overall, there are several di¤erences between the types of warlord com-
petition: First, generalized competition is more intense, as measured by the
resources devoted to capturing the surplus. Second, production is lower un-
der generalized competition. Third, the presence of rents under localized
competition discourages production less than it does under generalized com-
petition; that is, ’crowding out’ of ordinary production by rents take place
in under both kinds of competition but it is higher under generalized com-
petition.
2.3 External Intervention
We shall now brie‡y interject a note on the e¤ects of external intervention,
the participation of players in con‡ict who would be considered outsiders
by the other parties in the con‡ict. In the current turmoil in the Congo,
for example, almost every country from Uganda in the north to Zimbambwe
in the south appears to be involved to a lesser or greater extent either in
support of Kabila’s government or with the forces opposing him. Similarly,
in Afghanistan all the neighboring countries, as well as more distant ones,
have at one time or another participated on the side of some of the evolving
parties to the long civil war there. These are by no means the only examples
of con‡ict that have drawn some form of external intervention; it is the rule
rather than the exception.
Within the framework we have just examined the generalized kind of
competition wouldperhaps be more appropriate. Onee¤ectof outsideparties
wouldworkthrough thesubsidizationofsomeof the contestants, or simply by
becoming one of the contestants themselves. In either case the e¤ect would
be to increase the resources devoted to capturing the surplus and therefore
to increase the intensity of con‡ict
There is, however, another type of external intervention, by those who, by
circumstance, interest, or even altruism, contribute to the increase in rents
in the a¤ected area. Foreign investments in natural resource extraction and
various forms of foreign aid, including possibly humanitarian, contribute to
5
We could determine that number by equating the warlord’s equilibrium payo¤ in (11)
to a ’…xedcost’ of entry intothe business of war; the resultant equationalong withequation
(12) would determine the number of warlords and the number of producers as functions
of
9

the rents contested by the di¤erent warlords and therefore increase the inten-
sity of con‡ict. Moreover, such externally generated rents crowd out some
domestic production, and especially in the case of generalized competition
crowding out can be nearly complete.
External forces can of course play another, more positive, role by facili-
tating con‡ict management and cooperation, an issue to which we now turn.
3 Why not Cooperate?
In both models we have examined, there is no e¤ective distinction between,
on the one hand, actual, overt con‡ict according to which one side emerges
as winner and the others are defeated and, on the other hand, the condition
of ’armed peace’ or ’armed cooperation’, whereby the warlords divide up the
rents under the threat of overt con‡ict.
6
In general, we can expect, overt
con‡ict and armed peace to have di¤erent welfare consequences. We will now
…rst examine the forces that generate a di¤erence between overt con‡ict and
armed peace and then discuss why, despite the seeming superiority of armed
peace over overt con‡ict, we observe so much overt con‡ict. At the end of
the section, we will brie‡y discuss how institutions of con‡ict management
and peace could emerge to mediate disputes between warlords.
3.1 Overt Con‡ict versus Armed Peace
Forsimplicityof presentation,suppose therearejusttwowarlords. Then, the
two types of competition lead to the same payo¤ functions and equilibrium.
In addition, suppose the two warlords choose …rst their respective number
of warriors and then they have the option of either inducing overt con‡ict
or negotiating and settling under the threat of con‡ict. If both were to
choose negotiation, then they would settle in an armed peace; otherwise,
overt con‡ict would occur. We are interested in what occurs in this second
phase - whether and under what circumstances, once they have chosen their
warriors, the two sides would negotiate and settle. As we shall next see there
are several seemingly compelling reasons for not engaging in overt con‡ict.
The question that might be raised, however, is: If the warlords can ne-
gotiate and make binding agreements on other things, why can’t they make
6
I would like to thank Jack Hirshleifer for having suggested in conversation the term
’armed peace’.
10

