SOLVING THE GAME
We solve the game by finding subgame perfect equilib- ria, starting at the bottom of the game tree and working sequentially backward through each decision. As such, the analysis of each stage is done with the knowledge of actors’ anticipated responses in subsequent decisions. Having already examined reselection above, we move to the preceding decision: the level of resources dedi- cated to prosecuting the war.
If attacked, the leader of B chooses how many of his available resources, RB, to dedicate to the war effort:
gB E [0, 1]. The advantage of spending more on the war is that he improves B’s prospects of victory, but trying hard also involves risks. By trying harder, B’s leader reduces the amount of resources available to reward his supporters through private goods. Political institutions influence the effort decision because they determine the relative importance for political reselec- tion of saving resources to use as private goods versus increasing the odds of military victory by spending those resources on the war effort. Let Y(gB) represent the expected payoff of B’s leader from dedicating gB of the available resources to the war, where PB(9B) is the
12 One might argue that the value of remaining in office, P, is a function of regime type. As Goemans (1995) points out, being ousted is more often fatal for autocrats than democrats. Our assumption, however, is that the primary goal of all leaders is to keep their job. Given this, the principal, component in every leader’s objective function is reselection.
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An Institutional Explanation of the Democratic Peace December 1999
probability that nation B wins given an effort level of
gB. This probability of victory also depends upon A’s effort and the military balance, but since we are currently focusing on B’s decision, we suppress this notation. Similarly, we suppress all unnecessary sub- scripting:
R Y(gB) =pNW) -k + (1-gB) –
+ P(PB(gB)F VB + (1 – gv)
+ (1 -P(gB))F(lB+ (1-gB)
where VB = 1 – k – RBISB + PB and ‘B = -k – RB/SB + P1B
The term PB(gB) – k refers to the expected value of the war to the nation as a whole. (1 – gB) RIW is the leader’s share of the private goods rewards. The final term, T(pB(gB)F(VB + (1 gB) RIW) ? (1 P(gB))F(lB + (1 – gB) RIW)), is the product of the value of officeholding, P, and the expected probability of surviving in office. This expected probability is made up of two components. The first,PB(gB)F(VB + (1 – gB) RIW), is the probability of victory (PB(gB)), multiplied by the probability that B’s leader survives in office given victory, F(VB + (1 – gB) RIW). The second component, (1 – p(gB))F(lB + (1 – gB) RIW), is the probability of military defeat (1 – p(gB)), multiplied by the probability that B’s leader survives in office given defeat, F(lB + (1 – gB) RIW).
Leaders choose the effort level that maximizes their expected payoff. In general, the larger the winning coalition, the greater is this optimal effort level. This leads to our substantive conclusion that democrats try harder in wartime than do autocrats. Before we explain the origins of this result, it is important to add a qualifier. In some cases, the outcome of the war may be so important relative to private goods that all leaders, whatever their domestic political institutions, try all out to win. At the other extreme, the salience of the war may be sufficiently low that no political arrangements induce additional effort. Between these extremes, how- ever, it is large winning coalitions that induce high effort levels and small coalitions that induce the hoard- ing of resources for subsequent distribution as private rewards to the winning coalition.
The game reveals that large winning coalitions en- courage leaders to dedicate additional resources to the war effort. As for all the technical results, the formal proof is in the Appendix. The key insight concerns how coalition size influences the importance of private goods as a means of rewarding supporters. As leaders increase their level of effort during a war, they increase the probability of victory. A military victory benefits everyone in nation B, including members of the win- ning coalition. The marginal benefit of increased effort is independent of political institutions, since everyone benefits from the policy success, whether leader, mem- ber of the winning coalition, member of the selector-
798
ate, or part of the disenfranchised portion of society. Yet, increased effort comes at the expense of having fewer resources with which to provide private goods for supporters.
Resources not spent on the war effort go to the winning coalition in the form of private goods. The value of these private goods depends upon how many people must be rewarded. Each supporter’s share of the private goods is RIW. As the leader allocates resources to the war effort, he reduces the private goods rewards for his supporters. The rate at which increased effort diminishes supporters’ benefits de- pends upon W. When the winning coalition is small, each member’s share of the resources is high. Given these concentrated benefits, increased war effort dras- tically reduces the utility of members of the winning coalition. In contrast, when W is large, each member receives only a small share of the private goods in the first place. Thus, when the winning coalition is large, the reduction in supporters’ utility from having re- sources channeled into the war effort, instead of being retained as private benefits, is small. It is incentive compatible with a leader’s goal of remaining in office to maximize his supporters’ utility. In terms of the sup- porters’ rewards, the cost of improving the probability of victory increases as the winning coalition gets smaller. Thus, the marginal benefit of increased ef- fort-the increase in the probability of victory-is independent of political institutions but the cost of increased effort is dependent on those institutions. To make the institutional comparison as stark as possible, consider the following limiting case.
