THE GUARDIANSHIP DILEMMA

The Guardianship Dilemma has plagued regimes for centuries, and has proven a tough challenge even during the last century, when militaries deposed more rulers than all other forms of political instability combined. Between 1945 and 2002, more than two-thirds of the extraconstitutional leadership changes in dictatorships were caused by coups d’etat (Svolik Reference Svolik2009). Even among all leaderships changes between 1919 and 2004, the 260 coups represent nearly 9% (Goemans, Gleditsch, and Chiozza Reference Goemans, Gleditsch and Chiozza2009).

The Guardianship Dilemma depends on the threat environment faced by states’ political regimes: stronger external threats increase the need for a powerful military, but the more powerful the military, the more dangerous it can be to the regime’s political autonomy and even its survival (Acemoglu, Ticchi, and Vindigni Reference Acemoglu, Ticchi and Vindigni2008; Feaver Reference Feaver1999; Finer Reference Finer1988; Huntington Reference Huntington1957; Svolik Reference Svolik2012).

Some exceptional studies do hold that the strong foreign threats can enhance civilian control of the armed forces. Desch (Reference Desch1999) argues that civil-military relations depend on the nature of the threat environment faced by the state. Civilians have greatest control over the military when the state faces grave international threats, and least control when the state must deal with domestic challenges. Staniland (Reference Staniland2008) adds that this relationship depends on the extent to which the regime is deemed legitimate and is adequately institutionalized. It is not, however, clear why one should expect militaries to have the least influence over policy when their services are in highest demand, or why domestic and international threats should have such dramatically different effects on civil-military relations.

Rulers who worry about their own militaries do have another option at their disposal: they can purposefully limit the strength of their armed forces, leaving them too weak to mount a coup but also making them grossly ineffective against the external threat (Feaver Reference Feaver1996; Svolik Reference Svolik2013, 154). At its most extreme, this strategy could deprive the state of a military altogether, as it has done in Costa Rica and some remote island states such as Kiribati and Samoa. More realistically though, most rulers must content themselves with finding ways of maintaining reasonably useful guardians without becoming their victims. This is what nearly all studies of civil-military relations investigate as well. Strategies discussed vary from institutional constraints involving limitations on the autonomy of military organizations and the creation of parallel armed forces, to efforts to control the disposition of military agents by providing patronage or by fostering a professional culture among military personnel (Finer Reference Finer1988; Pilster and Boehmelt Reference Pilster and Boehmelt2011; Powell Reference Powell2012; Quinlivan Reference Quinlivan1999).

A key strategy for ensuring the loyalty of militaries is to control the membership of the officer corps. The calculus for rulers in this context is straightforward: where the loyalty of potential guardians might be questionable, appoint those for whom the status quo is most profitable and who will therefore have the weakest incentives to overthrow the ruler. These privileged groups are generally among the regime’s “communities of trust” (Enloe Reference Enloe1975; Quinlivan Reference Quinlivan1999). Saddam Hussein, for instance, pulled heavily from his minority Sunni-Arab ethnoreligious group when selecting personnel for the Iraqi security apparatus (al-Marashi Reference al-Marashi2002). Scholars have often argued that making these personnel decisions on the basis of implied loyalty rather that competence can seriously erode the military effectiveness of the armed forces (Brooks Reference Brooks1998; Gaub Reference Gaub2013; Huntington Reference Huntington1957, 231–2). Some have even gone as far as suggesting that rulers might actually recruit less competent officers on purpose as a means of ensuring their loyalty (Egorov and Sonin Reference Egorov and Sonin2011). We shall have an occasion to address these particular claims.

While the logic of the Guardianship Dilemma serves as the foundation of our existing understanding of civil-military relations, one must wonder if this logic is convincing. Most of the work that explores this logic explicitly suggests that the problem turns on the ability of the rulership to commit to resource transfers or policy concessions to the military. A failure to manage the dilemma then reflects features of the social, political, or economic environment that prevent rulers from making credible promises to their guardians. Besley and Robinson (Reference Besley and Robinson2010) argue that if social conflict over public spending is serious enough, rulers cannot commit to paying a wage that is sufficiently high to ensure military loyalty when the armed forces are optimally sized. The ruler’s best response is to limit the size of the armed forces and avoid a coup altogether at the cost of having a weaker military. Leaving aside the question of why authoritarian rulers would be unable to secure sufficient resources for the military, the theory cannot explain why coups occur; after all, the equilibrium probability of a coup is zero.

