The Road to Hell?

Third Party Intervention to Prevent Atrocities

Andrew H. Kydd and Scott Straus∗

March 9, 2011

∗Both at the University of Wisconsin, Madison, kydd@wisc.edu, sstraus@wisc.edu. The authors thank

the participants at a presentation at the Elliott School of International Affairs for their helpful comments,

in particular Holger Schmidt, Charles Glaser, Jim Goldgeier, Harris Mylonas, Jim Lebovic and Elizabeth

Saunders. The authors also received helpful comments at the International Relations Colloquium at the

University of Wisconsin, Madison, and the 2010 meetings of the American Political Science Association

1

Abstract

Preventing and stopping genocide and other large-scale atrocities have emerged as

important policy goals of the post-Cold War. However, a critical but stalled debate

exists about the effects of institutionalizing third-party commitments to halt atrocities.

From a deterrence perspective, some argue that the credible threat of intervention

increases costs on perpetrators, thereby decreasing the level of atrocities. Others argue,

invoking the economics literature on “moral hazard,” that third party intervention

may actually encourage rebellions by weak minorities that would otherwise have no

prospects of success, and hence make war and its associated atrocities more likely.

To break the impasse, we develop a new intervention game to model the effects of

third-party commitments to end atrocities. We find that the points made by both

camps have merit. However, based on the insights into the dynamics of violence that

the model provides, we derive a set of remedies to minimize the negative impacts

of increasing third-party commitments to end atrocities. We conclude that in most

situations and with the proper institutional design, the net impact of stronger third-

party commitments to end atrocities will be to lower the expected level of atrocities.

2

Since the end of the Cold War, an important policy debate and a substantial body of

literature has emerged around the question of third-party military intervention to prevent or

stop mass atrocities, in particular genocide and mass killing (Wheeler 2003; Weiss 2007). One

important debate has focused on the legality and legitimacy of such third-party interventions,

which are often labeled “humanitarian interventions.” Such actions generally require the

coercive deployment of force by an external actor or coalition of actors, which runs contrary

to sovereignty protections in the United Nations Charter (Hoffmann 1996; Holzgreze and

Keohane 2003; Rotberg 2010; Teson 1997; Weiss 2007.) Advocates of intervention have

stressed the need to protect innocent life, while opponents have emphasized the sovereign

rights of weak states against international interference. The debate game to a head in the

context of the NATO intervention to prevent Serbian atrocities against ethnic Albanian

civilians in Kosovo in 1998-1999. In that case, strong sovereignty objections from Russia,

among other countries, blocked action in the United Nations Security Council, prompting

NATO to plan and implement the intervention (Wheeler 2003).

Advocates of intervention typically assume that it will have beneficial effects by prevent-

ing atrocities, and lament the lack of the “political will” required to intervene. Driven by

understandable normative concerns, they claim that intervention failures simply reflect weak

political commitments to risk blood and treasure in the name of protecting the human rights

of people in distant lands (Power 2002; MIGs 2009). Several recent policy initiatives are

designed to address these problems. The Responsibility to Protect (R2P) is a framework

developed within the United Nations system to clarify the sovereignty question and to pro-

vide criteria for intervention, among other third-party commitments such as reconstruction

(Evans 2008). The Genocide Prevention Task Force, also called the Albright-Cohen Report

3

(2008), is a U.S. framework for building political will and developing a policy framework.

Both seek to institutionalize international rhetorical commitments to prevent and stop mass

atrocities.

However, a recent stream of literature challenges the underlying assumption that the

threat of third-party intervention will have a salutary effect. In particular, some scholars

argue that the threat of intervention encourages weak parties to a conflict to fight when

they would not otherwise do so and to provoke atrocities in order to generate bias against

their more powerful military opponents. In that way, greater institutionalization and greater

resolve to intervene in cases of mass atrocity will perversely increase the probability of war

and atrocities in war, in a grim illustration of the adage that the road to hell is paved with

good intentions. Advocates of this critique analogize the situation to the “moral hazard”

literature in economics in the sense that the threat of third-party intervention prompts

actors to engage in risky action they would not otherwise take (Crawford and Kuperman

2006; Kuperman 2008 a,b). The moral hazard position challenges the implicit deterrence

framework underlying the pro-intervention position, which assumes that stronger and more

credible commitments to intervene will increase the costs of committing atrocities thereby

creating disincentives to engage in such behavior.

This debate between advocates of intervention and their moral hazard critics has crys-

talized the question of what effect institutionalizing third-party commitments to end mass

atrocities would actually have, a question with clear and important theoretical and policy im-

plications. Unfortunately, the debate cannot be resolved empirically for two reasons. First,

third-party intervention that is even purported to be motivated by stopping atrocities is his-

torically quite rare, and usually accompanied by additional stated or unstated motivations

4

like saving one’s own nationals, aiding friendly local forces or attempting to overthrow un-

friendly regimes. Second, because the proposed policy change of greater institutionalization

has not happened yet, it is impossible to evaluate its effects empirically. On the theoretical

level, the debate also suffers from over reliance on argument by analogy to economic or other

strategic models, and a consequent lack of precision in understanding the strategic dynamics

of this specific problem. Third party intervention to stop atrocities is a complex enough

phenomenon, and distinct enough from the typical insurance context in which the moral

hazard literature arose, that it deserves serious strategic modeling in its own right.

In this paper we develop a game theoretic model of third party intervention to stop

mass atrocities, the first such model in which a third party, motivated by the desire to

reduce atrocities, attempts to establish a threshold on the allowable level of atrocities and

enforce this threshold by threats to intervene. The model builds on existing insights from

the literature on third-party interventions in armed conflict, but applies those insights to a

situation where one party in a conflict threatens to commit mass atrocities against civilians.

Two assumptions underlie the modeling in the paper: first, that mass atrocities are most

common in the context of armed conflict (Ulfelder and Valentino 2008; Straus 2007) and,

second, that parties to a conflict act strategically when they engage in atrocities (Kalyvas

2006; Valentino 2004).

The model clarifies a number of issues which are sometimes submerged in the existing

literature but are nonetheless central to resolving the debate. First, what should be the

criterion for evaluating whether institutionalizing a capability to intervene in the case of

atrocities is good or bad? Advocates of intervention implicitly argue that the main criterion

should be reducing the level of atrocities that occur in war, or simply, minimizing the number

5

of civilians killed per war. This would seem unobjectionable, wars happen and it would be

good to make them less costly. The moral hazard critics claim, however, that this will

make war more likely by encouraging otherwise hopeless rebellions. The frequency of war is

another important variable that should be minimized. However, as our model shows, there

is a tradeoff between these two goals, because making war less costly makes it more likely in

incomplete information settings. What this tradeoff implies, however, is that we should care

not about the costs per war or the likelihood of war, but the expected costs of war over time,

which is the product of the costs per war and the probability of war. What is important

is not how many people die per war, or how many wars there are per year, but how many

people die from war per year. We therefore derive expressions for the expected costs of war

and discuss how this variable responds to various policy innovations.

Second, the model clarifies the mechanisms that underly both the good and bad effects

of intervention. Basically, our model illustrates two mechanisms by which the prospect of

intervention can affect the strategic interaction between two sides in a conflict: 1) altering

the expected outcome of the conflict and 2) reducing the costs of the conflict. The intervenor

can alter the expected outcome of the conflict, either by altering the distribution of power

between the two sides or by making outcomes preferred by the third party more likely than

they otherwise would be. Altering the balance of power between the two sides is sometimes

argued to have little impact on the likelihood of war or atrocities, since strengthening one

side should make the other side more accommodating in the negotiations. This is indeed

the case if the parties are risk neutral, but we show that if the parties are risk acceptant,

then strengthening the weaker side can precipitate war, as the moral hazard critics contend.

However, this effect is minimized if the third party has a relatively neutral ideal point, that

6

is, it fights not to achieve victory for one side or the other, but to impose a compromise

settlement. Thus altering the expected outcome of war can increase the likelihood of war,

but with a neutral third party it need not.

The second mechanism, reducing the costs of war, is of course the main goal of the

pro-intervention school. This has the beneficial effect of reducing the level of atrocities

per war. However, as the moral hazard critics contend, this also makes war more likely.

The net effect on the expected level of atrocities is complex, and depends on the values

of certain parameters. However, the model also shows that the imposition of alternative

costs on the leadership of the atrocity committing side can compensate for the reduction in

costs on the part of the victims of atrocities. In effect, a well designed intervention regime

can transfer costs from the civilian victims of atrocities to the leadership of the atrocity

committing side, thereby keeping the likelihood of war fixed while reducing the cost per war

(for civilians), and so reduce the expected level of atrocities. This highlights the importance

of a multidimensional approach to the intervention problem, making use of compensating

policy tools to mitigate or eliminate undesirable consequences of imposing a threshold on

the permissable level of atrocities.

