Who Wins The Peace? Elites, Citizens, and

the Decision for War

⇤

Colin Krainin

†Kristopher W. Ramsay

‡

December 7, 2016

Abstract

We build a model of bargaining and war over public and private

goods to explore how domestic institutions and international issues inter-

act to influence the probability of war and the distribution of benefits in

peace. We show that half-measures toward democracy such as expand-

ing the size of the elite or taxing the elite as a form of executive control

can increase the potential for conflict, while full liberalization reduces

the potential for conflict. When international bargains are peaceful, rel-

ative democracies deliver more public goods to citizens while the private

goods obtained by non-democracies may contribute to greater levels of

inequality.

⇤We thank participants at the University of Calgary Economics Seminar, 2016 PeaceScience Society Annual Conference in South Bend IN, 2016 Annual Meeting of the AmericanPolitical Science Association in Philadelphia PA, and the NYU Political Economy Seminarfor helpful comments. We also thank David Carter and Mehdi Shadmehr for comments aswell as Bella Wang for excellent research assistance.

†Princeton University, ckrainin@princeton.edu‡Princeton University, kramsay@princeton.edu

1

Introduction

Issues at stake in international bargaining rarely have uniform implicationsto all groups within the participating states. Furthermore negotiations of-ten contain multiple elements. Trade deals may increase the overall pie, butnegatively impact workers in a specific industry. Arms reduction agreements,territorial transfers, and government to government cash transfers all lead toa different distribution of benefits in a society and rent to elites.

For example, such a negotiation was central to the establishment of theborder between Kuwait and Saudi Arabia in the early 20th century. At the endof World War I the collapse of the Ottoman Empire left the victorious groupsto create states out of the desert throughout the middle east and the ArabPeninsula. In 1922 Kuwait signed the Uqair Convention with the sultanateof Najd, which later became Saudi Arabia in 1932, to define the boundary ofthe sultanate and the British protectorate of Kuwait. Rather then drawing adistinct border, the agreement created a neutral zone of shared control. Thisterritory was of little interest until the discovery of near by oil fields in 1938.

What followed was an international negotiation over the creation of a defini-tive administrative boundary between the two states that split the territoryand a separate agreement over granting exploration rights to the oil foundin the region. The elites largely captured the benefits from the oil incomewhile territorial control largely had institutional and political benefits for thepopulations of the two states.

Similar private-public agreements can be found all over the world, from thenegation of commercial rights in Trieste after World War II to negotiations inLatin America over joint investment and water way access. In order to beginto explore these types of interactions, we develop a model of internationalconflict bargaining with two new elements.1 First we model states bargaining

1First formally explored in Brito and Intriligator (1985), the bargaining model of wardraws inspiration from the classic analysis of Clausewitz (1976), intuitive arguments ofSchelling (1960), and the game theoretic strike literature in economics (Admati and Perry1987; Hart 1989; Card 1990; Haller and Holden 1990; Fernandez and Glazer 1991; Cramptonand Tracy 1992). The seminal analysis of Fearon (1995) argued persuasively that all modelswith costly conflict as an outcome must demonstrate why a more efficient, peaceful bargain

2

over both public goods that benefit all of society and private goods that onlyelites capture. Second, we consider different institutional setups by varyingthe key decision makers for international bargaining. We vary the decisionmaking institution in the home country in two ways. First, we consider adecision making process where elites, who share private goods in additionto consuming public goods, decide whether there is war or peace. Next, weconsider an institution that expands the ruling elite, possibly to be very large.We can think of this as an institution that co-opts large groups of citizensand then distributes, potentially small, fractions of the private good amongthe in-group. Finally we consider a model of liberalization where the majoritycitizens, who do not share in the benefits of private spoils, decide whether toaccept a peace or go to war.

Our main finding is that while fully liberalized democracies have advan-tages in obtaining peaceful outcomes in international disputes, transitional orhalf-measures– such as expanding the size of the elite class or redistributivetaxation– can often increase the potential for conflict. We also find that thepresence of private goods, interpreted as directed economic resources, oftenmakes war more likely between non-democracies. However, in mixed dyadswith one democracy and one non-democracy, more private goods can lead tomore peace.

A further implication of this type of international bargaining is that stateswith more democratic domestic institutions have advantages in capturing pub-lic goods for its citizens. On the other hand, the elites in less democratic statesare frequently paid off with private goods. This outcome identifies an inter-national political channel by which democracies deliver relatively more publicgoods to their citizens while non-democracies potentially increase domestic in-equality through this channel by focusing on acquiring private goods for their

was not possible. Two main explanations have been explored. The first, utilized in thispaper, relies on private information to generate a risk-return trade-off in proposals (Banks1990; Wagner 2000; Reed 2003; Slantchev 2003; Powell 2004a; Fey and Ramsay 2007, 2011;Yared 2010) while the second investigates how shifts in power among adversaries in a limitedcommitment environment can lead to conflict between states (Powell 2004b, 2006, 2012,2013; Krainin 2015; Krainin and Wiseman 2016) in a manner analogous to how similarshifts may lead to price wars between firms (Wiseman 2016).

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elite. Interestingly the story is somewhat complicated in the case where a for-eign state finds it more cost effective to bargain away public goods rather thanprivate goods to a non-democracy. In this case, less democratic institutionsgive the elites in non-democracies more leverage to demand a greater propor-tion of public goods since they would be better able to benefit from seizingprivate goods in a victorious conflict.

In our model, instead of bargaining over a single object (Fearon 1995),states simultaneously bargain over both public goods, x, and private goods,y. One state, Foreign (F ), with known strength makes a take-it-or-leave-itoffer to Home (H).2 Home is modeled as having one of two “types,” eitherstrong or weak, with a known prior probability. Home is composed of twogroups, elites (E) and ordinary citizens (or out group) O. We consider twoinstitutional forms: a liberalized democracy, where the median voter (a memberof O) decides whether or not to accept Foreign’s offer and an oligarchy, whereonly members of the elite decide whether or not to accept a peace proposal.In extreme cases, the ruling group in an oligarchy can be large and include themedian citizen.

The key determinant of conflict in this setting is the attractiveness toForeign of a risk free (pooling) offer that both types of Home will acceptversus a risky (separating) offer that only weak types of Home will accept.In our setup, who gets to make this decision within Home is critical in deter-mining the relative attractiveness of these two types of offers. When Home isan oligarchy, we find that the following institutional changes all increase thepotential for conflict: (1) decreasing the elite’s cost of war; (2) expanding thesize of the elite; and (3) increasing the ability of citizens to capture privategoods from the elite (possibly through redistributive taxation).

Collectively, these results lead to our conclusion that partially transition-ing from a small oligarchy to a more inclusive but non-democratic regime fre-quently increases the potential for conflict. The intuition behind this family of

2We use this simple form of bargaining both to ease exposition and to reflect that in ourdata one state is identified as the “challenger” in a given dispute, while the other state isthe “target.”

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results is that efforts to include more citizens in the decision making process,or to transfer some of the benefits of private goods from elite decision makersto all citizens, frequently encourages the elite decision makers to increase theirbargaining demands. This effect is driven by a need to compensate a smallerproportion of the bargaining pie domestically with a larger overall share ofthe international bargaining pie. Generally, these demands are increasing bya larger proportion for strong types than weak types, increasing the incentivefor risky (separating) offers.

We can also obtain three additional results conditional on increasing theamount of private goods. When Home is a relative democracy, then increas-ing the amount of private goods available decreases the potential for conflict.Alternatively, if Home is an oligarchy, then increasing the amount of privategoods available increases the potential for conflict. When there are sufficientlyhigh levels of private goods, liberalization (switching from an oligarchy to ademocracy) decreases the potential for conflict. These results imply that alter-ing the level of private goods has differing impacts on the potential for conflictfor different pairs of countries in conflict. Increasing the level of private goods(1) increases the potential for conflict for two oligarchies, (2) decreases thepotential for conflict in mixed dyads, and (3) does not affect the potential forconflict between democracies.