binding agreements on the number of warriors and thus disarm? The prob-
lem with making a contract on the number of warriors is that such a contract
would need warriors to be enforceable – there is no higher authority over the
warlords – and, therefore, would not be binding. With warriors at hand,
though, each side would have the force, the ’threat’, to make a contract en-
forceable on other things, including the division of the surplus. That is, there
is incomplete contracting on arming but not on other types of contracts that
can be enforced through reversion to …ghting.
7
3.1.1 Destruction
Overt con‡ict rarely takes places without destroying people and material
goods. Suppose then that if con‡ictwere to occura constant proportion1¡µ
of the surplus would be destroyed, thus leaving a net surplus of µ(T + ®P)
to be contested between the two adversaries (0 < µ < 1). In the event of
overt con‡ict, the winner would receive this surplus whereas the loser would
receive nothing. The payo¤ of warlord l = 1;2 under con‡ict would then be:
V
l
c
=
w
l
w
1
+ w
2
µ(T +®P) ¡ ¯w
l
(13)
Without con‡ict, the surplus remains intact. Therefore, if warlord l were
to receive a share
w
l
w
1
+w
2
of total surplus his payo¤ would be
w
l
w
1
+w
2
(T +®P)¡
¯w
l
>
w
l
w
1
+w
2
µ(T +®P)¡¯w
l
= V
l
c
. Consequently, each warlord would prefer
to settle rather than engage in overt con‡ict regardless of the number of war-
riors he or his opponent possesses. The division of the surplus in accordance
with
w
l
w
1
+w
2
is not however the only possible division that Pareto-dominates
con‡ict. In fact, there is a continuum of such possible divisions yielding a
typical bargaining problem to be dealt with by the two warlords. As is well
known, there is not a single plausible bargaining rule (or, bargaining solu-
tion) that can be universally considered superior, but the Nash Bargaining
solution enjoys much support in the economic theory literature. (For an
overview of bargaining solutions, Roth, 1979; for a noncooperative justi…ca-
tion of the Nash solution, see Binmore, Rubinstein, & Wolinsky, 1986.) In
7
There is a whole literature in economics that allows for such incomplete contracting
and bargaining that is mostly associated with the theory of the …rm. Grossman and Hart
(1986) is a …rst paper in a long line in which incomplete contracting in on the level of
relationship-speci…c investments that parties make, although a contract can be signed on
the division of the surplus once these investments have been made.
11

cases of risk neutrality, as it is in our model here, the Nash solution also
coincides with other symmetric solutions. Without going into the details, if
the adversaries were to follow such a symmetric solution at the negotiation
and settlement stage, the payo¤ function of warlord l would be the following:
V
l
p
= (
w
l
w
1
+ w
2
µ +
1 ¡µ
2
)(T + ®P) ¡¯w
l
(14)
Note that the ’division rule’ is
w
l
w
1
+w
2
µ +
1¡µ
2
and how the e¤ect of de-
struction enters into the determination of this payo¤ under armed peace.
The more destructive con‡ict is (that is, the lower is the value of µ), the less
important are the warriors in determining the division of the surplus. The
equilibrium choice of warriors for both warlords turns out to be:
w
p
=
µ(T + ®P)
4¯
(15)
Again, note how the greater the possibility of destruction is, the lower
is the equilibrium choice of warriors. It turns out that this is also the equi-
librium number of warriors if the two sides expected overt con‡ict to take
place under the payo¤s in (12). Perhaps the more basic point,then, is that
peace and the degree of cooperation involved under such conditions simply
require arming that does not have to be lower than the arming that would be
undertaken by the adversaries if they were expecting over con‡ict. Moreover,
in more complex environments than the one just examined, di¤erent sharing
’norms,’ di¤erent bargaining solutions, can have very di¤erent e¤ects on arm-
ing and the welfare of the adversaries (see, Anbarci, Skaperdas & Syropoulos,
forthcoming).
3.1.2 Risk Aversion
Another feature of con‡ict situations that is important for whether adver-
saries engage in overt con‡ict is their attitudes towards risk. Since there are
winners and losers in wars, con‡ict is risky even if no destruction were to
take place. But risk is disliked by most people, even those like generals and
warlords who might be preparing their whole lives for it. For some risks inlife
there is insurance available but there is not any insurance available against
losing a war. What can be done instead is for the adversaries to choose not
12