The intervention model developed in the paper contributes to breaking an intellectual

logjam about the likely effects of strengthening an international regime to prevent gross

violations of human rights. The paper also provides a theoretical foundation, rather than

simply a normative one, for developing international anti-atrocity mechanisms. Furthermore,

the findings from the model have direct policy implications. Finally, the paper puts the

formal theory literature on armed conflict and third party intervention in conversation with

the literature of genocide and mass killing, thereby helping to break down an artificial, but

7

entrenched boundary.

1 The Debate

Two broad positions can be found in the literature on the effect of the prospect of interven-

tion on the civil conflicts. What can loosely be characterized as the deterrence perspective

argues that credible threats to intervene to prevent atrocities should in fact reduce the level

of atrocities observed in war, ensuring that “never again” will the world stand by as geno-

cide takes place. The provocation or moral hazard perspective argues that humanitarian

intervention, by reducing the costs of rebellion for weak actors and increasing their chances

of success, makes war more likely and hence causes more civilian deaths. The existing game

theoretic literature tackles portions of the question but does not provide an adequate answer.

Some models exhibit a neutrality result, in which intervention alters the balance of power

but does not affect the likelihood of war, or, implicitly, the level of civilian casualties. Others

find that the relationship between intervention and atrocities is non-monotonic.

1.1 The Deterrence Perspective

The deterrence perspective, influenced by the international relations literature on deter-

rence (Huth 1988, Huth 1999, Zagare & Kilgour 2000), argues that threats of third party

intervention in the event of atrocities should moderate conflict and facilitate conflict resolu-

tion, and the more credible the threats are the more effective they will be. In international

relations theory, the extended deterrence problem is usually understood as how to use threats

to prevent an antagonist from attacking a protege or client. The underlying game, at its sim-

8

plest, has one player deciding whether to attack another and if an attack takes place the third

party decides whether to intervene on behalf of its client or not (Signorino & Tarar 2006).

The client state is typically treated as a non-strategic actor. The central problem to be

solved is one of making the threats credible, given that carrying them out would entail costs

for the threatener as well, particularly in the nuclear arena (Powell 1990).

Deterrence theory has found a natural application to third party intervention. Harvey

analyzes the Bosnia conflict and finds that early threats lacked credibility (Harvey 1998).

Timothy Crawford develops a theory of “pivotal deterrence” in which the third party acts as

a pivot between the two antagonists, threatening to intervene against either one if it starts

a war (Crawford 2003). To the extent that a third party could make such threats credible

to both sides of a civil conflict, it could presumably prevent war and hence atrocities.

In line with this perspective, supporters of intervention argue that what is needed to

prevent atrocities is clear and credible threats by the international community to intervene

forcefully to prevent them. This will have the effect of deterring would be human rights

violators, and ensure that wars, if they are fought at all, will not be accompanied by atrocities.

1.2 The Moral Hazard Perspective

While this logic seems intuitive and compelling, some argue that intervention may actu-

ally make atrocities more likely by encouraging rebellion by organizations representing the

potential victims. Timothy Crawford and Alan Kuperman have applied the logic of moral

hazard to the problem (Crawford & Kuperman 2006). Most incidents of mass killing take

place in the context of a war in which an organization from the victim group challenges

9

state authority. The prospect of intervention from the international community may encour-

age such rebellion from groups too weak to succeed on their own. Kuperman argues this

dynamic was at work in the Kosovo conflict in 1999, in that Kosovo rebels realized they

were too weak to successfully confront Serbia by themselves but hoped to provoke massacres

which would bring in the international community (Kuperman 2008b). The logic of moral

hazard holds that the prospect of international intervention on behalf of weak victim groups

encourages risky rebellions, much as insurance is said to encourage greater risk acceptance

and the prospect of public bailouts may encourage people to live in flood plains. The usual

remedies for this kind of problem in economic contexts are difficult to apply in the inter-

vention context, but Kuperman recommends very close attention to whether rebel groups

provoke state genocides or are genuinely responding to them, and only intervening in the

latter case (Kuperman 2008a). The ability of states to monitor rebel group behavior, in fact,

raises questions as to whether the problem is really one of moral hazard, or the alternative

adverse selection in which information, rather than actions, is hidden (Rauchhaus 2009).

The idea that the possibility of intervention can be provocative is also found elsewhere in

the intervention literature. Jenne (2004) argues that third party support radicalizes minority

groups and makes war more likely. In response to Chaim Kaufmann’s argument that third

parties should support partition as a solution to ethnic civil wars, James Fearon argued that

this would create incentives for aspiring ethnic entrepreneurs to cause trouble in the hope

that the international community would eventually hand them a state (Fearon 2004).

The moral hazard argument, that intervention causes war rather than peace, is certainly

provocative. The analytical framework is problematic, however, because it treats the state

actor in the conflict as non-strategic. The state is compared, by analogy, to fires, floods, and

10

other acts of nature against which insurance is purchased. But the state actor should also be

making calculations about the likelihood of intervention, and should scale back its demands

the more likely intervention is to take place against it (Grigoryan 2006, Rauchhaus 2006).

Thus a full explanation of how the prospect of intervention encourages genocide would have

to explain why rebel group demands escalate faster than state concessions in the face of an

increase in the likelihood of intervention. Some scholars also challenge the moral hazard

argument empirically, showing that a rise in multidimensional peacekeeping has not seen a

similar rise of atrocities and that in past mass atrocities there is little evidence that promises

of intervention spurred rebels to take actions they would not have otherwise taken (Bellamy

and Williams 2011).

1.3 Game Theoretic Approaches

While there is a small related game theoretic literature on third party intervention, few

authors tackle the debate between deterrence and moral hazard head on. Two papers by

Carment and Rowlands examine the impact of intervention on the likelihood of war and

the fighting effort of the parties. In the first, they focus on the interaction between the

third party and the stronger of the two warring parties, with the weaker side assumed to be

willing to accept whatever the third party can secure for it. They find that the greater the

salience of the conflict to the third party, the more likely the warring party is to concede and

therefore the more likely the intervention is to be successful (Carment & Rowlands 1998).

In the second paper, Rowlands and Carment examine a model influenced by Hirshleifer

(1995) in which two antagonists allocate their resources between fighting and productive

11

activity (Rowlands & Carment 2006). They find that third party intervention can increase

or decrease the fighting effort of the two parties. Both models lack any explicit bargaining,

so cannot illuminate how intervention affects the bargaining between the two antagonists.

Rupen Cetinyan argues, in contrast to both the deterrence perspective and the moral

hazard perspective, that the prospect of third party intervention should have no impact on

the likelihood of conflict, only on the terms of the agreement (Cetinyan 2002).1 However,

his model differs from the usual setup in that the outcome of war is a deterministic result

of the balance of power and effort between the third party and the state actor. If the third

party stays out, the state imposes its ideal point with certainty. The more effort the third

party expends, the more the outcome shifts in its preferred direction, but the outcome is

always deterministic. This leaves open the question of whether the result holds when war is

considered a risky outcome, as it usually is.

The closest analysis to ours is Grigoryan (2010). Grigoryan examines escalation within

a civil conflict to higher levels of violence such as mass killing. The model assumes that the

third party is biased in favor of the weaker side and posits uncertainty about the resolve of

the third party to intervene in the conflict. A low likelihood of intervention generates an

equilibrium in which a deal is reached based on the bilateral strength of the parties. Raising

the likelihood of intervention can cause war because of uncertainty about whether the third

party will intervene and the temptation to demand more in the face of such uncertainty. A

high likelihood of intervention leads to a deal on terms preferred by the third party.2

1See Wittman (1979), Fearon (1993) and Powell (1996) for related work on the effect of the balance of

power on stability.2For a somewhat similar result in the context of mediation, see Favretto (2009).