The intuition behind these results on increasing the level of private goodsis that the decision makers in democracies cannot obtain them and thereforedo not care to bargain for them. Hence, the elites in democracies lose outon access to private goods relative to oligarchies. If one of the states is ademocracy, but the other is not, then increasing the level of private goodsallows the democracy to compensate an oligarchy with private goods withoutdecreasing the utility of the the median voter. Liberalizing from an oligarchyto a democracy can cause Home to increase its demands in public goods, butwhen the level of private goods is sufficiently high, there always exists enoughprivate goods to compensate a foreign oligarchy. However, if both states areoligarchies, the potential for conflict increases as the level of private goodsincreases because for each additional unit of total private goods, Foreign keeps

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a greater proportion of a bargain when facing a known weak type rather thana known strong type. Hence, under private information, the spread betweensize of a bargain necessary to satisfy both types versus only one type increases,increasing the incentive for a risky offer.

A final implication of our model is that decreasing the ability of citizensto capture private goods specifically in war time (possibly through redistribu-tive taxation), decreases the potential for conflict. Hence, if citizens can setdiffering tax rates on peaceful bargains and war spoils, then the citizens candirectly determine the decision making group’s incentives toward or againstwar. Hence, this type of taxation policy provides a microfoundation for theconcept of political bias used in some agency models of conflict. Politicalbias leads to a qualitatively different effect than simply altering the decisionmaker’s cost internalization of war since it can lead to war even in the case ofcomplete information (Jackson and Morelli 2007; Krainin and Slinkman 2016).Different taxation structures will imply different bias levels for the elites. In-creasing (decreasing) the effective bias of the elites will increase (decrease) theproportion of the international bargaining pie captured by Home, but alsoincrease (decrease) the potential for conflict in crisis bargaining.

In the last section of this paper we take some of these hypotheses to data oninternational territorial disputes. Our observational analysis provides empiri-cal support for two of our most nuanced results: that democracies bargainingwith oligarchies in the presence of private goods, like natural resources, aremore peaceful and that autocratic regimes with different bases of support willalso have different probabilities of war when natural resources are present.While our empirical analysis is quite simple, finding results so consistent withvery specific hypotheses suggest that this is a fruitful framework for thinkingabout bargaining in territorial disputes.

As a model that takes direct account of the impact of domestic politicson international bargaining and war outcomes, this paper adds to a literaturethat began with the introduction of the two-level game in Putnam (1988).Several strands of the literature have taken different approaches to connectingthe domestic level to the international level. This paper connects most closely

6

with agency models of war (Jackson and Morelli 2007; Fearon 2008; Kraininand Slinkman 2016).

Other approaches include the selectorate model (Bueno de Mesquita et al1999) where a leader makes international decisions in order to maintain herability to remain in power and signaling models that investigate the infor-mational role of internal opposition (Schultz 1998). The selectorate model isexpanded to include international bargaining in Fey and Goemans (2009) andthis model is empirically analyzed in the context of the democratic peace inDebs and Goemans (2010). Weeks (2008) argues that non-democratic leadersare frequently able to signal as well as democratic leaders while Weeks (2012)suggests that there is significant variation among nondemocratic regimes intheir domestic constraints and, consequently, their likelihood of conflict initi-ation.

Our paper also relates to the literature on resource wars. Acemoglu et al(2012) study how the dynamic exploitation of resources may lead to commit-ment problems that generate war. This approach is quite different from ours,however, their analysis of how firm structure impacts the likelihood of war hasthe flavor of our analysis of differing political institutions. Caselli, Morelli, andRohner (2015) seek to demonstrate that the desire to seize natural resourcesis a source of conflict. Their method for doing this is to investigate how theprevalence of conflict depends on the proximity of oil to the border betweenpotential foes. Since it is more costly to seize oil far away from the border,they reason that if oil is indeed the motivating factor, it will be a more power-ful factor the closer it is to the border. Schultz (2015) further analyzes theseclaims with data from precise digital maps. He finds that this result is drivenby false positives since the conflicts that lead to the Caselli et al (2015) resultare often over territory that does not contain the oil in question. Our modelviews conflict over privately exploitable resources such as oil and other issueswith a more public good aspect as inextricably linked.

Empirically, our results most clearly have implications for the large lit-erature that investigates conflict proneness in authoritarian regimes versustransitional democracies versus full democracies (Mansfield and Snyder 1995;

7

Thompson and Tucker 1997; Ward and Gleditsh 1998; Gleditsh and Ward2000; Goemans 2000; Narang and Nelson 2009; Baliga, Lucca, and Sjostrom2011; Colgan 2013). This literature is inconclusive as to the likelihood of con-flict in transitional democracies. Our model indicates a previously unidentifiedforce for the increased conflict potential of transitional democracies. However,shifting fully from an oligarchy to a democracy is often peace enhancing in ourmodel. Since our model plays out in a simple, one-shot setting we see a morefully dynamic extension of our model as the logical next step. Our expectationis that the foreign power experiences a tension between the increased static in-centive for conflict with transitional democracies and the desire to wait out thetransition period in order to enjoy the more favorable bargaining environmentonce democracy fully takes root.

The rest of our paper proceeds as follows. The next section presents ourbaseline model. Section 2 presents our main results. Sections 3 and 4 brieflyextend the baseline model to incorporate taxation and political bias respec-tively. Section 5 provides some empirical analysis for our claims. A final sec-tion concludes. Online Appendix A provides the proofs omitted from the textwhile online Appendix B provides further details on our empirical analysis.

1 The Model

We describe our model on two levels: the international level and the domesticlevel. Our focus is on how domestic institutions impact international bargain-ing and the potential for war. In order to cleanly present these effects, wesimplify both levels as much as possible.

1.1 Domestic Level

Two states, Home and Foreign (i 2 {H, F}), are characterized by theirdomestic institutions. These institution dictate how the state values publicgoods, x 2 [0, x], relative to private goods, y 2 [0, y], in international bargains.Each state contains ni � 1 actors divided into two groups: E (for elites) and

8

O (for outside group). In each state, there are mi � 1 members of E, whilethe rest of the population (ni�mi) belongs to the outside group. We generallyassume that mi is small relative to ni. The only difference between the groupsis that members of E receive private goods from an international bargain,while members of O do not.

We consider two institutional settings. We refer to the first setting as anoligarchy. In an oligarchy, the members of E possess the power to agree toa bargain or not. While we use the term oligarchy, this first setting capturesa number of political structures ranging from a pure dictatorship (mi = 1)to various forms of limited democracy. We refer to the second setting as ademocracy. In a democracy, we assume that the median voter has the powerto agree to a bargain or not. Moreover, we typically assume that mi is smallenough that the median voter is a member of O.

It is possible to imagine cases where mi is high enough in the oligarchysetting that the median voter is needed to agree to a deal.3 In fact, we willthink of cases where mi is higher as cases where a state is more democraticthan one with a lower mi. However, the democracy setting is distinctive inthat we cover the case where the median voter has decision making power,but may not have the same incentives as the, possibly quite small, elite thatreceives private goods in a bargain.

Within a state, public goods are non-rival and non-excludable4, so bothgroups receive the same amount of public good utility, while private goodsmust be divided among the elite. We assume that individuals value publicand private goods using a linear utility function.5 Hence, in peace for a given

3An example might be a society where a minority group is excluded from voting andprivate goods.

4We use the term public good throughout, but our model also applies to common re-source goods (non-excludable, but rivalrous). The only modeling difference, which does notqualitatively impact the analysis, is that an individual’s value of common resource goodsare scaled down to reflect the population size.

5Other separable utility functions featuring sufficient substitutability between the goodsproduce similar results, but can be considerably more complicated. The key aspect of theutility function is that y must be split among elite users while x is shared by all users.

9

offer (x, y), elites in Foreign receive utility6

uF,E (x, y) = x� x+

y � y

mF,

while O receivesuF,O (x, y) = x� x.

Groups in H receive

uH,E (x, y) = x+

y

mH, uH,O (x, y) = x.

1.2 International Level

On the international level, Home and Foreign bargain over the public good,x, and private good, y. The presence of more than one type of good is the onlyaspect of the international level that is qualitatively distinctive from previouscrisis bargaining models featuring asymmetric information.

At the beginning of the game, Foreign makes a take-it-or-leave-it offer ofa bundle of public and private goods (x, y) to Home. Home can then acceptthe offer, leading to peace, or reject the offer and fight a war to obtain thegoods.

Home has a probability of victory in war dependent on Home’s type. Withprobability q 2 (0, 1), Home is a weak type (l) and with probability 1 � q,Home is a strong type (s). When Home is type s, then Home wins withprobability p 2 (0, 1), while when Home is type l, Home wins with probability0 < p0 < p. Foreign then wins a war with probability 1 � p against a strongtype and 1� p0 against a weak type.