Acemoglu, Ticchi, and Vindigni (Reference Acemoglu, Ticchi and Vindigni2008) do tackle this question head on. In their view, the transition from autocracy to democracy can end in a coup because the incoming democratic regime no longer needs a well-paid military for internal repression. Since the democratic government cannot credibly commit not to reform the military after it comes to power, the military has incentives to prevent the transition. It is, however, unclear why the government would not be able to make such a commitment: since the military cannot be disbanded overnight, the continuing threat of a coup should give the government enough reasons to maintain the high wages.

Other studies suggest that the problem arises from political or military elites holding private information about relevant features of the strategic environment. Informational asymmetries are common in civil-military politics, reflecting the functional differentiation in tasks between political and military actors, and are troublesome to the extent that militaries and political regimes have dissimilar preferences over outcomes (Brooks Reference Brooks2008). Svolik (Reference Svolik2013, Reference Svolik2012) argues that militaries leverage their coercive power to demand favorable policies from the regime. Coups can occur when the military believes that the ruler has reneged on their agreement, which can happen because the military lacks complete information about the government’s activities. However, even though some policies might be opaque to the military, most large issues—such as the military’s budget or regulations affecting the armed forces—tend to be highly visible and the policies themselves formulated with the active participation of the military.

In this respect, Egorov and Sonin’s (Reference Egorov and Sonin2011) assumption that the ruler’s agent (“vizier”) has private information about the threat environment is much more plausible. A competent agent is more likely to observe whether the enemy is weak, and so its incentive to betray the ruler by doing nothing to counter that threat is higher. To counter this, the ruler hires a less competent agent and since the expected loyalty is higher, the required pay is lower. The only reason the ruler does not hire total dolts is because their inability to distinguish whether the enemy is weak would cause them to squander valuable resources. One might wonder about a notion of competence that is unrelated to the agent’s ability to defeat the enemy. After all, if the enemy is more likely to prevail in the presence of an incompetent vizier, the ruler’s money-saving imperative that drives down his desire to hire a competent agent will be, well, much less imperative.

In order to assess the logic of the Guardianship Dilemma, we distill the dilemma to the most essential characteristics identified by previous research: (1) The leaders of political regimes must defend against external threats. Unfortunately for them, the guardians appointed to defend the state can also be a threat to the regime. (2) Rulers have the “power of the purse,” and manage the flow of resources to the armed forces in response to both external threats and the risk of a coup. (3) Rulers control who is charged with running the state’s armed forces, and may select these agents on the basis of both competence and their affiliation with a social, political, or economic group. (4) The more competent the military agents, the more likely they are to prevail against the external threat and against the ruler should they choose to execute a coup.

MODEL

Consider a model with two players, R (ruler of the political regime) and G (general).Footnote ¹ The status quo distribution of benefits in this society privileges certain groups over others, and may be based on ethnicity, religion, geography, or other cleavages within the state. In South Africa during Apartheid, for example, a racial divide between whites and nonwhites determined access to social, political, and economic opportunities (Thompson Reference Thompson2001). For the sake of parsimony, we abstract away from the precise nature of these cleavages and assume simply that the benefit a member of some group i derives from the status quo is $b_i\in [\underline{b},\overline{b}]$ such that $0<\underline{b}<\overline{b}<1$ . Some groups have higher status quo benefits than others, so their incentive to overthrow the regime will be weaker. Ugandan ruler Milton Obote was a Northerner, and knew that for fellow Northerners, a coup to address ethnic grievances would be unnecessary. The loyalty of the alienated Southerners, in contrast, was far more questionable (Horowitz Reference Horowitz1985, 488, 501). These status quo benefits are normalized such that 0 represents obtaining nothing (e.g., because one is dead or in prison) and 1 represents the maximal benefit of personal rule. We shall further normalize R’s competence to 1, and her security resources to 1.