12

Grigoryan’s analysis is very helpful, but he makes certain assumptions that renders it

not perfectly appropriate for our purposes. First, he assumes that the demand made by the

minority group is fixed, rather than subject to adjustment. Given the well known result that

issue indivisibilities can cause conflict as well as uncertainty, it leaves unclear what is driving

the conflict in the model, the indivisibility or the uncertainty. We assume instead that the

parties can make any demand along a continuum, and so can smoothly adjust the demand

in response to changes in relative power, uncertainty, or other factors. Second, by assuming

that the third party’s payoff is a function of one of the two bargainers, Grigoryan cannot

consider the case where a third party is relatively unbiased and intervenes with the aim of

reducing atrocities and achieving some compromise solution. In fact, in his discussion of

the Kosovo case he agues that third parties do not try to restrain provocative rebel groups

because they share their antipathy to the state and are using the rebellion as a convenient

pretext to weaken their shared opponent. While this may be true in some cases, it is not a

fair characterization of what advocates of humanitarian intervention are proposing, namely

a more or less unbiased intervention capability designed to limit atrocities in war. Finally,

the way Grigoryan structures the model, escalation to high levels of atrocities can only

happen after an initial intervention by the third party. While this closely corresponds to the

Kosovo case, it ignores the fact that many cases escalate to high levels of atrocities without

any international intervention. A model that fairly evaluates the utility of an unbiased

intervention capability must at least have a possibility for high levels of atrocities without

international intervention.

13

2 A Model of Intervention

There are three actors, the government side, player 1 and the rebel side, player 2, and

the third party and potential intervenor, player 3. The players confront a set of possible

issue resolutions, represented by the unit interval X = [0, 1], illustrated in Figure 1. Player

1 has increasing preferences, player 2 has decreasing preferences, and player 3 has single

peaked preferences and an ideal point, I3 ∈ [0, 1], that can be anywhere in the interval. The

bargaining parties utility functions are normalized so that they value their own ideal point at

1 and their adversary’s at 0, ui(Ii) = 1, ui(Ij) = 0. The third party also values its own ideal

point at 1 and values the government and rebels’ ideal points equally at zero, u3(I3) = 1,

u3(0) = u3(1) = 0. This last assumption implies that the third party will be motivated to

intervene primarily by a desire to reduce the costs of the conflict rather than to affect the

bilateral probabilities that the parties achieve their most desired outcome.

The three players play a game illustrated in Figure 2. Player 1 starts the game by making

an offer to player 2 of some issue resolution x ∈ X. If Player 2 accepts the offer the game ends

with payoffs u1(x), u2(x), u3(x). If player 2 rejects the offer, a war breaks out. Player 1 then

has the choice of how to fight the war. Specifically, it chooses a level of atrocities to commit,

a ∈ [0, 1] where 0 indicates a “clean” counterinsurgency campaign that scrupulously avoids

targeting non-combattants, and 1 indicates an all-out genocidal campaign against civilians

associated with the rebels. Player 3 then has a choice to impose sanctions on the party

committing atrocities, or to intervene in the war. We assume that sanctions remain in place

even if there is an intervention, so the choice is to impose sanctions alone or in combination

with intervention. Sanctions impose a cost s1 on player 1.

14

Figure 1: The Player’s Utility Functions

15

Figure 2: The Intervention Game

16

We model war, following the usual convention, as a lottery in which the victor imposes

its ideal point. Departing somewhat from convention, we assume that this holds true in a

trilateral war as well as a bilateral one. That is, we assume that the third party fights to

impose its own ideal point, rather than aligning with one of the two parties and helping them

impose their ideal point. This assumption is motivated by the fact that there is no reason

for a third party to fight to impose a solution more extreme than the one it prefers. If a

third party intervenes on behalf of the weaker of the two sides, say, and prevents its defeat

why should it then go on to destroy the other side and impose it’s ally’s preferred outcome?

It would make much more sense to stop fighting once the outcome approximates its ideal

point or even switch sides if its ally becomes too powerful and threatens to achieve a total

victory. Of course, if the third party’s ideal point is near 1 or 0, it will effectively fight for

its ally’s ideal point, so this can be considered a special case of the model. But by assuming

that third parties fight to impose their own ideal points, we can consider a range of more

realistic scenarios in which third parties have interior ideal points and so prefer, and fight to

achieve, compromise solutions.

We assume that the government’s chance of victory against the rebels depends on the

level of atrocities. Specifically, we assume that player 1’s chance of winning a bilateral war,

denoted pb1(a), is an increasing function of a, so the government side increases its chances of

winning by engaging in more atrocities. We fully realize that this may not be the case in all

civil wars, but in such cases the government would not be tempted to engage in atrocities,

so the international community would not face a question of whether to intervene to prevent

them. Since we are concerned with the effects of intervention motivated by atrocities, we

focus on the case in which the war participants at least believe that they have incentives to

17

commit them.3 We define the rebel’s chance of winning a bilateral war as pb2(a) = 1− pb

1(a)

so the rebels are less likely to win the higher the level of atrocities. We assume that the third

party’s chance of winning if it decides to intervene, denoted p3 is unaffected by the level of

atrocities. The chance of winning a trilateral war after an intervention for the government

and rebels are defined as pti(a) = (1 − p3)pb

i(a). The trilateral chances of winning therefore

also sum to 1 as they should, (1− p3)pb1(a) + (1− p3)pb

2(a) + p3 = 1.4

The parties pay costs if there is a conflict. The direct cost for player i of fighting is denoted

ci. The third party only incurs direct costs if it decides to intervene. The rebel group and the

third party also suffer costs as a function of the level of atrocities, denoted k2a and k3a, where

ki > 0. These costs from atrocities are incurred by the third party regardless of whether

it intervenes. Finally, if the third party does intervene, it punishes player 1 for committing

atrocities by imposing an additional cost k1. This represents the additional sanctions and

other punishments that accompany interventions targeted at coercing a state into refraining

from atrocities, such as the punishment of leaders involved in atrocities before international

tribunals.

Finally, we assume that intervention prevents some atrocities from occurring. That is, we

assume that intervention reduces the level of atrocities by a factor of δ ∈ [0, 1] so that if the

government selects a level a and the third party intervenes, the resulting level of atrocities

3We assume that the government side has a positive chance of winning even if it commits no atrocities,

pb1(0) > 0, and that it may still lose even if it engages in all out genocide, pb

1(1) < 1.4The familiar assumption that the probability of winning equals the ratio of military power exhibits this

feature. If we assume each side has military power, mi, player 1’s chance of winning a bilateral war with

player 2 is pb1 = m1

m1+m2but if player 3 joins the war, making it trilateral, player 1’s chance of winning falls

to pt1 = m1

m1+m2+m3.

18

Table 1: The War Payoffs

Without Intervention With Intervention

Player 1 pb1(a)− c1 − s1 pt

1(δa) + p3u1(I3)− c1 − s1 − k1

Player 2 pb2(a)− c2 − k2a pt

2(δa) + p3u2(I3)− c2 − k2δa

Player 3 −k3a p3 − c3 − k3δa

will be δa where δa < a. Note, it may be that in some cases intervention increases the level of

atrocities, in such cases the third party should not intervene for humanitarian reasons.5 Here

we are focusing on the potential effects of a humanitarian regime motivated by preventing

atrocities, so we will assume that the intervention, if it occurs, actually does so.

Putting all of this together, the war payoffs are shown in Table 1. If the third party

stands aside, the two parties fight a bilateral war and the third party pays the indirect cost

of fighting, k3a, associated with refugees, humanitarian aid, etc. If the third party intervenes,

the war becomes trilateral. The third party has a p3 chance of imposing its ideal solution,

pays the direct costs of fighting, c3, and its intervention reduces the level of atrocities to δa.

2.1 The Complete Information Case

We first solve the game assuming complete information between the two bargaining parties,

using subgame perfection as the solution concept. Starting at the end of the game, the third

5For instance, Grigoryan (2006) makes the point that the high level of Serbian ethnic cleansing in Kosovo

was a response to rather than cause of NATO intervention in 1999.

19

party will intervene if

−k3a < p3 − c3 − k3δa.

or if the level of atrocities exceeds a certain threshold

a > a† ≡ c3 − p3

k3(1− δ). (1)

Note, if the third party’s power exceeds the cost of intervention, p3 > c3, then the third

party will intervene even in the absence of atrocities, when a = 0. Given the low probability

of this holding true in the context of humanitarian intervention, we assume that c3 > p3, so

that the intervention threshold is positive, a† > 0.

Turning to player 1’s choice of the level of atrocities to commit, any level a < a† is

dominated by a† since the latter results in no intervention and a greater chance of winning.

Any level greater than a† but less than 1 is dominated by 1 because intervention is assured

in any case, so player 1 might as well maximize atrocities. Player 1 therefore compares the

utility of a† with no intervention and a = 1, with intervention. Player 1 will choose to abide

by the threshold if

pb1(a

†)− c1 − s1 > pt1(δ) + p3u1(I3)− c1 − k1 − s1

or rearranging slightly

pb1(a

†)− pb1(δ) + p3(p

b1(δ)− u1(I3)) + k1 > 0. (2)

The greater the threshold, a†, the the more likely equation 2 will hold and player 1 will

observe the threshold. The lower the threshold, the lower the left hand side is and the more

danger there is of player 1 escalating beyond the threshold.