We assume that the costs of war are potentially borne differently betweengroups. All n players divide the cost, however, a deciding member’s cost

6It would be easy to include a parameter, ↵i > 0, to multiply by the number of publicgoods received in i (so H would value x as ↵Hx). This parameter would measure howmembers of state i value public goods relative to private goods. Additionally, the ratio ↵F

↵H

would measure how the two states value public goods relative to one another. So if ↵F

↵H> 1

(↵F

↵H< 1), then Foreign values public goods more (less) than Home. Since it does not

qualitatively affect our result, we set ↵H = ↵F = 1 for purposes of parsimony.

10

is modified by � > 0 to reflect that they may pay a proportionally differentamount of costs.7 These assumptions grant the model a great deal of flexibility.For instance, if mH = 1 and � = nH , then we are back in the standard unitaryactor case.

When Home is a strong type and an oligarchy, war gives a decision makerin Home the value

wH = p

x+

y

mH

�� �

cHnH

.

When Home is a strong type and a democracy, gives a decision maker in Home

the value8

wH = px� cHnH

.

Foreign’s value of war is defined analogously.

2 Results

In any peaceful bargain, Foreign seeks to maximize its utility given the con-straints described in the model section. Lemma 1 characterizes these valueswhen Home is known to be strong.

Lemma 1. Let Foreign be an oligarchy and assume Home is known to bestrong. In the unique subgame perfect equilibrium, bargains are set as follows

7Note that costs need not sum to cH if � 6= 1. Altering the level of �, alters the totalcost faced by H. An alternative assumption would be to set elite cost to � cH

nHand citizen

cost to (1� �) cHnH

. This change would not qualitatively impact any of our results in thispaper, but may quantitatively impact the results presented here as well as substantivelyimpacting the results of certain possible extensions. These alternative ways of formulatingcosts have different real world implications. Our assumption is that the institutional struc-ture of government affects how elites are impacted by war, but it does not directly affectordinary citizens. So, for instance, election outcomes may be affected by war decisions. Thealternative assumption is that there is a direct trade-off in the costs paid by elites and thoseborne by citizens. In this case, costs are the literal payment for war.

8Note, a potential alternative assumption would be that citizens in Home would splitthe value y in victory when Home is a democracy. This value will be negligible when nH

is large, which is our general assumption. Therefore, we exclude this potential value forsimplicity.

11

(1) If Home is a democracy, then

(x⇤, y⇤) =

8<

:0, 0 x cH

pnH

px� cHnH

, 0 x > cHpnH

(2) If Home is an oligarchy and x �cHnHp �

ymH

, then

(x⇤, y⇤) = (0, 0) .

(3) If Home is an oligarchy and x > �cHnHp �

ymH

, then

(x⇤, y⇤) =

8>>>>>>><

>>>>>>>:

0, p [mHx+ y]� �mH

nHcH

mH

mF 1, y � 1

1�p

hpmHx� �mH

nHcH

i

px+ (p� 1)

ymH

� � cHnH

, y mH

mF 1, y < 1

1�p

hpmHx� �mH

nHcH

i

phx+

ymH

i� � cH

nH, 0

mH

mF> 1, x � 1

1�p

hp ymH

� � cHnH

i

x, (p� 1)mHx+ py � �mH

nHcH

mH

mF> 1, x < 1

1�p

hp ymH

� � cHnH

i

A similar characterization follows if Home is known to be weak with p0sinstead of ps.

In the democracy setting, Home only has a positive war threat when x ishigh relative to the population weighted cost of war, modified by the probabil-ity of victory. Therefore, Home only receives positive amounts of the publicgood when this threshold is reached. As seems natural, when Home’s bargainvalue is positive, it is increasing in Home’s probability of victory and the totalamount of public goods available, while declining in war costs. Democraciesnever receive any private goods since the median voter does not value them,hence Foreign optimizes by setting y = 0.

In the oligarchy setting, bargain values are more complex. Similarly to thedemocracy case, if the total amount of public and private goods per recipientis not high enough relative to a modification of war costs, then Home doesnot receive any portion of the international bargain.

There are four other cases. In all these cases, the total amount of public

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and private goods are high enough that Home receives a positive portion ofthe international bargain. In two of the cases, Foreign maximizes by keepingeither all of the public goods or all of the private goods for itself and paysHome off entirely in the other type of goods. In the other two cases, Foreign

would prefer, on the margin, to substitute more private goods (public goods)for less public goods (private goods) in the bargain offer Foreign makes toHome. However, Foreign is constrained from making this substitution by theresource constraint on y (x). In these cases, Foreign gives Home all of onetype of good and the minimum amount of the other type of good to maintainpeace.

The key drivers of whether Foreign prefers to pay Home with private orpublic goods are the parameters mH and mF . When the ratio mH/mF is lessthan or equal to 1, Foreign prefers to pay Home in private goods. The value 1represents the utility loss to Foreign of increasing Home’s utility in a peacefulbargain by 1.9 Similarly, mH/mF represents the utility loss for Foreign frompaying Home off in private goods. If there are 10, 000 elites in Home and20, 000 elites in Foreign, relaxing Home’s constraint by 1 causes the utilityfor Foreign’s decision makers to drop by 1/2. In this case, it is cheaper interms of utility for Foreign to pay Home in private goods rather than publicgoods. Hence, the optimal bargain bundle is determined by a combination ofhow Foreign and Home value public goods relative to to one another andthe relative level of democracy (inclusiveness of the elite) in the two states(mH/mF ).

Lemma 1 allows us to compare the welfare implications of peaceful bargainsfor citizens in a democracy versus an oligarchy. When Home is an oligarchy,but relatively more democratic than Foreign, Home always receives morepublic goods than when relatively less democratic than Foreign. However,once this threshold is reached, increasing the inclusiveness of Home’s institu-tions only serves to reduce the amount of public goods received. The intuition

9Generally, it is easy to include a parameters (↵H and ↵F ) that would alter this trade-offto values other than 1. See Footnote 4. When this is the case, the cut-off value for Foreignwanting to switch from paying in private goods to public goods may happen at a point otherthan when mH/mF > 1 (in fact, this value would be mH/mF > ↵F /↵H).

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is that more the more democratic Home becomes, the less Home’s elite canleverage the amount of private goods it could win in a war to get more publicgoods for everyone. At the extreme, in a full democracy, the decision maker inHome no longer values private goods at all, so the level of private goods pro-vides no leverage at all. Finally, when Home has more inclusive institutionsthan Foreign, elites and citizens benefit equally from international bargain-ing. However, when Home has less inclusive institutions than Foreign, onlyelites receive benefits from international bargaining. While less stark assump-tions would make this inequality effect less extreme, this effect that the mix ofbenefits from international bargaining would favor the elites in less inclusiveinstitutions remains under more relaxed conditions.

An implication of Lemma 1, that will be important in later results, is thatin order for Foreign to make a nonzero offer for a given level of x and y, Home

must be sufficiently strong.

Corollary 1. When Home is an oligarchy, Foreign makes Home a nonzerooffer if and only if

p >�cH

nH

⇣x+

ymH

⌘ (1)

2.1 The Potential for Conflict

When Home’s strength level is known, Foreign can safely make an offer thatHome is just willing to accept. However, Home’s strength level is unknownand may be strong (type s) with probability 1� q or weak (type l) with prob-ability q. Home cannot credibly communicate its strength level to Foreign

before bargaining since whenever Home is weak, it has the incentive to misrep-resent its strength level as strong. Foreign then has three options: (1) makean offer that neither type of Home will accept; (2) make an offer that bothstrength types will accept; or (3) make an offer that Home will only accept ifit is a weak type.

In the (Perfect Bayesian) equilibrium of the baseline model, Foreign nevertakes option 1 since the cost of war implies that there exists bargains where

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both players do better than in war. Under option 2, Foreign optimizes byoffering Home just enough that a strong type will accept. We call this therisk free proposal (pooling proposal). With this option, Foreign avoids riskingwar, but possibly pays too much to a weak type. Under option 3, Foreign

optimizes by offering Home just enough that a weak type will accept. We callthis a risky proposal (separating proposal), because if Home is a strong type,war will result.