to go to war, negotiate and settle their di¤erences in a fashion similar to the
way we have just seen in the case of destructive con‡ict.
To be more precise, suppose con‡ict is not destructive but both warlords
are risk averse and both have a von Neuman-Morgenstern utility function
U(¢): Then the payo¤ of warlord 1 under overt con‡ict would equal (the
payo¤ of warlord 2 is similarly de…ned):
V
1
c;risk
=
w
1
w
1
+ w
2
U[µ(T + ®P) ¡¯w
1
] +
w
2
w
1
+ w
2
U[¡¯w
1
] (16)
Again, following the logic in the case of destructive con‡ict, suppose the
two adversaries were to divide the surplus in accordance with their winning
probabilities. That is, suppose warlord 1 receives
w
1
w
1
+w
2
(T +®P) as his share
of the total surplus, thus ensuring a sure payo¤ of U[
w
1
w
1
+w
2
(T +®P)¡¯w
1
] =
U[
w
1
w
1
+w
2
((T +®P)¡¯w
1
)+
w
2
w
1
+w
2
(0¡¯w
1
)], which by the concavity of U(¢)
implies that this sure payo¤ is strictly higher than the expected utility payo¤
under con‡ict in (16).
8
Given that there is always an incentive to negotiate under risk aversion,
the question is how many warriors and resources are the warlords going to
expend in jockeying for a better negotiating position. As with the case of
destructive con‡ict, much depends on the rule of division the adversaries
expect to use at the negotiating phase of their interaction.
3.1.3 Complementarities in Production and Consumption
The contestable rents andproductioncould be complementary to othergoods
that are deemed useful by producers and warlords alike but which are not
contestable. The leisure or even labor of producers, for example, cannot be
appropriated by the warlords but it is usually complementary in utility (for
the case of leisure) or in production (for the case of labor). If one were
to lose the complementary contestable surplus in con‡ict, however, these
other goods would typically be a worth a lot less. The winner, on the
other hand, might have too much of the contestable surplus and too little of
the other non-contestable goods. Without going into the technical details,
9
8
With risk-seeking warlords, of course, the opposite would be true and overt con‡ict
would be preferable. U(¢) in such a case would be convex and therefore the payo¤ under
overt con‡ict in (16) would be higher.
9
See Anbarci, Skaperdas & Syropoulos (forthcoming) for a formal speci…cation and
derivation of the incentives to negotiate under such complementarities.
13

con‡ict distributes resources ine¢ciently and therefore the adversaries could
instead negotiate fora peaceful, andmore e¢cient, divisionof the contestable
resources.
As we have just seen, then, there are plenty of reasons for settling in the
shadow of con‡ict in a ’balance of power’ state in which the adversaries arm
in order to maintain their negotiating position. The level of arming itself,
however, depends on the ’norm’ or rule of division the adversaries expect
to adopt, with some rules being more sensitive to arming than others. A
limiting case of a rule is the one that is completely insensitive to arming and
according to which the two sides maintain a …xed portion of the surplus.
That is the case that the adversaries completely trust one another, property
rights are completely speci…ed and enforceable, as they are supposed to be in
ordinary economic environments. However, despite the variety of incentives
that may exist for armed peace, we still observe not just arming but overt
con‡ict as well. We then next discuss some of the reasons that may induce
overt con‡ict.
3.2 Why Overt Con‡ict Occurs
Against the incentives to negotiate there are others that could actually pre-
cipitate con‡ict. One clear incentive would be that of risk-loving (or, risk-
seeking) preferences by warlords. In such a case, if destruction were not too
high, the adversaries would prefer to take the risk of war over the sure bet
of dividing up the surplus. While this can be a factor in inducing con‡ict
under some circumstances, it is a cheap way of trying to understand why
overt con‡ict occurs; attributing a phenomenon to a preferential parameter
should probably be a last resort. For the case of con‡ict we can …nd alter-
native, plausible sets of explanation, one more well-known within economics
and another less so.
3.2.1 Incomplete Information
In the models we have examined, the adversaries know the exact size of the
rents and the level of production; the number of their adversaries and their
preferences; the exact nature of the contest success function that determines
the disposition of the surplus; and in the case of negotiation and settlement
they are supposed to share a norm about how to divide up the surplus. In
14

short, they face what economists and game theorists refer to as complete
information about all aspects of the game.
In reality of course adversaries face incomplete information in at least
one of the above dimensions. They might have only a general estimate of
the size of the surplus, the strengths and preferences of their adversaries, the
nature of the contest, and they might have no shared norms, or at least they
are not sure about them, in the event of negotiations. If the beliefs of the
adversaries about any of these dimensions deviate signi…cantly from one an-
other, then it would be perfectly possible to have equilibria (in appropriately
de…ned games) in which overt con‡ict is the outcome despite the presence of
incentives to negotiate and settle. Bester and Warneryd (2000) examine such
an environment where there is war because at least one side underestimates
the strength of the other. There is much other research that shows how
suboptimal outcomes occur under incomplete information in many di¤erent
contexts, but Brito and Intriligator (1985) is another paper that speci…cally
considers the possibility of war.
Many wars can at least partly be attributed to the presence of incomplete
information. World War I, for example, has been described to have occurred
after a series of misunderstandings, miscalculations, and even inattention to
details by some leaders at a time that trade and other interdependencies
among the future combatants made war unthinkable in the minds of opin-
ionmakers on both sides (see Joll, 1992, pp.10-41 ). If war could occur, then,
between the great powers of Europe that had established channels of commu-
nication, regular diplomatic exchanges, and norms of conduct that had been
evolving for centuries, it would be far easier to take place between warlords
who face a far less predictable environment, possibly without regular chan-
nels of communication and without established norms of conduct to guide
many of their critical moves.
3.2.2 How a Long Shadow of the Future Can Induce Con‡ict in-
stead of Cooperation
It has become a rather common belief in economics and political science that
con‡ict typically yields to cooperation as adversaries value the future more
highly, or, as the shadow of the future becomes longer (Axelrod, 1984). This
belief is based on folk-theorem type of arguments in conditions of repeated
interaction. A long shadow of the future encourages long-term relationships
and the development of a live-and-let-live attitude between the adversaries.
15