20

Turning now to player 2’s choice, there are two cases to consider. If player 1 will choose

a†, the war will be bilateral and player 2 will reject the offer if

u2(x) < pb2(a

†)− c2 − k2a†

and accept it otherwise. Let rb2 be player 2’s reservation value, or the level of x that solves

this equation with equality. If player 1 opts for a = 1, there will be intervention and player

2 will reject the offer if

u2(x) < pt2(δ) + p3u2(I3)− c2 − k2δ

Let rt2 be the level of x which solves this with equality.

Finally, consider player 1’s offer. If the war will be bilateral, player 1 compares player

2’s bilateral reservation value with its war payoff and will make an offer that satisfies player

2 if it is better for player 1 than war, or if

u1(rb2) ≥ pb

1(a†)− c1 − s1. (3)

If player 1 will violate the threshold and intervention will take place, player 1 will make the

peaceful offer if

u1(rt2) ≥ pt

1(δ) + p3u1(I3)− c1 − s1 − k1 (4)

What is the relationship between intervention and war in the complete information ver-

sion of the game? We show in the Appendix that with risk neutral preferences, there will be

no war in the complete information version of the game, regardless of whether intervention

takes place or not. However, with risk acceptant preferences, there can be war in complete

information bargaining games (Fearon 1995). We therefore consider the following questions.

If the parties have risk acceptant preferences that cause war, can intervention reduce the

21

level of atrocities in these wars? Does the prospect of intervention ever cause war when it

would not have taken place otherwise? If it does, what can be done to reduce the likelihood

of this occurring?

A few numerical examples, presented in Table 2, can help answer these questions. In

the example, we assume that player 1 and player 2 are both risk acceptant, u1(x) = x2 and

u2(x) = (1−x)2. Some parameters are the same in all the cases considered, namely, δ = 0.9,

k1 = .01, and c1 = s1 = c2 = k2 = 0.1. Parameters that vary are listed in the table.

The first two cases, 1a and 1b, illustrate the ability of the shadow of intervention to lower

the level of atrocities that occur in wars that are brought on by risk acceptant preferences.

In these cases, the two sides are relatively evenly matched. Shifting from a clean counterin-

surgency to maximal atrocities increases player 1’s chance of winning from 40% to 60%.6

Because the two sides are evenly matched and risk acceptant, war is likely since balanced

compromises are undervalued by both sides. The third party is quite powerful in comparison

to the parties, p3 = 0.8, and heavily biased in favor of player 2, I3 = .1. In case 1a, the third

party is uninterested in atrocities, with a relatively low k3 of 0.5. This produces an a† of 1,

which means that the third party will not intervene for any level of atrocities that player 1

selects. As a result, player 1 maximizes the level of atrocities, but the war occurs anyway

because of the even matching of the two parties.

In case 1b, the third party cares more about atrocities, k3 has increased to 2. This means

player 3 will be willing to intervene if the level of atrocities goes over a† = .5. The fact

that player 3 is so powerful and so biased in favor of player 2 convinces player 1 to observe

the threshold, so intervention does not take place. War still occurs however, but the level

6The function is assumed to be linear, pb1(a) = 0.4 + 0.2a.

22

Table 2: The Complete Information Case: Numerical Example

Case 1a Case 1b Case 2a Case 2b Case 2c

p3 0.80 0.80 0.25 0.25 0.25

c3 0.90 0.90 0.30 0.30 0.30

k3 0.50 2.00 0.50 2.00 2.00

a† 1.00 0.50 1.00 0.25 0.25

I3 0.10 0.10 0.10 0.10 0.50

u1(I3) 0.01 0.01 0.01 0.01 0.25

u2(I3) 0.81 0.81 0.81 0.81 0.25

pb1(a

†) 0.60 0.50 0.85 0.59 0.59

pb2(a

†) 0.40 0.50 0.15 0.41 0.41

pt1(δ) 0.12 0.12 0.61 0.61 0.61

pt2(δ) 0.08 0.08 0.14 0.14 0.14

Player 3 Stays Out Stays Out Stays Out Intervenes Intervenes

r2 0.55 0.41 1.00 0.61 0.89

r1 0.63 0.55 0.81 0.64 0.68

Outcome War War Peace War Peace

23

of atrocities is lower because player 1 restrains its conduct in order to avoid intervention.

Thus the contrast between case 1a and 1b illustrates the potentially beneficial effect of the

shadow of intervention, it can cause states that fight to moderate their conduct, even when

intervention does not take place.

In the next three cases we consider the potential unintended consequences of intervention

and how they can be mitigated. In these cases, the third party is weaker, with p3 only equal

to 0.25. We also assume that the balance of power between the two sides is more lopsided

in favor of player 1, so with no atrocities player 1’s chance of winning is pb1(0) = 0.5 and

with maximal atrocities it is pb1(1) = .85. In case 2a we again assume that the third party is

uninterested in stopping atrocities so k3 = .5 and a† = 1. In this case, player 1 will maximize

the level of atrocities if war occurs, and this will produce a very lopsided balance of power

in its favor. This imbalance of power is conducive to peace, however, for it convinces player

2 to accept any deal in preference to war. The result is a peaceful bargain, favoring player

1, backed up by the threat of a very brutal war.

In case 2b, the third party has become more concerned about atrocities, with k3 = 2.

The threshold for intervention falls to a† = 0.25, so the third party is attempting to enforce

a fairly low threshold. However, its weakness, in combination with the great military utility

of atrocities, convinces player 1 to violate the threshold and escalate its level of atrocities

to a = 1. The third party therefore intervenes if war occurs. Unfortunately, the prospect

of friendly intervention encourages player 2 to hold out for more in the negotiations, since

although the third party is weak, at least it is on their side, which boosts their overall

chances of “winning” into the middling range where compromise becomes difficult with risk

acceptant preferences. Case 2b, therefore, illustrates the moral hazard argument. A lopsided

24

peace, case 2a, is disrupted by a weak threat of intervention which encourages intransigence

on the part of the weaker side, which ends up causing war and atrocities, the very outcome

intervention was supposed to prevent.

Can this unintended consequence be avoided? In case 2c we alter only one variable by

making player 3 more neutral between the players, by setting I3 = 0.5. Because of player 3’s

weakness and low threshold, player 1 would still violate the threshold, and player 3 would

intervene in a war. However, the neutral ideal point of the third party depresses player 2’s

appetite for war, because a victory for the third party is no longer nearly equivalent to a

victory for player 2. Since player 3 would impose an undesirable compromise settlement, it

does not raise player 2’s way payoff as much as in the case when player 2 is more heavily

biased in favor of player 2. The result is that player 2 becomes less intransigent in the

negotiations and there is now a bargaining range that both sides prefer to war. A peaceful

settlement is reached, just as in case 2a. The only difference is that player 2’s bargaining

position has been somewhat strengthened by the intervention regime, so it does better in

the negotiations.

We can sum up the results from the complete information case as follows. If the parties

have risk acceptant preferences, war is possible with complete information, especially when

power is relatively balanced between the two sides. The threat of intervention if a side

commits atrocities above a certain threshold can reduce the level of atrocities suffered in

these wars. However, the moral hazard perspective is correct in arguing that intervention

can provoke war as well. When power is imbalanced, and the third party is biased in favor

of the weaker side it may help move the balance of power into the middling range which

makes compromise impossible. However, this problem is less severe when the third party

25

has a more neutral ideal point, and does not overly favor one side or the other.

The complete information case sheds some light on the debate over intervention. However,

the assumption of risk acceptant preferences may not hold in many cases. An alternative

mechanism that can produce war even with risk neutral preferences is private information

about the costs of conflict. We turn next to an exploration of this case.

2.2 The Incomplete Information Case

We introduce uncertainty over player 2’s costs for fighting. Assume that player 2’s direct

costs for fighting are uniformly distributed over the interval [0, 1]. This assumption ensures

a full spectrum of behavior for player 2, in that the lowest cost type will fight if player 1

demands anything more than its relative power would justify, that is anything over p1, while

the highest cost type will accept any deal at all rather than fight. The likelihood that player

2 has costs below c2 is F2(c2) = c2. Player 2 learns its own cost when the game begins, the

other players are uncertain.