Let usF be Foreign’s payoff when it makes a risk free proposal that a

strong type will just accept. Let ulF be Foreign’s payoff when it makes a risky

proposal and the weak type accepts. Foreign prefers to make a risky proposalwhen

qulF + (1� q)

h(1� p)

hx+

ymF

i� cF

nF

i� us

F > 0.

The second term on the left hand side is Foreign’s war value multiplied by theprobability of war. In our simple model, either this inequality is not satisfiedand the probability of war is zero or it is and war occurs with probability1 � q.10 Since this inequality separates cases where war never occurs fromcases where it occurs with positive probability, we will refer to it as the warrisk inequality. Therefore, holding all other parameters constant, any changein a single parameter that causes the left hand side of the war risk inequalityto increase in value increases the space of parameters for which the war riskinequality is satisfied. When increasing a parameter increases (decreases) thevalue of the left hand side of the war risk inequality, we say that the potentialfor conflict is increasing (decreasing) in that parameter.

10One might note at this point that a war resulting from the mechanism is likely to beshort. In our simple model, a state should identify that it is facing a strong type after asingle period of conflict. However, a generalization of this type of model demonstrates thatwars may in fact be quite lengthy when Home may be one of several types and Foreignmust physically destroy some of Home’s military capacity in war (Krainin, Thomas, andWiseman 2016).

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2.2 Expanding the Elite

In the oligarchy setting, the elite expands as mi increases. This may be viewedas a limited type of democratization. As mi increases, a greater percentage ofsociety is involved in the decision making process over international bargainsand conflict. As a first step toward understanding the effects of democratiza-tion, Lemma 2 demonstrates how Foreign’s utility is affected by increases inthe number of elites in Home.

Lemma 2. Assume Home and Foreign are oligarchies and Home is knownto be type s. Assume that inequality 1 holds. uF is strictly decreasing in mH

if and only if mH

mF 1. Otherwise, uF is strictly increasing in mH .

Lemma 2 states that increasing democratic involvement increases Home’sdemands in a way that is unfavorable to Foreign given their marginal rates ofsubstitution between private an public goods. But when Foreign prefers thepublic good, increasing the size of the elite in Home makes Foreign betteroff.

The intuition for Lemma 2 is as follows. Increasing the population in Home

(mH) receiving private goods decreases the payoff for each member of the elitein peacetime since private goods received in a bargain are spread over greaternumbers of elites. For the same reason, H’s war payoffs are also loweredwhen mH increases. However, these payoffs are modified by the probability ofvictory and costs. When the probability of victory is high and costs are low,then war payoffs drop more slowly than peacetime payoffs as mH increases.Thus, Home requires higher peace values to avoid war leading to lower utilityfor Foreign. In this case, it is as if the price of paying Home off in privategoods is increasing, so the cost of the bargain to Foreign is increasing (uF

is decreasing). However, eventually the price gets high enough that Foreign

switches to paying Home off in public goods. When paying Home with publicgoods, increasing mH only serves to lower Home’s war value, but does notaffect the value of the public goods transfer. Hence, once mH becomes largeenough to satisfy mH/mF > 1, then the amount of public goods transferredto Home is decreasing in mH (uF is then increasing).

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Before proceeding to Proposition 1, we must define a condition on the sizeof private goods, that ensures that the amount of private goods is sufficientfor Foreign to pay Home off in private goods if Foreign so desires. In otherwords, the amount of private goods is high enough that our current modeldoes not effectively reduce to a one good model. Condition 1 presents thisrestriction y.

Condition 1. y � 11�p

hpmHx� �mH

nHcH

i

Utilizing Lemma 1 and Lemma 2, Proposition 1 demonstrates a sufficientcondition for the potential for conflict to be increasing in mH .

Proposition 1. Suppose Home and Foreign are oligarchies. If inequality 1holds for p (sufficient strength), Condition 1 holds (sufficient private goods),and mH

mF 1 (relative oligarchy/transitional democracy), then the potential for

conflict is strictly increasing in mH .

The key implication of Proposition 1 is that, on its own, expanding the elitehas an ambiguous direct effect on the potential for conflict in crisis bargaining.While the expansion of the elite can alleviate the potential for conflict whenmH is high relative to mF , Proposition 1 demonstrates that it is also possiblethat democratization actually increases the potential for conflict. In particular,this is the case when Home is sufficiently strong so as to get nonzero offers,the amount of private goods is nontrivial, and Home starts out relatively lessdemocratic than Foreign.

The intuition is that when these conditions are satisfied, increasing thesize of the elite increases Home’s demands when Home is a strong type whileincreasing them by less when Home is a weak type. Moreover, mH does notfactor into Foreign’s utility in the event that Foreign wins a war. These fac-tors combine to imply that when Home is initially less democratic, increasingthe size of the elite causes a decrease in the value of the risk free proposal forForeign while weakly increasing the value of the risky proposal.

17

2.3 Oligarchy versus Democracy

In this section we compare the potential for conflict in oligarchies versus democ-racies. An immediate implication of comparing the two institutional setting isthat as � shrinks, the potential for conflict in oligarchies is increasing while thepotential for conflict in democracies is static. Hence, oligarchies with institu-tions implying a low �, will have a potential for conflict that is high relative toa state that is similar in every way, except that it has democratic institutions.This type of effect is a very old idea going back to Kant (2006). Proposition2 states this formally.

Proposition 2. If inequality 1 holds for p, then decreasing � strictly increasesthe potential for conflict. Democracies are unaffected by changes in �.

Besides differing costs, oligarchies and democracies also differ in their val-uation of public versus private goods. The major difference being that themedian voter values public goods, but not private goods while decision makersin oligarchies care about both goods. Hence, the total amount of private goodsrelative to the total amount of public goods to be determined by internationalbargaining is potentially critical in determining whether oligarchies or democ-racies are more conflict prone. In order to elucidate this effect, Proposition 3characterizes the impact of increasing the amount of private goods relative topublic goods on the potential for conflict in democracies and oligarchies.

Proposition 3. Suppose Foreign is an oligarchy, then

1. Increasing the amount of private goods, y, decreases the potential forconflict when Home is a democracy.

2. If inequality 1 holds for p (sufficient strength), Condition 1 holds (suffi-cient private goods), and mH

mF 1 (relative oligarchy/transitional democ-

racy), then increasing the amount of private goods, y, increases the po-tential for conflict when Home is an oligarchy.

3. If inequality 1 holds for p (sufficient strength) and x � 11�p

hp ymH

� � cHnH

i

(sufficient public goods), then there exists an ⌘ > 1 such that for all mH

mF>

18

⌘, increasing the amount of private goods, y, decreases the potential forconflict when Home is an oligarchy.

Proposition 3 states that as the amount of private goods, y, increases,democracies become less conflict prone while oligarchies often become moreprone to conflict. Hence, when private goods are a relatively large proportion ofwhat is being bargained over, democracies are more peaceful than oligarchies.Alternatively, as private goods decrease relative to public goods, democraciesbecome relatively more conflict prone.

The intuition behind the result is straightforward. As the amount of privategoods increases, Foreign is more and more willing to pay a democracy offin public goods since Foreign is able to keep a greater amount of privategoods for itself (Proposition 3.1). A similar effect holds when Home is not atrue democracy, but is sufficiently more democratic than Foreign (Proposition3.3). On the other hand, when Home is relatively oligarchy, the risky proposalbecomes more attractive as the amount of private goods increases (Proposition3.2). This is because for each additional unit of total private goods, Foreign

keeps a greater proportion when facing a weak type than a strong type. Hence,as the amount of private goods increases, Foreign becomes more and morewilling to gamble on the risky proposal.

This result is contingent on Foreign valuing private goods. If Foreign

does not value private goods (perhaps because Foreign is also a democracy),the potential for conflict will be invariant in the level of private goods whenHome is a democracy. In this case, our model is qualitatively the same as astandard crisis bargaining model (Fearon 1995). When Foreign is a democ-racy, but Home is an oligarchy, increasing the amount of private goods willactually decrease the potential for conflict. The general implication being thatmixed dyads are relatively peaceful when there are sufficient private goods topay off elites within the oligarchy while allowing the democracy to retain aconsequently higher proportion of the public good. When oligarchies bargainwith other oligarchies, increasing the amount of private goods only exacer-bates the situation, while the amount of private goods is irrelevant for twodemocracies bargaining with one another.