However, there is a di¤erent e¤ect a long shadow of the future can have.
A warlord by pursuing war now could weaken his adversaries permanently or
even possibly eliminate them and become ’king’ well into the future. There-
fore, a warlord who values the future highly could indeed take the chance of
war instead of pursuing negotiation, despite the short-term bene…ts of ne-
gotiation, because the expected long-run pro…ts could be higher in case the
opponents become permanently weakened or eliminated. In environments
in which those who win gain an advantage well into the future, both the
intensity of con‡ict, as measured by the amount of resources devoted to it,
increases (Skaperdas and Syropoulos, 1996) and the choice of overt con‡ict
over negotiation becomes more common (Gar…nkel and Skaperdas, 2000) as
the future becomes more important.
The argument of many parties that initiate wars is that they are forced
to do so because otherwise they would lose any advantage they might have
and thus have a lower probability of winning as a result. Again, during the
fateful summer of 1914, Germany felt that, to have any chance of swiftly
defeating France before Russia fully mobilized, it would have to call for gen-
eral mobilization as early as possible and before the intentions of the Entente
powers became fully known. But the call for mobilization by Germany would
certainly hasten war as it actually did. Thus, both the various forms that
incomplete information takes and the attempts by adversaries to gain a per-
manent strategic advantage over their opponents by initiating war are factors
that induce con‡ict, despite the presence of incentives in the short-run to ne-
gotiate.
3.3 Con‡ict Management in the Long-Run
The visitor to the Northern Italian city of Bologna today cannot miss the
tall, skinny towers that de…ne its skyline. They were built during the twelfth
and thirteen centuries when the city was wracked by clan warfare. The fact
that about 60 of the original 200 towers still stand is testament to how en-
during con‡ict can be. Other Italian cities had similar experiences to those
of Bologna at about the same time. To the people living then, that was the
only possible state of the world they could imagine. It was a state of what
we have called armed peace, punctuated by outright warfare when conditions
changed and one or more sides thought it could gain an advantage over the
others. Some periods were a lot more peaceful than others and the sides to
the con‡ict could relax and go about their business without feeling threat-
16

ened. Informal and formal understandings would develop until some internal
or external force would change the apparently fragile equilibrium. This con-
dition did not end with the end of the thirteenth century. It continued in
di¤erent forms. The …fteenth to the sixteenth centuries, for example, was
the world in which Machiavelli lived and the Tuscan countryside was guest
to French and German troops, Swiss papal guards, and the multitude of con-
dottieri - the various warlords o¤ering their services to cities who at the end
of their designated service would more often than not sack the homes of their
former employers. Italy did not unify until the second half of the nineteenth
century, and of course since then the country has not been completely free
of foreign troops or domestic contention.
Compared to other places, Italy has not been especially con‡ictual. Af-
ter all, this is the country in which the Renaissance and the commercial
revolution occurred. In closing with the example of Italy, we would like to
underscore the tremendous di¢culties in building the trust, the commitment,
and the institutions that will allow for disarmament and the elimination of
overt con‡ict. The transition from settling scores in the battle…eld to settling
them in courts and parliaments is a process that has only began to be in-
vestigated by economists. It takes a very long time to build institutions and
not much to destroy them. Only recently have economists come to recognize
the central importance of institutions of con‡ict management for economic
development. (Recent prominent examples of this recognition are Rodrik,
1999, and Oslon, 2000.) Though we cannot expect to …nd a recipe for end-
ing the many civil wars that are still taking place and those that are sure
to erupt in other countries, economists could complement the long-standing
e¤orts of other social scientists in identifying more direct paths than those
known to building institutions of con‡ict management.
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[2] Axelrod, Robert, 1984. The Evolution of Cooperation. New York: Basic
Books.
17

[3] Bester, Helmut & Karl Warneryd, 2000. ’Con‡ict Resolution’, working
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18

[15] Konrad, Kai & Stergios Skaperdas, 1999. ’The Market for Protection
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Tollison, & G. Tullock.
STERGIOS SKAPERDAS, b. 1959, PhD in Economics (Johns Hopkins,
1989). Associate Professor, University of California, Irvine (1996-); area
of research: political economy. Co-editor of The Political Economy of
Con‡ict and Appropriation (Cambirdge University Press, 1996).
19