The intervention decision by the third party is the same as in the complete information

case, as is the decision by player 1 on the level of atrocities to select. When we turn to

player 2’s decision, however, there are now a continuum of types and a resulting probability

of acceptance and rejection.

If player 1 will choose a†, the war will be bilateral and player 2 will reject the offer if

c2 < pb2(a

†)− k2a† − u2(x)

The probability of bilateral war, denoted P (W b), is just the the likelihood that the offer is

26

rejected, or

P (W b) = F2(pb2(a

†)− k2a† − u2(x))

= pb2(a

†)− k2a† − u2(x)

If player 1 opts for a = 1, there will be intervention and player 2 will reject the offer if

c2 < pt2(δ) + p3u2(I3)− k2δ − u2(x)δ

The likelihood of trilateral war in this case is

P (W t) = F2(pt2(δ) + p3u2(I3)− k2δ − u2(x))

= pt2(δ) + p3u2(I3)− k2δ − u2(x)

Finally, consider player 1’s offer. Any offer less than p1 will be dominated by offering

x = p1 since the result will be certain acceptance for any such offer. If it demands more than

p1, then there will be some chance of war. Once again we consider two cases, one in which

player 1 will opt for a† and one in which it will choose a = 1.

When player 1 will choose a†, the payoff for offering x = pb1(a

†) is u1(pb1(a

†)). Demanding

more than this will result in some chance of war and a payoff of

P (W b)(pb1(a

†)− c1 − s1) + (1− P (W b))u1(x) (5)

When player 1 will choose a = 1, then the payoff for offering x = pt1(δ) is u1(pt

1(δ)). De-

manding more will result in a chance of war and a payoff of

P (W t)(pt1(δ) + p3u1(I3)− c1 − s1 − k1) + (1− P (W t))u1(x) (6)

Player 1 will choose an offer, denoted x∗, that maximizes its payoff, depending on its future

behavior in war.

27

Table 3: Comparative Statics: Incomplete Information Version

Equilibrium Quantities

a† x∗b x∗t P (W b) P (W T ) E(a|W b) E(a|W t)

p3 - -

c3 +

k3 -

I3 +

δ + + - +/-

a† + - +/-

pb1 + +

c1 - - - - - -

s1 - - - - - -

k1 - - -

k2 + + - - - -

There are four main variables the values of which are determined in equilibrium: the

intervention threshold, player 1’s offer, or demand, the likelihood of war, and the expected

level of atrocities. We discuss each in turn. All results assume risk neutral preferences, and

proofs are in the appendix. A table summarizing the comparative statics results is given in

Table 3.

28

2.2.1 The Intervention Threshold

The influence of the parameters on the intervention threshold, a†, are straightforward. In-

creasing the cost of intervention, c3, raises the threshold, so player 1 can get away with more

atrocities. Increasing the power of the third party, p3, decreases the threshold, reducing

the level of atrocities that will be possible without intervention. Increasing the sensitivity

to atrocities, k3, and lowering the level of post-intervention atrocities, δ, will decrease the

threshold, further constraining player 1.

2.2.2 The Equilibrium Offer

If player 1 will observe the threshold and set a = a†, the equilibrium offer that player 1

chooses is

x∗b = pb1(a

†) +1 + k2a† − c1 − s1

2(7)

If player 1 will not observe the threshold and set a = 1, the equilibrium offer in the case of

intervention is as follows.

x∗t = (1− p3)pb1(δ) + p3u1(I3) +

1 + k2δ − c1 − s1 − k1

2(8)

The equilibrium demand is increasing in player 1’s power, pb1, and decreasing in player

1’s costs for fighting, c1 and the costs of the economic sanctions, s1. Sanctions, by punishing

player 1 for fighting, convey some bargaining leverage to player 2. Conversely, the demand is

increasing in player 2’s sensitivity to atrocities, k2. The more costly player 2 finds atrocities,

the better player 1 does in the bargaining.

If the war will remain bilateral, then the offer is increasing in the threshold of atrocities,

a†. The higher the threshold, the more atrocities player 1 can get a way with, so the worse

29

the bargain for player 2. Lowering the threshold will therefore favor player 2 by lowering

player 1’s demand.

If the war will involve intervention, then the more powerful the third party is, p3 and the

more costly the intervention is to player 1, k1, the lower the demand and the better player 2

does in the bargaining. The higher player 3’s ideal point, I3, that is the closer it is to player

1’s, the better player 1 does since this improves the war payoff for player 1. Finally, the

higher the post-intervention level of atrocities, δ, the better the deal for player 1, since this

will increase player 1’s war payoff.

2.2.3 The Probability of War

If player 1 will obey the threshold and the war will remain bilateral, then the equilibrium

likelihood of war is

P (W b) =1− k2a† − c1 − s1

2(9)

If player 1 will escalate to a = 1 and the third party intervenes, the probability of war is

P (W t) =1− k2δ − c1 − s1 − k1

2(10)

Note, these are identical except for two factors. First, player 1’s costs for intervention, k1,

enters negatively in the trilateral case, lowering it in comparison with the bilateral case.

Second, δ replaces a†, and since δ > a†, this also lowers the trilateral probability. Therefore

war is more likely in the bilateral than in the trilateral case.

The comparative statics are straightforward. Anything that increases the cost of war

makes war less likely. Increasing player 1’s costs for combat and sanctions, c1 and s1, both

decrease probability of war. Increasing player 2’s sensitivity to atrocities, k2, decreases the

30

likelihood of war. Raising the threshold of intervention, a†, lowers the probability of bilateral

war by increasing player 2’s costs for war. Lowering the threshold, conversely, makes war

more likely by lowering its costs for player 2.

In the trilateral case, δ plays a similar role. Increasing the post intervention level of

atrocities, δ, makes war less likely and lowering it makes war more likely, by lowering its

costs for player 2. Increasing player 1’s costs for intervention, k1, decreases the probability

of trilateral war by making it more costly.

An important point to note is that the impact of the level of atrocities, a† and δ, on the

probability of war depends on how much player 2 cares about atrocities, k2. If player 2 cares

a great deal about atrocities, this impact will be large, since lowering the level of atrocities

will affect player 2’s decision calculus greatly. On the other hand, if player 2 is relatively

“brutal” and does not care much about atrocities, so k2 is low, then reducing the level of

atrocities will have little impact on the likelihood of war.

2.2.4 The Equilibrium Level of Atrocities

The expected level of atrocities is the probability of war times the level of atrocities. In the

bilateral case this is

E(a|W b) =1− k2a† − c1 − s1

2a† (11)

and in the trilateral case, it is

E(a|W t) =1− k2δ − c1 − s1 − k1

2δ (12)

Increasing the costs of war decreases the expected level of atrocities. If player 1’s costs for

combat, sanctions and intervention go up, c1, s1 and k1, then the expected level of atrocities

31

goes down. If player 2’s sensitivity to atrocities goes up, then the expected level of atrocities

goes down. These variables reduce the likelihood of war without having any countervailing

impact on the level of atrocities per war, so their impact is unambiguous.

Changing the threshold level of atrocities, a†, and the level of post intervention atrocities,

δ, has a more complicated effect. Lowering the level of atrocities makes each war that occurs

less costly, but makes the occurrence of war more likely. These two effects work at cross

purposes in terms of the overall impact on the expected level of atrocities.

The derivative of the expected costs of war in the bilateral case with respect to a† is

∂E(a|W b)

∂a† =1− c1 − s1

2− k2a

† (13)

The corresponding term in the trilateral case is

∂E(a|W t)

∂δ=

1− c1 − s1 − k1

2− k2δ (14)

If these expressions are positive then the expected level of atrocities will go up as the

level of atrocities increases, and decline if the level of atrocities is lowered. The expression

will be positive if the costs of war, c1, s1 and k1, are relatively low.

Once again the role of player 2’s concern for the level of atrocities, k2 is crucial. If player

2 is very concerned with atrocities, k2 will be high and these expressions could be negative,

because lowering the level of atrocities makes war more likely and this effect dominates. On

the other hand, if the rebel group is brutal, with low k2, then this expression will be positive,

and reducing the level of atrocities per war will reduce the overall expected level of atrocities.

32

2.2.5 The Marginal Player 1

Finally, we consider the effect of converting a marginal player 1 from pursuing all out genocide

to observing the threshold on the level of atrocities. If a marginal state 1 switches from a = 1

to a = a†, then the likelihood of war will increase, the atrocities per war will decrease and

the expected level of atrocities may rise or fall. Converting the marginal threshold observer

to a threshold violator will have the opposite of these effects.