Suppose a leader chooses between making an all-out effort that guarantees victory (gB = 1 andPB (1) = 1) and no additional effort at all, even though this makes defeat inevitable (gB = 0 and PB(O) = 0). The expected payoff of a leader who makes the all-out effort
is YB(gB = 1) = 1 – k + TF(VB), where VB = 1 – k – RB/SB + P1B. Alternatively, by making no addi- tional effort, the leader receives YB(gB = 0) = -k + RIW + PF(lB + RIW), where ‘B = -k – RB/SB + P1B. Each of these equations has terms relating to the leader’s direct rewards and terms relating to the pros- pects of reselection. We examine these components separately.
In terms of direct rewards, an all-out effort gets the leader a payoff of 1 – k as opposed to no additional effort, which generates a direct payoff of -k + RIW. Therefore, if the winning coalition is larger than R, then the leader makes an all-out effort (W > R). Although the direct benefits are illustrative of why leaders with large W try hard, we think of our argument as predominately reselection driven. The reselection related rewards associated, respectively, with an all-out effort and no additional effort are TF(VB) and TF(lB + RIW). Since VB = 1 – k – RB/SB + pi and
‘B = -k – RBISB + p, and since F(.) is an increasing function, the all-out effort term is greater than the no-effort term when 1 > R/W. Again, in this limiting case, leaders make an all-out effort to win only when W > R. Otherwise, leaders hoard their resources for private goods provision and make no additional effort,
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American Political Science Review Vol. 93, No. 4
even though military defeat is inevitable. Such leaders could improve their chances of victory by trying harder, but this is not incentive compatible with their desire to stay in office.
Thus far we have shown how political institutions affect the amount of resources dedicated to the war effort for B. Similar logic applies for A. Although A’s leader’s decision calculus is slightly more complicated, because she must anticipate B’s effort level, the same motivations persist. Again, the larger A’s winning coalition, the less important private goods become relative to foreign policy success. Therefore, all else being equal, the larger the winning coalition, the more resources A dedicates to the war effort.13
The game shows that democratic leaders, because they require large winning coalitions, try harder in war than do autocrats, who only need support from a small coalition to stay in office. One might think that auto- crats have an interest in fighting hard to protect the pool of resources they need to distribute as private goods, but to stay in office they must only provide more than their challenger can credibly promise. The chal- lenger cannot promise to distribute any resources that have been lost as a consequence of defeat in the war. Therefore, the incumbent autocrat’s comparative ad- vantage in distributing private goods and in reserving resources for that purpose remains unaltered following military defeat.
The deduction from our model that democratic leaders try harder in wars than do autocrats is, we believe, a novel theoretical result. It is interesting to note, therefore, empirical evidence that fits our deduc- tion. Bates et al. (1998, 7) report that Rosenthal
finds a “selection effect:” parliamentary governments, for example, fight fewer wars [than monarchies or autocra- cies]. They are only willing to fight wars that are profitable, and they are more willing to adequately finance, and therefore more likely to win, the wars they choose to sponsor. His conclusion is reinforced by the argument of Levi, which explores thd impact of increased democratiza- tion and industrialization upon military mobilization. Faced by an increase in both variables, she argues, gov- ernments have to invest more in convincing their popula- tions of the importance of the war and in winning their consent to fight.
That is, democratic leaders invest their effort and resources in mobilizing their societies to produce the public good of victory in war, as predicted. Lamborn (1991) presents additional direct evidence for the deduction that democracies try harder in war. He shows that, before World War I, Germany devoted a larger percentage of its gross national product to the military than did Britain or France.-Nevertheless, the latter mobilized greater resources once the war began because they were better able than the Germans to increase revenue extraction for the war effort.
We have demonstrated that the incentives of leaders
13 In general, the interaction between the effort levels of A and B depends upon the precise function mapping effort into probability of victory,p(gA, ge). For the special case in whichp(gA, gB) is the force ratio model, however, increased effort by one side elicits increased effort from the other.
in war differ as a function of their institutional settings. All else being equal, institutional arrangements pro- vide democratic leaders with greater incentives to try hard relative to autocrats. To show how this influences the empirical regularities associated with the demo- cratic peace, we now assess the incentives to negotiate rather than fight.
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