19

Proposition 4 considers how shifting from an oligarchy to a democracy(what we call liberalization) affects the potential for conflict in comparisonto how expanding the elite to capture the median affects the potential forconflict.11

Proposition 4. Suppose Foreign is an oligarchy, then

1. There exists a y⇤, such that for all y > y⇤, liberalization decreases thepotential for conflict.

2. If inequality 1 holds for p, Condition 1 holds, and nF > nH

2 , then thereexists a m̂F such that for all mF > m̂F , expanding the elite to capturethe median increases the potential for conflict.

Intuitively, Proposition 4 demonstrates that while certain types of democ-ratizations, namely the full liberalization of the state from an oligarchy to ademocracy, may decrease the potential for conflict, limited democratization,even when the decision making class is expanded greatly, can increase thepotential for conflict.

That part 2 of Proposition 4 holds is a consequence of Proposition 1. Home

captures the median when mH increased to m0H where m0

H � nH/2. If mF issufficiently large, then mH will be increasing the potential for conflict for thisentire range or a significant portion of it. When this is the case, the conflictinducing effects of expanding the elite when mH/mF 1 dominate the conflictreducing effects that occur when mH/mF > 1.

Part 1 of Proposition 4 follows from allowing private goods to be sufficientlylarge. When liberalization occurs, Foreign gets to keep the private goods thatit previously used to pay off the elite in Home. It is possible that this comes atthe cost of paying more public goods to Home. However, if the total amountof private goods is sufficiently large, then the loss of some public goods isoutweighed by the gain in private goods. Again, note that this is contingent

11An example of expanding the elite to capture the median might be as follows. Considera society with three ethnic groups that is initially controlled by a single group. In somecases, the elite group may be able to capture the median by expanding elite status to onegroup, but not the other.

20

on Foreign being an institutional type whose decision makers value privategoods.

3 Taxation

In this section, we expand on the baseline model to allow for redistributivetaxation. Consider the oligarchy case where E has the power to accept orreject bargains. However, members of the out group, O, have a limited amountof power to demand some percentage of the private goods offered to Home

through a redistributive tax rate ⌧ 2 [0, 1]. This ability to tax is meant torepresent various ways political institutions can allow out groups to constrainthe decision making of the elite. The larger the tax rate, the more power O

has to impact policy.In this case, a member of E in Home has the following utility in peace for

a bargain (x, y)

uE (x, y) = x+

y(1�⌧)mH

while a member of O’s utility for the same bargain is

uO (x, y) = x+

y⌧nH�mH

.

As seems natural, we assume that nH �mH > mH .In war, when Home is strong, E receives

wE = p

✓x+

y (1� ⌧)

mH

◆� �

cHnH

,

while O receiveswO = p

✓x+

y⌧

nH �mH

◆� cH

nH.

Under this setup we derive the following results

Proposition 5. If inequality 1 holds for p, Condition 1 holds , and mH

mF 1�⌧ ,

then

21

1. In peace, y⇤ and hence uO is increasing in ⌧ .

2. The potential for conflict is increasing in ⌧ .

Proposition 5 demonstrates the effects of increasing the tax rate, ⌧ . Thefirst effect is that y⇤ is increasing in ⌧ as the elites are forced to bargain harderin order to get the same amount of utility. Hence, the out group benefits intwo ways from taxation. Increased taxation directly increases the proportionof private goods the out group receives while also incentivizing the elites todemand a higher portion of the private good pie.

The second effect demonstrates the darker side of increased taxation power.As ⌧ increases E may bargain too hard, inducing conflict more frequently as⌧ increases. Hence, the out group may wind up losing out if their taxationpower becomes too high and induces conflict. When this is the case, the outgroup would counterintuitively prefer institutions that put greater limits ontheir ability to redistribute private goods.

Finally, the third effect is that increasing ⌧ decreases the range for whichthe potential for conflict is increasing in ⌧ . That is, once ⌧ reaches a highenough level, the price of paying Home in private goods gets too high andForeign switches to public goods. From that point on, further increases in ⌧

only serve to reduce the elite’s war value. Therefore, the potential for conflictmay begin to decrease in ⌧ once it reaches a high enough level.

4 Political Bias and War

Building on the taxation section, we are able to extend our model in a waythat provides a microfoundation for the concept of political bias in Jacksonand Morelli (2007). In that paper, a leader (or more generally here, the elite)makes a decision over whether or not to accept a bargain or go to war withsome bias over how the acquisition of resources are valued in peace and war.For instance, a leader (or elite member) who is biased toward war is able tocapture a higher percentage of resources after a successful war than from apeaceful bargain. In our model, it is easy to incorporate this notion as the out

22

group having different taxation technologies available in peace versus war. Inthis case, everything is the same as in the taxation section, except that in war,a different tax rate, ⌧ 0 2 [0, 1] is applied so that war utilities become

wE = p⇣x+

y(1�⌧ 0)mH

⌘� � cH

nH

and

wO = p⇣x+

y⌧ 0

nH�mH

⌘� cH

nH.

It follows immediately from Jackson and Morelli (2007) that, under thissetup, war is possible even when Home’s strength type is known for certain.This war result holds for certain parameters when ⌧ 0 becomes small. When⌧ 0 is low, members of E have a strong incentive to go to war since they cankeep a higher percentage of the private goods pie gained through war than ofthose gained through peaceful bargaining. When ⌧ 0 is low enough, it is pos-sible that E’s incentive to capture goods through war eliminates the peacefulbargaining space, inducing war with certainty. An important point to note isthat this effect is qualitatively different from changes in �. While low � levelscan increase the potential for war when Home’s type is unknown, they neverinduce war when Home’s type is known since there always exists a non-emptybargaining space.

Going beyond the Jackson and Morelli (2007) result, we can derive resultson how ⌧ 0 effects the potential for conflict in the incomplete information game.

Proposition 6. If inequality 1 holds for p and Condition 1 holds, then

1. In peace, uO is decreasing in ⌧ 0.

2. The potential for conflict is decreasing in ⌧ 0.

In this case, lowering the out groups ability to capture rents in war (whichis analogous to increasing E’s war bias) causes E to bargain harder, increasingO utility. However, as E begins to bargain too hard as ⌧ 0 becomes small, thepotential for conflict increases. Note that these effects are the potentially the

23

opposite of the tax described in the previous section, which was not contingenton whether the tax was collected in peace or after a war.

Taken together, Propositions 5 and 6 are quite striking. Institutions thatincrease the level of redistribution in peacetime, but decrease it during a war,increase a state’s bargaining power. However, these kinds of institutions alsomaximize the potential for conflict. Propositions 5 and 6 also demonstrateexactly which aspects of redistributive institutions increase the potential forpeace. Namely, allowing elites to retain high levels of private goods in peace-time, but depriving them of the spoils of war, minimizes the potential forconflict.

5 Empirical Evidence

Although our model is very simple, it does generate specific and transparentpredictions about how the nature of political institutions influences the out-comes of international crisis bargaining. In this section, we explore three spe-cific predictions of our model about empirical relationships that can be testedon observable data on territorial disputes. We focus on the implications fromProposition 3, that changes in the amount of private goods can influence theprobability of conflict as the institutional structure of the participating statesvary. Specifically we test whether the presence of natural resources reducethe probability of violent military action between democracies and autocraticregimes and how differences in the base of support for autocratic leaders in-fluences the probability of military fatalities between these pairs of countries.Though there are many results frrm our analysis we could try to test, our focuson these particular results is justified, we argue, because they are empiricallymeasurable and unique to our model.

5.1 Data

We draw our observations from the Issues Correlates of War Database onterritorial disputes between 1816 and 2001 (Frederick et. al 2017). The data is

24

in the form of dyadic territorial claim panels. A territorial claim occurs when:there is an explicit competing claims to territorial sovereignty, the competingclaims concern specific territory (vague statements made without specifying aspecific geography do not qualify), and the claim is made by official governmentrepresentatives who are authorized to make foreign policy.

Each territorial claim is identified as a relationship between two countries,called the challenger and target, where the challenger has made a claim onsome territory currently under the administrative control of the target. Asingle territory may be involved in multiple claims, as in the case of variousislands in the South China Sea. Each year of our data has an indicator markingthat a particular dispute has a militarized conflict that leads to casualties. Inthe data, of the 13,673 conflict years, about 2% (296) have fatalities.