In comparing the probability of war in the trilateral case to the bilateral case, it is lower

in the trilateral case because k1 is subtracted in the numerator and we assume that δ > a†.

These additional costs for war make it less likely in the trilateral case. Shifting player 1 to

observing the threshold will therefore increase the probability of war.

In looking at the effect of switching from a = 1 to a = a† on the expected level of

atrocities, we see that k1 is no longer subtracted from the numerator in the bilateral case,

which raises the expected level of atrocities. However, δ is also replaced by a†, which is a

lower level of atrocities. As before, the result of this depends on the costs of war. If war is

less costly, that is if c1, s1, and k2 are low, then switching to the bilateral war may decrease

the expected level of atrocities. The more costly war is, the more likely switching to the

bilateral case will increase the expected level of atrocities.

3 Implications and Analysis

To more clearly spell out the implications of the model we consider five topics. First we

compare a world in which there is effectively no intervention policy with one in which there

is a threshold at which intervention will take place. Second, we assess the effect of lowering

33

an existing threshold, to reduce the level of atrocities per war. Third, we consider multi-

dimensional policy changes, designed to mutually reinforce each other and lead to a better

outcome than each one individually. Fourth, we consider what has been thought to be the

problem of the brutal rebel group. Finally, we address the topic of whether the threshold

for intervention does or should vary from country to country.

3.1 From No Threshold to Some Threshold

Many would argue that there is effectively no policy in place for humanitarian interven-

tion to prevent atrocities today. Some interventions are justified by humanitarian concerns,

but there is no widely accepted policy in place to establish a mechanism for humanitarian

intervention that could operate in a transparent fashion to achieve that goal.

We can represent the no-intervention world by considering the model when c3 is pro-

hibitively high, so that a† > 1 and therefore the third party never intervenes. In this case,

all wars are bilateral, and the level of atrocities is a = 1.

If we then consider a policy change that has the effect of lowering c3, say establishing

an international organization to prepare the logistics for humanitarian interventions and for

clarifying the conditions and rules under which intervention takes places, this will lower a†

to some level below δ. This will divide the population of cases into two, because some will

obey the new threshold and some will not. Those who obey the new threshold will continue

to fight bilateral wars at the new threshold level of atrocities, a†, so the level of atrocities for

these wars will decline. The probability of war will therefore go up in these cases. The net

effect on the expected level of atrocities will depend, as discussed above, on the cost of war.

34

If c1, s1, and k2 are low, then the effect will be to reduce the expected level of atrocities. If

they are high, it may increase the expected level of atrocities.

Those cases that refuse to obey the new threshold will now incur intervention, and the

atrocity level will be δ. The atrocity level per war will therefore decline. The likelihood of war

may or may not increase. Shifting from the bilateral to the trilateral war increases player 1’s

costs for fighting by k1, which makes war less likely. However, changing the level of atrocities

from 1 to δ reduces player 2’s costs for fighting, which increases the likelihood of war. The

net effect could go either way, or cancel out. Consequently, the effect on the expected level

of atrocities could also go either way. If the probability of war declines, because increasing

player 1’s costs dominates decreasing player 2’s, then the result will be a decrease in the

expected level of atrocities. Otherwise the expected level of atrocities may increase if the

probability of war increases enough. Note, if k2 is low, then the effect of increasing player

1’s costs will dominate, and the expected level of atrocities will fall.

3.2 From One Threshold to a Lower Threshold

Next, consider the effects of lowering an existing threshold, to further reduce the level of

atrocities per war. If a† is lowered, there are three types of state to consider, those who obey

the new threshold, those who were not obeying the old threshold, and those who switch from

obeying the threshold to violating it.

Those who continue to obey the threshold are still fighting bilateral wars. Their level of

atrocities goes down, and the likelihood of war goes up. Once again, the net effect depends

on the costs. If war is less costly, the expected level of atrocities will decline, if war is more

35

costly, then it will increase.

Those who were not obeying the original threshold will still fight trilateral wars. Nothing

will change for this population, so there will be no impact on the expected level of atrocities

in this case.

Finally, some will switch from obeying the threshold to not obeying it, in accordance

with equation 2. For these types, war that was once bilateral is now trilateral. The level of

atrocities per war goes up from the old threshold to the post intervention level of atrocities,

δ. The likelihood of war goes down, as a result, since player 1 suffers the additional cost

of intervention, k1, and player 2 suffers the cost of the increased level of atrocities. The

effect on the expected level of atrocities is therefore mixed, but in the opposite way from the

previous comparisons. If the costs of war are low, then raising the level of atrocities is likely

to raise the expected level of atrocities in this case, if the costs of war are high, then raising

the level of atrocities per war will lower the expected level of atrocities.

3.3 Multidimensional Policy Changes

The mixed effects of policy changes that solely target the intervention threshold, a†, is

clear from the previous discussion. Most importantly, lowering the threshold of intervention

often has the undesired consequence of raising the probability of war and convincing some

belligerents to escalate their level of atrocities beyond the threshold. This suggests the need

to consider a broader set of policy tools that could potentially be manipulated together to

negate these unwanted effects.

First, consider the fact that lowering the threshold of intervention can cause some actors

36

that previously abided by the threshold to ignore the new threshold and escalate to a = 1.

Can this be compensated for by manipulating other variables? If we examine equation 2

we can see that there are three variables that can be manipulated to keep the expression

constant, despite lowering a†. First, if the post intervention level of atrocities, δ is lowered,

this will raise the left hand side of equation 2. Second, since player 1 dislikes intervention,

(pb1(δ) > u1(I3)), increasing the strength of the intervention, p3 will also raise the expression.

Finally, increasing the cost imposed on player 1 for committing atrocities, k1, will also raise

the expression, making player 1 more likely to observe the threshold.

Note, δ and p3 enter into both the expression for a† and equation 2. Making the interven-

tion stronger by increasing p3, and better able to prevent atrocities by lowering δ will both

lower the threshold of intervention and increase the expression in equation 2, counterbal-

ancing the effect of lowering a† and making player 1 more likely to obey the new threshold.

However, these effects might not balance out exactly, which could lead a marginal player 1

to change their decision. To deal with this problem we note that player 1’s costs for inter-

vention, k1 appears in 2 but does not appear in the expression for a†, so it can be used to

adjust 2 at will to compensate for changes in a†. That is, one can always find an increased

level of punishment for states that commit atrocities sufficient to convince them, if they

were willing to abide by the threshold limit on atrocities before, to continue to do so even

if that threshold is lowered. This is particularly true if the threshold reduction has been

accomplished by making the potential intervention stronger and more capable of reducing

atrocities.

Now consider the probability of war. The crux of the moral hazard objection to lowering

the level of intervention is that it raises the probability of war. Can an alternative variable

37

be found to negate this unfortunate side effect? The sanctions variable, s1, is the obvious

candidate. By increasing the level of sanctions, the international community can make war

more costly for player 1. If we examine equations 9 and 10, it is easy to see that the positive

effect on the probability of war of reducing a†, can be easily compensated for by increasing

s1, so that the probability of war remains the same. In fact, one could argue that this kind

of change is itself normatively desirable, particularly if the sanctions are “smart” and target

the leaders with travel restrictions, financial barriers and the like. Transferring the costs of

civil war from the civilian victims of atrocities to the bank accounts of the leaders is all to

the good, and all the more practical since leaders may often care more about their own well

being than that of their followers.

3.4 The Brutal Rebel Group

This leads naturally to a consideration of the supposed problem of the brutal rebel group.

Moral hazard proponents have often pointed to the existence of brutal rebel groups as a

problem for any intervention regime designed to reduce atrocities. The argument goes that

if rebel groups are brutal, that is, they do not care that much about the victims of atrocities

even when those victims are the people they claim to represent, then they will be especially

likely to attempt to try to provoke atrocities in order to trigger international intervention that

will result in a political win for them. Therefore, having an international regime to prevent

atrocities plays into the hands of brutal rebel groups and will cause wars and atrocities that

would have otherwise not occurred.

The model shows the flaw in this line of reasoning. If the rebel group is brutal, it will

38

have low k2. The model shows that the lower k2, the less impact lowering the threshold of

atrocities has on the likelihood of war. This is because brutal rebel groups are willing to

rebel even when they face high levels of atrocities, so lowering the level of atrocities has little

impact on their decision calculus. The more brutal the rebel groups, the greater the need for

an intervention regime to lower the level of atrocities in the wars that they will provoke in

any event. The danger, in fact, is that some rebel groups might not be brutal, so that they

would be moved to rebel if the level of atrocities were lowered. But as we discussed above,

if the costs of the conflict can be transferred from the civilian victims of atrocities to the

leaders through increased smart sanctions, then the likelihood of war can be held constant

so that the expected level of atrocities declines.

3.5 Country Specific Thresholds

Finally, we consider the issue of whether the threshold is or ought to vary from country to

country. Some of the variables in the model would vary significantly from place to place.

Most obviously, the more powerful the target of intervention, the less powerful (relatively)

the intervention must be, lowering p3, which raises the threshold for intervention, a†. This

accords with the common complaint that more powerful countries can get away with levels

of atrocities that other countries might not. For instance, the Russian wars in Chechnya

and Georgia have aroused international criticism, to be sure, but no talk of intervention.

More subtly, the other exogenous parameters might vary from country to country, producing

variations in the ability or willingness of an international regime to intervene.

Another important source of variation would be whether the international community is

39

able to adequately compensate for lowering the threshold of intervention by increasing k1

and s1. If there were some cases where for some reason it was difficult to impose sanctions

or increased intervention costs on player 1, then the possibility that lowering the threshold

of atrocities increases the likelihood of war becomes greater. Therefore, we find that the

international community might hesitate before imposing a low threshold on conflicts where

it cannot also impose compensating costs to keep the likelihood of war from increasing.

4 Conclusion

As the uprising in Libya began to degenerate into widespread conflict and civilians were

increasingly targeted, UN Secretary General Ban Ki Moon was asked about the relatively

hard line he had taken against the Libyan regime. He answered as follows.

First of all, we have seen intolerable tragedies, genocide [and mass atrocities],

which happened in Rwanda, Srebrenica, and in Darfur. We have learned great

and very painful lessons in the past. We have reaffirmed that this should never

happen and this kind of crime against humanity and genocide should be pun-

ished. And the United Nations since then has taken strong action. We have all

these frameworks and I have appointed a Special Adviser on [the prevention of]

genocide [and] a Special Adviser for the Responsibility to Protect. As you will

remember in 2005, during the World Summit, all the leaders of the world got

together and they reaffirmed that this should never happen. That is why the Se-

curity Council and the Human Rights Council, they reacted swiftly and with one

voice. The Security Council has taken a unanimous decision to impose sanctions

40

- imposing asset freeze, travel ban and referring this case to the International

Criminal Court. And this is quite important and unprecedented, and I’ll make

sure that these measures will be implemented swiftly.

As Ban noted, the existing anti-atrocities regime is ad-hoc. A United Nations Genocide

Convention exists, with widespread ratification; the Convention includes language on how

signatories to the Convention are obligated to prevent genocide. However, the mechanisms

for how such prevention would take place are vague. Darfur is a case in point. Darfur was

considered a landmark case in which national authorities publicly declared genocide to occur,

but Darfur also revealed the limits of the Genocide Convention in the sense that calling the

violence “genocide” did not trigger specific intervention action (Straus 2005). Outside the

Convention, no agreed-upon policy framework exists to prevent or stop atrocities where

they occur in either a multilateral (United Nations or NATO) or foreign policy framework.

Given that deficit, a series of policy initiatives exist to put in place a firmer and clearer

anti-atrocities regime, in particular the Responsibility to Protect (R2P) doctrine (Evans

2008, Weiss 2006), which has been endorsed in the U.N. system and the Cohen-Albright

Commission report, which recommends a suite of policy proposals to identify, prepare, and

prevent genocide as part of U.S. foreign policy7 Examples such as Libya make this an all the

more urgent question for the international community.

In this paper, we do not evaluate the politics of whether a stronger anti-atrocities policy

will likely be implemented at the international or domestic levels. We recognize significant

obstacles to reaching international consensus. However, in a number of countries, including

the United States, and within the United Nations system there exists a strong current of

7See also the symposium in Genocide Studies and Prevention, 4:2, 2009.

41

momentum to create an anti-atrocities regime. The moral hazard position holds that, per-

versely, strengthening such a regime would increase the risk of war and provoke atrocities. In

the model we build to evaluate the claim, we find some truth to it, but overall we find that

if compensating measures are taken the net impact of an anti-atrocities regime conforms to

the wishes of advocates. Imposing a cap on the level of atrocities in civil conflicts, if done

impartially and with compensating costs for the parties who commit atrocities, can lower

the expected level of atrocities and achieve the goals of the policy without undue negative

unintended consequences.

42

References

Carment, David & Dane Rowlands. 1998. “Three’s Company: Evaluating Third-Party In-

tervention in Intrastate Conflict.” Journal of Conflict Resolution 42(5):572–599.

Cetinyan, Rupen. 2002. “Ethnic Bargaining in the Shadow of Third-Party Intervention.”

International Organization 56(3):645–677.

Crawford, Timothy W. 2003. Pivotal Deterrence: Third Party Statecraft and the Pursuit of

Peace. Ithaca: Cornell University Press.

Crawford, Timothy W. & Alan J. Kuperman, eds. 2006. Gambling on Humanitarian Inter-

vention: Moral Hazard, Rebellion and Civil War. Abingdon: Routledge.

Evans, Gareth. 2008. The Responsibility to Protect: Ending Mass Atrocity Crimes Once and

For All. Washington, DC: Brookings.

Favretto, Katja. 2009. “Should Peacemakers Take Sides? Major Power Mediation, Coercion

and Bias.” American Political Science Review 103(2):248–263.

Fearon, James D. 1993. Threats to Use Force: Costly Signals and Bargaining in International

Crises Dissertation University of California at Berkeley.

Fearon, James D. 1995. “Rationalist Explanations for War.” International Organization

49(3):379–414.

Fearon, James D. 2004. “Separatist Wars, Partition and World Order.” Security Studies

13(4):394–415.

43

Grigoryan, Arman. 2006. Third Party Intervention and Escalation in Kosovo: Does Moral

Hazard Explain It? In Gambling on Humanitarian Intervention: Moral Hazard, Re-

bellion and Civil War, ed. Timothy W. Crawford & Alan J. Kuperman. Abingdon:

Routledge pp. 45–64.

Grigoryan, Arman. 2010. “Third Party Intervention and the Escalation of State-Minority

Conflicts.” International Studies Quarterly 54(4):1143–1174.

Harvey, Frank. 1998. Deterrence Failure and Prolonged Ethnic Conflict: The Case of Bosnia.

In Peace in the Midst of War: Preventing and Managing International Ethnic Conflicts,

ed. David Carment & Patrick James. Columbia: University of South Carolina Press.

Hirshleifer, Jack. 1995. “Anarchy and Its Breakdown.” Journal of Political Economy

103(1):26–52.

Huth, Paul K. 1988. Extended Deterrence and the Prevention of War. New Haven: Yale

University Press.

Huth, Paul K. 1999. “Deterrence and International Conflict: Empirical Findings and Theo-

retical Debates.” Annual Review of Political Science 2:25–48.

Jenne, Erin. 2004. “A Bargaining Theory of Minority Demands: Explaining the Dog that

Did Not Bite in 1990’s Yugoslavia.” International Studies Quarterly 48(4):729–754.

Kuperman, Alan J. 2008a. “Mitigating the Moral Hazard of Humanitarian Intervention:

Lessons from Economics.” Global Governance 14(2):219–240.

44

Kuperman, Alan J. 2008b. “The Moral Hazard of Humanitarian Intervention: Lessons from

the Balkans.” International Studies Quarterly 52(1):49–80.

Powell, Robert. 1990. Nuclear Deterrence Theory: The Problem of Credibility. Cambridge:

Cambridge University Press.

Powell, Robert. 1996. “Stability and the Distribution of Power.” World Politics 48(1):239–

267.

Rauchhaus, Robert W. 2006. Conflict Management and the Misapplication of Moral Hazard

Theory. In Gambling on Humanitarian Intervention: Moral Hazard, Rebellion and Civil

War, ed. Timothy W. Crawford & Alan J. Kuperman. Abingdon: Routledge pp. 64–73.

Rauchhaus, Robert W. 2009. “Principal-Agent Problems in Humanitarian Intervention:

Moral Hazards, Adverse Selection and the Commitment Dilemma.” International Stud-

ies Quarterly 53(4):871–884.

Rowlands, Dane & David Carment. 1998. Moral Hazard and Conflict Intervention. In The

Political Economy of War and Peace, ed. Murray Wolfson. Boston: Kluwer pp. 267–285.

Rowlands, Dane & David Carment. 2006. “Force and Bias: Towards a Predictive Model of

Effective Third-Party Intervention.” Defence and Peace Economics 17(5):435–456.