The database also records a number of factors relating to the territory. Wecan know if the claimed territory is known or believed to have valuable naturalresources, if it is strategically located, if it is populated or uninhabited, if it is“homeland territory”, if the territory is ethnically tied to a claiming country,or if there has been a historical transfer of the territory from one challengerto the target in the last 200 years. In our analysis we are interested in theeffect of private goods because, in many cases, it is the rights to monetize andshare in these kinds of resources that makes up the private component of theinternational negotiations in territorial disputes.12

To measure institutions we use two sources. For the first prediction ofProposition 3, that democratic targets of oligarchic or autocratic challengerswill have more peaceful territorial disputes, we use the Polity IV databasedemocracy index. This data gives coverage over the same time series and allowsus to distinguish between democracies, intermediate regimes, and autocraticoligarchies. The Polity IV data is widely used in the study of political regimes.Here, we use the standard cut of a composite polity score of 7 to separatedemocracies from non-democracies.13

12Though these are not the only sources of private benefit. Sometimes it can be aboutinvestment, commercial, or transportation rights.

13Results are robust to considering different cut offs for democracy and intermediateregimes.

25

For the other two hypotheses from Proposition 3, that oligarchic regimeswith different bases of support will be more or less conflict prone, we useWeek’s (2012) data on autocratic regimes. We measure oligarch regimes aseither personalistic or machine. This data runs from 1946-2001.

Personalistic regimes may be civilian or military, but are always autocraticregimes where one individual controls the instruments of government. Exam-ples would be the Kim Jong Il, Stalin, or Idi Amin. Machine systems, on theother hand, are non-democracies that have a wider elite base. The elite maybe civilian, like in a single party system, or it may be a military elite, as in ajunta. Examples of the former might be the PRI in Mexico or the while thelater are like the Junta led by Jorge Rafael Videla, Emilio Eduardo Massera,and Orlando Ramon Agosti in Argentina.

In what follows we look at how the differences in the mean rate for a ter-ritorial claim to escalate to violent military action changes in the presence ofnatural resources in order to test the usefulness of our simple model for think-ing about the international effects of institutional variation within countries.

5.2 Results

Our first result goes after the implication that, for foreign oligarchies, theprobability of a conflict between it and a democratic target is lower if resourcesare present. To test this prediction we analyze the subsample of territorialdisputes where the challenger is a non-democratic and compare means acrossgroups. To this end, we run a regression of the presence of fatalities frommilitarized violence on interacted indicator variables for the democratic natureof the target and the presence of natural resources, where we then interact thepresence of natural resources and the target’s institutional type to estimatethe difference effect.

The difference of means is presented in Figure 1.14 Of the 13,673observations in the database, 10,229 are observations where the challenger isnon-democratic. Interpreting the findings in the figure is straight forward

14Table 3 in Appendix B presents our results.

26

Figure 1: Resources and Democratic Targets

These effects are relative to a territorial dispute between two non-democracies for which there are no natural

resources present. Base rate of military fatalities in the sample of 13,329 dispute years between 1816-2001

is 0.022. Regression tables can be found in Appendix B.

because our measures are indicator variables. When the target isnon-democratic and natural resources are present, the two countries are morelikely to have a conflict with fatalities than when resources are present. Forthis comparative static the prediction of our theory depends onunmeasurable parameters in the data. When there are no resources present,then our model predicts there is no effect of the target’s regime type on thelikelihood of fatalities. However, when the target is democratic and there areresources, our theoretical result predicts a decrease in conflict andempirically we find this decrease to be substantial.

Our second analysis looks at the predictions of our theory regarding theavailability of private goods and conflict between different types of oligarchic

27

Figure 2: Effect of Resources on Conflict between Elite Governed Countries

These effects are relative to a territorial dispute for which there are no natural resources present. Base rate

of military fatalities in the sample of 13,329 dispute years between 1816-2001 is 0.022. Regression tables

can be found in Appendix B.

28

regimes. Proposition 3 parts 2 and 3 show that if the challenger has a largerelite among whom private benefits must be shared and is facing a regimethat is more personalistic, then the probability of war is increasing in thepresence of private goods, here natural resources. If, however, the challengeris a personalist regime, and therefore has a smaller base of elite support thatshares in the private good, but the target is a political machine, then theprobability of conflict should decrease when private goods (natural resources)are available.

Figure 2 shows the results on these two subsets of the ICOW database.There are 245 territorial claims with machine challengers of personalist targetsand 136 with personalist challengers of machine targets. The result presentedin Figure 2 is then the difference in the means between the claims with nat-ural resources and the claims without natural resources with 95% confidenceintervals. The results predict that the probability of conflict increases by0.12 in the presence of resources when the territorial claim originates with anoligarchic machine but decreases by 0.05 when the claim comes from a per-sonalistic oligarchy. These effects are large given that the rate of militarizedfatalities between all pairs of oligarchies with conflicting territorial claims from1946-2001 is 0.03.

6 Conclusion

In many instances, the nature of the goods at the center of international dis-putes have mixed elements. Some of the components are public goods likestate territory, national security, or policy adjustments. Others are privategoods that elites can consume if offered. In such a world the nature of domes-tic politics can be important for both determining a country’s incentives to goto war and who really benefits from peace. Similarly in such situations, whopays the cost of war is also important.

In this paper, we modified the standard incomplete information crisis bar-gaining model in two ways to explore the implications of the these facts. Weallowed for countries to bargain over these mixed goods and we allowed the

29

countries to be made up of two groups (elites and citizens). Both groups ben-efited from public goods, while only the elites had access to the private goods.This led to a series of results on how the internal institutional makeup of Home

impacts the potential for conflict. Counterintuitively, while the full liberaliza-tion of a oligarchy (limited democracy) can reduce the potential for conflict,half-measures often exacerbate the potential for conflict. For instance, ex-panding the decision making class (the elite) and increasing the redistributivepowers of the citizens (out group) often increases the potential for conflict.

There are three immediate extensions of the model. First, it is easy toimagine that the two countries are bargaining over not just public and privategoods, but a variety of goods that impact the utility of a country’s internaldivisions differently. This is especially relevant when bargaining over the gainsfrom trade. Second, the internal structure of Home presented here is quitereduced form. A more sophisticated model of internal voting and taxationmight capture subtleties missed here. In particular, when the level of strengthis endogenous to taxation (as in Chapman, McDonald, and Moser 2015), theredistributive and strength increasing properties of taxation may combine tointeresting effect. Third, a dynamic extension where an oligarchy expandedthe elite or liberalized over time would likely demonstrate that such a processinduces conflict in a limited commitment environment.

Finally, we note that our model may be applied to situations beyond inter-national conflict bargaining. On August 24, 2016, the Colombian governmentsigned an accord with FARC (Revolutionary Armed Forces of Columbia) toend a conflict that had endured for over 50 years. Less than two months later,the Colombian people voted down a referendum supporting the accord. Evenin a civil conflict, the groups that make up each side may have sharply differentinterests in a peace deal. Beyond conflict, the United Kingdom’s June 2016vote to leave the European Union demonstrated how the political divergencesof groups within a state can lead to the costly breakdown of internationalagreements. While such explicit cases may be infrequent, our study suggeststhat the interaction between mixed goods and domestic institutions may be acritical force in determining the success or failure of international bargaining

30

in a wide variety of circumstances.

31

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Appendix A (For online publication)

Lemma 1

Proof. First consider the case where Home is a democracy. When this is thecase, Foreign chooses (x⇤, y⇤) as the solution to the following programmingproblem

maxx,y (x� x) +⇣

y�ymF

⌘

subject to x � px� cHnH

x � 0, y � 0

It is then immediate to calculate the solution as

x⇤= px� cH

nH.

Clearly, x⇤ < x. So x⇤ is always feasible when the right hand side of theequation is positive. However, Foreign cannot transfer a negative amount ofx to H, so there is a corner case where x⇤

= 0 whenever

px� cHH

0

x cHpnH

Therefore, when Home is a democracy, we can summarize equilibrium bargainsas

(x⇤, y⇤) =

8<

:0, 0 x cH

pnH

px� cHnH

, 0 x > cHpnH

Now consider the case where Home is an oligarchy. Foreign chooses

37

(x⇤, y⇤) as the solution to the following programming problem

maxx,y (x� x) +⇣

y�ymF

⌘

subject to x+

ymH

� phx+

ymH

i� � cH

nH

x � 0, y � 0

Generically, there is no interior solution. Foreign maximizes its utility bycalculating a value akin to the “bang-per-buck” of paying Home off in publicgoods versus private goods. Or, how much utility is lost to Foreign by pro-viding one additional unit of utility to Home through either private or publicgoods.. So, here, bang-per-buck of public (private) goods is the marginal util-ity to Foreign with respect to public (private) goods divided by the marginalutility to Home with respect to public (private) goods. The marginal utilityto Home functions like a “price” to Foreign for relaxing Home’s constraint.