Signorino, Curtis S. & Ahmer Tarar. 2006. “A Unified Theory and Test of Extended Imme-

diate Deterrence.” American Journal of Political Science 50(3):586–605.

Straus, Scott. 2005. “Darfur and the Genocide Debate.” Foreign Affairs 84(1):123–133.

45

Table 4: Notation in the Game

x A possible issue resolution

ui(x) Utility functions over x

I3 Player 3’s ideal point

a The level of atrocities

a† The threshold level of atrocities that triggers intervention

δ Reduction in atrocities resulting from intervention

pi Probability of victory

ci Cost of conflict

ki Player i’s costs for atrocities

s1 Cost of sanctions on player 1

Weiss, Thomas. 2006. “R2P after 9/11 and teh World Summit.” Wisconsin International

Law Journal 24(3):741–760.

Wittman, Donald. 1979. “How a War Ends: A Rational Model Approach.” Journal of

Conflict Resolution 23(4):743–763.

Zagare, Frank C. & D. Marc Kilgour. 2000. Perfect Deterrence. Cambridge: Cambridge

University Press.

5 Appendix

Notation in the model is summarized in Table 4.

46

With complete information and risk neutral preferences, player 1 will offer player 2 its

reservation value, player 2 will accept, and peace will obtain. To see this, note that risk

neutrality implies that u1(x) + u2(x) = 1. First consider the case in which intervention is

not anticipated, so player 1 will choose a†. We start with the implication of risk aversion,

u1(rb2) = 1− u2(r

b2)

u1(rb2) = 1− (pb

2(a†)− c2 − k2a

†)

u1(rb2) = pb

1(a†) + c2 + k2a

†

u1(rb2) > pb

1(a†)− c1 − s1

and end with the condition that player 1 prefers to offer player 2’s reservation value rather

than fight. Now consider the case in which intervention is anticipated. We perform a similar

calculation

u1(rt2) = 1− u2(r

t2)

u1(rt2) = 1− (pt

2(δ) + p3u2(I3)− c2 − k2δ)

u1(rt2) = 1− ((1− p3 − pt

1(δ)) + p3u2(I3)− c2 − k2δ)

u1(rt2) = 1− 1 + p3 + pt

1(δ)− p3u2(I3) + c2 + k2δ

u1(rt2) > pt

1(δ) + p3 − p3u2(I3)− c1 − k1

u1(rt2) > pt

1(δ) + p3(1− u2(I3))− c1 − k1

u1(rt2) > pt

1(δ) + p3u1(I3)− c1 − k1

and end with the same conclusion, player 1 prefers to offer player 2’s reservation value rather

than fight.

47

In the incomplete information case, to find the equilibrium offer, we maximize player 1’s

payoff with respect to its offer.

P (W b)(pb1(a

†)− c1 − s1) + (1− P (W b))u1(x)

With risk neutral preferences, we have u1(x) = x and u2(x) = 1 − x. We can therefore

re-express the above as follows

(pb2(a

†)− k2a† − (1− x))(pb

1(a†)− c1 − s1) + (1− (pb

2(a†)− k2a

† − (1− x))x

or

(pb2(a

†)− k2a† − (1− x))(pb

1(a†)− c1 − s1 − x) + x

Taking the derivative with respect to x we get

(pb2(a

†)− k2a† − (1− x))(−1) + (pb

1(a†)− c1 − s1 − x) + 1

Setting equal to zero and solving for x we get

0 = (pb2(a

†)− k2a† − (1− x))(−1) + (pb

1(a†)− c1 − s1 − x) + 1

0 = −pb2(a

†) + k2a† + (1− x) + pb

1(a†)− c1 − s1 − x + 1

2x = −pb2(a

†) + k2a† + 1 + pb

1(a†)− c1 − s1 + 1

2x = pb1(a

†) + k2a† + pb

1(a†)− c1 − s1 + 1

x∗ ≡ pb1(a

†) +1 + k2a† − c1 − s1

2

Therefore the demand is increasing in k2 and a†, which increase the costs for player 2,

and decreasing in c1 and s1, player 1’s costs for conflict and international sanctions.

48

Now we substitute back into the equation for the likelihood of war. The likelihood of war

in the bilateral case is pb2(a

†)− k2a† − u2(x), so the equilibrium likelihood of war is

P (W b) = pb2(a

†)− k2a† − u2(x

∗)

P (W b) = pb2(a

†)− k2a† − (1− x∗)

P (W b) = pb2(a

†)− k2a† − 1 + x∗

P (W b) = pb2(a

†)− k2a† − 1 + pb

1(a†) +

1 + k2a† − c1 − s1

2

P (W b) = −k2a† +

1 + k2a† − c1 − s1

2

P (W b) =1− k2a† − c1 − s1

2

We turn to the expected level of atrocities. This is the product of the likelihood of war

with the expected level of atrocities

E(a) =1− k2a† − c1 − s1

2a†

The derivative of E(a) with respect to a† is

∂E(a)

∂a† =1− k2a† − c1 − s1

2− a†k2

2∂E(a)

∂a† =1− c1 − s1

2− k2a

†

Now consider the case where the threshold will be ignored, player 1 will choose a = 1,

and the third party will intervene. In this case, player 1’s payoff for an offer x is

P (W t)(pt1(δ) + p3u1(I3)− c1 − s1 − k1) + (1− P (W t))u1(x)

This can be rewritten as

(pt2(δ)+p3u2(I3)−k2δ−(1−x))(pt

1(δ)+p3u1(I3)−c1−s1−k1)+(1−(pt2(δ)+p3u2(I3)−k2δ−(1−x)))x

49

or

(pt2(δ) + p3u2(I3)− k2δ − (1− x))(pt

1(δ) + p3u1(I3)− c1 − s1 − k1 − x) + x

The derivative with respect to x is

(pt2(δ) + p3u2(I3)− k2δ − (1− x))(−1) + (pt

1(δ) + p3u1(I3)− c1 − s1 − k1 − x) + 1

Setting this equal to zero and solving for x we get

0 = (pt2(δ) + p3u2(I3)− k2δ − (1− x))(−1) + (pt

1(δ) + p3u1(I3)− c1 − s1 − k1 − x) + 1

0 = −pt2(δ)− p3u2(I3) + k2δ + 1− x + pt

1(δ) + p3u1(I3)− c1 − s1 − k1 − x + 1

2x = 1− pt2(δ) + 1− p3u2(I3) + k2δ + pt

1(δ) + p3u1(I3)− c1 − s1 − k1

2x = p3 + pt1(δ) + 1− p3u2(I3) + k2δ + pt

1(δ) + p3u1(I3)− c1 − s1 − k1

2x = pt1(δ) + 1 + p3(1− u2(I3)) + k2δ + pt

1(δ) + p3u1(I3)− c1 − s1 − k1

2x = pt1(δ) + 1 + p3u1(I3) + k2δ + pt

1(δ) + p3u1(I3)− c1 − s1 − k1

2x = 2pt1(δ) + 1 + 2p3u1(I3) + k2δ − c1 − s1 − k1

x∗ ≡ (1− p3)pb1(δ) + p3u1(I3) +

1 + k2δ − c1 − s1 − k1

2

Now we substitute back into the expression for the likelihood of war to find the equilibrium

likelihood of war in the trilateral case.

P (W t) = pt2(δ) + p3u2(I3)− k2δ − u2(x

∗)

P (W t) = pt2(δ) + p3u2(I3)− k2δ − (1− x∗)

P (W t) = pt2(δ) + p3u2(I3)− k2δ − 1 + x∗

P (W t) = pt2(δ) + p3u2(I3)− k2δ − 1 + (1− p3)p

b1(δ) + p3u1(I3) +

1 + k2δ − c1 − s1 − k1

2

50

P (W t) = (1− p3)pb2(δ) + p3u2(I3)− k2δ − 1 + (1− p3)p

b1(δ) + p3u1(I3) +

1 + k2δ − c1 − s1 − k1

2

P (W t) = 1− p3 + p3 − k2δ − 1 +1 + k2δ − c1 − s1 − k1

2

P (W t) = −k2δ +1 + k2δ − c1 − s1 − k1

2

P (W t) =1− k2δ − c1 − s1 − k1

2

Finally, we turn to the expected value of atrocities.

E(a) = P (W t)δ

E(a) =1− k2δ − c1 − s1 − k1

2δ

The partial derivatives with respect to k1, k2, and c1 are all negative. The derivative with

respect to δ is

∂E(a)

∂δ=

1− k2δ − c1 − s1 − k1

2− δ

k2

2∂E(a)

∂δ=

1− c1 − s1 − k1

2− k2δ

51