The bang-per-buck for x to F is �1. For y, the bang-per-buck to F is

�1mF1

mH

or rearranging

�mH

mF.

F should therefore only give the good that minimizes its loss of utility. So,F gives H all x when

mH

mF> 1.

This leaves us with five cases:Case 1: x = 0, y = 0

Similarly to the democracy case, it may be that the optimal offer to H is0. This occurs when the RHS of the constraint function is less than or equal

38

to 0. Or,

phx+

ymH

i� � cH

nH 0

x �cHpnH

� ymH

Otherwise, we must be in one of the other four cases.Case 2: x = 0, y > 0

ymH

= phx+

ymH

i� � cH

nH

y⇤ = p [mHx+ y]� �mH

nHcH

So, in this case, y is increasing in mH when px > � cHnH

or x > �cHnHp . But this is

always holds in this case, otherwise, we are in Case 1. This case occurs whenmH mF , x > �cH

pnH� y

mH, and there is sufficient y so that y⇤ y. This last

condition holds when

y � p [mHx+ y]� �mH

nHcH

y � 11�p

hpmHx� �mH

nHcH

i.

Case 3: x > 0, y = 0:

x⇤= p

hx+

ymH

i� � cH

nH

So x is always decreasing in mH . This case occurs when mH > mF , x >�cHpnH

� ymH

, and there is sufficient x so that x⇤ x. This last condition holdswhen

x � phx+

ymH

i� � cH

nH

x � 11�p

hp ymH

� � cHnH

i.

39

Case 4: x > 0, y = y

x+

ymH

= phx+

ymH

i� � cH

nH

x⇤= px+ (p� 1)

ymH

� � cHnH

So, always increasing in mH since p < 1. This case occurs when mH mF , x > �cH

pnH� y

mH, and there is not sufficient y so that y⇤ y, or y <

11�p

hpmHx� �mH

nHcH

i.

Case 5: x = x, y > 0

x+

ymH

= phx+

ymH

i� � cH

nH

y⇤ = (p� 1)mHx+ py � �mH

nHcH

So, non-increasing in mH when (p� 1) x� � cHnH

� 0 =) p � �cHnHx +1, but

this is impossible since p 1, therefore, this case is always decreasing in mH .Therefore, when Home is a oligarchy, we can summarize equilibrium bar-

gains as

(x⇤, y⇤) =

8>>>>>>>>>>>>>>>>>>>>>><

>>>>>>>>>>>>>>>>>>>>>>:

0, 0 x �cHnHp �

ymH

0, p [mHx+ y]� �mH

nHcH x > �cH

nHp �y

mH, y � 1

1�p

hpmHx� �mH

nHcH

i,

mH mF

px+ (p� 1)

ymH

� � cHnH

, y x > �cHnHp �

ymH

, y < 11�p

hpmHx� �mH

nHcH

i,

mH mF

phx+

ymH

i� � cH

nH, 0 x > �cH

nHp �y

mH, x � 1

1�p

hp ymH

� � cHnH

i,

mH > mF

x, (p� 1)mHx+ py � �mH

nHcH x > �cH

nHp �y

mH, x < 1

1�p

hp ymH

� � cHnH

i,

mH > mF

Finally, since war is costly, we need not worry about violating F ’s constraintsat the same time as Home’s constraints.

40

Lemma 2

Proof. uF is strictly decreasing (increasing) in mH when the size of the offerto Home is strictly increasing (decreasing) in mH . The assumption that in-equality 1 holds, eliminates the case of nonzero offers (Case 1 from Lemma1). From Lemma 1, mH

mF 1 in cases 2 and 4. In these cases, Foreign’s offer

value is strictly increasing in mH . Therefore, uF is strictly decreasing in thesecases. Additionally, from Lemma 1, mH

mF> 1 in cases 3 and 5. In these cases,

Foreign’s offer value is strictly decreasing in mH . Therefore, uF is strictlyincreasing in these cases. This exhausts all cases.

Proposition 1

Proof. Consider the case where the weak type of Home receives a nonzerooffer. The risk free proposal gives the elites in Foreign a payoff of

x+

y�hp[mHx+y]��

mHnH

cHi

mF

while the risky proposal gives a payoff of

q

x+

y�hp0[mHx+y]��

mHnH

cHi

mF

�+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Subtracting the risk free proposal from the risky proposal and then takingthe derivative with respect to mH gives

q�⇣p0x� �cH

nH

⌘

mF�

�⇣px� �cH

nH

⌘

mF

px� �cHnH

mF� q

p0x� �cHnH

mF.

This value is always positive by the nonzero offer condition for the strong typeand since q < 1 and p > p0.

When the weak type of Home receives a zero offer, mH no longer appearsin the risky proposal payoff. So, subtracting the risk free proposal from the

41

risky proposal and then taking the derivative with respect to mH gives

px� �cHnH

mF

which is positive by the nonzero offer condition for the strong type.

Proposition 2

Proof. Regardless of the case, so long as Home receives a nonzero offer whena strong, the derivative with respect to � of the risk-free proposal is

mH

nHmFcH .

In the case that Home receives a zero offer in the risky proposal, thensubtracting the the risk free proposal from the risky proposal and then takingthe derivative with respect to � always gives a negative value.

In the other case where Home receives a nonzero offer under the riskyproposal, then taking the derivative with respect to � of the risky proposalalways gives a value of

q mH

nHmFcH .

(Note: � does not appear in the Foreign’s cost function. We could imaginethat Foreign does in fact have a variable similar to � in its cost function, so�F for instance. However, this simply adds a parameter that does not affectthe analysis here.) Finally, this implies that subtracting the risk free proposalfrom the risky proposal and then taking the derivative with respect to � givesa negative value if

q mH

nHmFcH � mH

nHmFcH

which is always negative since q < 1. Hence, increasing � increases the poten-tial for conflict.

42

Proposition 3

Proof. Part 1:War can occur when Home is a democracy only when Foreign has to

make a nonzero offer and the risky proposal is more attractive than the risk-free proposal. The risk- proposal gives Foreign a value of

hx�

⇣px� cH

nH

⌘i+

ymF

while the risky proposal gives a payoff of

qhhx�

⇣p0x� cH

nH

⌘i+

ymF

i+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Subtracting the risk free proposal from the risky proposal and then takingthe derivative with respect to y gives a negative value if

q 1mF

+ (1� q) (1� p) 1mF

� 1mF

< 0.

The value on the LHS is strictly less than

q 1mF

+ (1� q) 1mF

� 1mF

,

which equals zero. Therefore, the effect of increasing y is to always make warless attractive.

Part 2:When the conditions of the proposition are met, the risk free proposal gives

the elites in Foreign a payoff of

x+

y�hp[mHx+y]��

mHnH

cHi

mF

while the risky proposal gives a payoff of

q

x+

y�hp0[mHx+y]��

mHnH

cHi

mF

�+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

43

Subtracting the risk free proposal from the risky proposal and then takingthe derivative with respect to y gives a positive value if

qmF

� qh

p0

mF

i+ (1� q) 1�p

mF� 1

mF+

pmF

> 0

q�1mF

� q p0

mF� q 1�p

mF+

1mF

> 0

qmF

� q⇣

p0

mF+

1�pmF

⌘> q

mF� q 1

mF= 0

Therefore, the effect of increasing y is to always make war more attractive.Part 3:When the conditions of the proposition are met, the risk free proposal gives

the elites in Foreign a payoff of

x�hp⇣x+

ymH

⌘� � cH

nH

i+

ymF

while the risky proposal gives a payoff of

qhx�

hp0⇣x+

ymH

⌘� � cH

nH

i+

ymF

i+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Subtracting the risk free proposal from the risky proposal and then takingthe derivative with respect to y gives a negative value if

� qp0

mH+

qmF

+

(1�q)(1�p)mF

+

pmH

� 1mF

< 0

p�qp0

mH+

qp�pmF

< 0

mH

mF> p�qp0

p�qp

Note that the RHS is greater than 1 since p > p0. Set ⌘ ⌘ p�qp0

p�qp .

Proposition 4

Proof. Statement (1):First, note that the there is no potential for conflict when Foreign op-

timally makes a zero offer to a strong type democracy. Second, note thatthere exists a y high enough that inequality 1 and Condition 1 hold. Com-

44

bining these two observations, we need only examine two cases. In both casesForeign makes a nonzero offer both before and after liberalization. In thefirst case, Foreign offers Home exclusively private goods before liberaliza-tion. In the second case, Foreign offers Home exclusively public goods beforeliberalization.

Case 1:Before liberalization, the risk free proposal gives the elites in Foreign a

payoff of

x+

y�hp[mHx+y]��

mHnH

cHi

mF.

Call this value 1A. The risky proposal gives a payoff of

q

x+

y�hp0[mHx+y]��

mHnH

cHi

mF

�+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Call this value 1B.After liberalization, the risk free proposal gives Foreign a value of

hx�

⇣px� cH

nH

⌘i+

ymF

.

Call this value 1C. The risky proposal gives a payoff of

qhhx�

⇣p0x� cH

nH

⌘i+

ymF

i+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Call this value 1D. The potential for conflict before liberalization is 1B � 1A

while the potential for conflict after liberalization is 1D � 1C. Therefore, thedifference in the potential for conflict is (1B � 1A)� (1D � 1C). Rearranginggives (1B � 1D) + (1C � 1A). This value is

q

⇣p0x� cH

nH

⌘�

hp0[mHx+y]��

mHnH

cHi

mF

�+

�⇣px� cH

nH

⌘+

hp[mHx+y]��

mHnH

cHi

mF

�.

45

we can divide this value into two terms,

q⇣p0x� cH

nH

⌘�

⇣px� cH

nH

⌘

which is not positive and is constant in y, whilehp[mHx+y]��

mHnH

cHi

mF� q

hp0[mHx+y]��

mHnH

cHi

mF

is positive and increasing in y. Therefore, there exists a y0 such thathp[mHx+y0]��

mHnH

cHi

mF� q

hp0[mHx+y]0��

mHnH

cHi

mF> q

⇣p0x� cH

nH

⌘�⇣px� cH

nH

⌘.

Therefore, the potential for conflict is greater before liberalization when thisholds in this case. Define y⇤ to be greater than or equal to the maximum ofy0 and the values for y such that inequality 1 and Condition 1 hold.

Case 2:Before liberalization, the risk free proposal gives the elites in Foreign a

payoff of⇣x�

hphx+

ymH

i� � cH

nH

i⌘+

ymF

.

Call this value 2A. The risky proposal gives a payoff of

qh⇣

x�hp0hx+

ymH

i� � cH

nH

i⌘+

ymF

i+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Call this value 2B.After liberalization, the risk- proposal gives Foreign a value of

hx�

⇣px� cH

nH

⌘i+

ymF

.

Call this value 2C. The risky proposal gives a payoff of

qhhx�

⇣p0x� cH

nH

⌘i+

ymF

i+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

46

Call this value 2D. The potential for conflict before liberalization is 1B � 1A

while the potential for conflict after liberalization is 1D � 1C. Therefore, thedifference in the potential for conflict is (2B � 2A)� (2D � 2C). Rearranginggives (2B � 2D) + (2C � 2A). This value is

qh�p0 y

mH+ (� � 1)

cHnH

i+

hp ymH

+ (1� �) cHnH

i

which is always positive since p > p0 and q < 1. Therefore, the potential forconflict is greater before liberalization in this case.

Statement (2):From Proposition 1, when the conditions states in this proposition are met,

than the potential for conflict is increasing when mH

mF< 1. Let m0

H =

⌃nH

2

⌥.

Set m̂F = m0H .

Proposition 5

Proof. Foreign chooses (x⇤, y⇤) as the solution to the following programmingproblem

maxx,y (x� x) +⇣

y�ymF

⌘

subject to x+

y(1�⌧)mH

� phx+

y(1�⌧)mH

i� � cH

nH

x � 0, y � 0

This changes the calculation for bang-per-buck of y for F to

�1mF1�⌧mH

� mH

mF (1�⌧)

Therefore, F prefers to pay with private goods when mH (1� ⌧)mF .Given our assumption, then x⇤

= 0 and y⇤ = 11�⌧

hp [mHx+ y (1� ⌧)]� �mH

nHcH

i

Hence, y⇤ is increasing in ⌧ . Therefore, uO is increasing in ⌧ .

47

The risk free proposal gives the elites in Foreign a payoff of

x+

y� 11�⌧

hp[mHx+y(1�⌧)]��

mHnH

cHi

mF

while the risky proposal gives a payoff of

q

x+

y� 11�⌧

hp0[mHx+y(1�⌧)]��

mHnH

cHi

mF

�+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Taking the difference and then the derivative with respect to ⌧ , we find thatthe potential for conflict is increasing when

� q(1�⌧)2mF

hp0mHx� �mH

nHcH

i+

1(1�⌧)2mF

hpmHx� �mH

nHcH

i> 0

which is always true since p > p0 and q < 1. Therefore, the potential forconflict is always increasing in ⌧ .

Proposition 6

Proof. Foreign chooses (x⇤, y⇤) as the solution to the following programmingproblem

maxx,y (x� x) +⇣

y�ymF

⌘

subject to x+

y(1�⌧)mH

� phx+

y(1�⌧ 0)mH

i� � cH

nH

x � 0, y � 0

This changes the calculation for bang-per-buck of y for F to

�1mF1�⌧mH

� mH

mF (1�⌧)

Therefore, F prefers to pay with private goods when mH (1� ⌧)mF .Given our assumption, then x⇤

= 0 and y⇤ = 11�⌧

hp [mHx+ y (1� ⌧ 0)]� �mH

nHcH

i

Hence, y⇤ is decreasing in ⌧ 0. Therefore, uO is decreasing in ⌧ 0.

48

The risk free proposal gives the elites in Foreign a payoff of

x+

y� 11�⌧

hp[mHx+y(1�⌧ 0)]��

mHnH

cHi

mF

while the risky proposal gives a payoff of

q

x+

y� 11�⌧

hp0[mHx+y(1�⌧ 0)]��

mHnH

cHi

mF

�+ (1� q)

h(1� p)

⇣x+

ymF

⌘� cF

nF

i.

Taking the difference and then the derivative with respect to ⌧ 0, we find thatthe potential for conflict is decreasing when

q p0ymF (1�⌧) �

pymF (1�⌧) < 0

which is always true since p > p0 and q < 1. Therefore, the potential forconflict is always decreasing in ⌧ 0.

49

Appendix B (For online publication)

This appendix contains some descriptive facts about the ICOW data and thedummy variable regressions that produce the difference in means plots above.

Table 1: Territorial claims by region

Table from Frederick et. al. (2017) “The Issues Correlates of War Territorial Claims Data, 1816-2001”

Journal of Peace Research.

50

Table 2: Salient issues of claimed territories

Table from Frederick et. al. (2017) “The Issues Correlates of War Territorial Claims Data, 1816-2001”

Journal of Peace Research.

51

Table 3: Conflict in Territorial Disputes

Dependent variable:

Dispute Fatalities

Natural Resources 0.009⇤⇤(0.003)

Democratic Target �0.002(0.004)

Democratic target ⇥ Natural Resources �0.013⇤⇤(0.006)

Constant 0.019⇤⇤⇤(0.002)

Observations 10,229R2 0.001Residual Std. Error 0.142 (df = 10225)F Statistic 4.544⇤⇤⇤ (df = 3; 10225)

Note: ⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01

52

Table 4: Resource effect for machine challengers and personalist targets

Dependent variable:

Dispute Fatalities

Resources �0.051⇤⇤(0.023)

Constant 0.059⇤⇤⇤(0.016)

Observations 245R2 0.020Adjusted R2 0.016Residual Std. Error 0.177 (df = 243)F Statistic 5.080⇤⇤ (df = 1; 243)

Note: ⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01

53

Table 5: Resource effect for personalist challengers and machine targets

Dependent variable:

Dispute Fatalities

Resources 0.124⇤⇤(0.054)

Constant 0.036(0.042)

Observations 136R2 0.038Adjusted R2 0.031Residual Std. Error 0.310 (df = 134)F Statistic 5.267⇤⇤ (df = 1; 134)

Note: ⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01

54