The timing of the game is as follows. The ruler chooses the group from which to pick the general, b_i , his level of competence, $\theta \in [0,\overline{\theta }]$ , and the amount of military resources to make available to him, m ⩾ 0. The marginal cost of giving the general a unit of military resource is 1. All these parameters are observable by the ruler when making her choices, and known to the general selected.

Powerful, well-endowed military forces are more likely to succeed in battle against an external threat. However, if the military attempts a coup, strong forces are also more likely to overcome the defenses that protect the regime, such as paramilitary units and progovernment militias, and can more easily capture strategic targets and members of the government (Powell Reference Powell2012, 1024). Furthermore, the ability of competent military leaders to marshal forces effectively is vital when the government faces external threats, but can be particularly dangerous if cunning generals turn against the regime. Returning again to the case of Uganda, Milton Obote began to fear General Idi Amin’s wiles. When the threat posed by Amin to the regime became clear enough, Obote demoted the general in an attempt to limit his influence (Horowitz Reference Horowitz1985).

We represent the probability that an actor of competence θ in control of military resources m ₁ prevails against an opponent—here, either the external threat or the ruler’s own defenses—with resources m ₂ with the familiar ratio contest-success function:

Following the ruler’s choice of a general and military resources, the selected general decides whether to execute a coup or remain loyal. If he executes a coup, he takes over with probability p(m, 1; θ), in which case his eventual benefit goes to 1, and he is defeated with complementary probability, in which case his benefit goes to 0. The coup is costly for the general: c > 0.

After the coup decision, the external threat of size T > 0 is realized. It is important to note that by “external” threat, we mean any threat from outside of the government—whether foreign or domestic—that threatens the survival of the rulership.Footnote ² If the general is still around when this threat is faced (because he remained loyal or after a successful coup), he defeats this threat with probability p(m, T; θ), in which case he obtains his benefit (b_i if he was loyal to the ruler and 1 if he took over in a coup), and he is defeated with complementary probability, in which case his benefit is 0. If the general was removed after an attempted coup, the ruler herself faces the external threat, and defeats it with probability p(m, T; 1), in which case she retains power with a benefit of 1, and is herself defeated with complementary probability, in which case her benefit is 0.

The highest expected payoff from a coup in the absence of an external threat is when there is no risk: 1 − c. If G would not want to execute a coup even when a favorable outcome is certain, then he will always remain loyal irrespective of his competence and resources. To make the model interesting, we shall assume that G’s loyalty is not so easily ensured:

Assumption 1 Every general is a would-be ruler: $\overline{b}+c<1$ .

We also make several additional assumptions because we want to focus on the basic tension between security against external threats and security against the force that is supposed to defend against these threats. Some are made for technical convenience and have no bearing on the results, while others can be defended on empirical grounds.

First, the benefit of membership in some group, b_i , is fixed and not borne by the ruler. We can think of this parameter as the consequence of social, economic, and legal institutions underpinning the order in the polity, and as such not really available to the ruler for private consumption. It is the “cost of doing business” and it is not the case that if the ruler picks a general from a less advantaged stratum then she would be saving on that cost.

Second, the ruler pays the cost of resources she transfers to the general but there is no budget constraint. It is highly unlikely that any particular general would be so expensive to get as to trigger a budget constraint, or that rulers are particularly constrained by budgets when it comes to their desire to endow the military with resources. If we were to assume that there was a hard budget constraint, then we might find that the ruler limits the size of the military because of poverty, and not because of any security issues, which is the goal of our analysis. As a result, even if one wanted to introduce a budget constraint, one would have to argue that it would bind, and even when it does bind all it will do is introduce a cap on military allocations, suppressing the mechanism we have in mind. We do assume that these transfers are costly, so there is a disincentive to put too much into the military, but as we shall see this is not going to be the concern in general.

Third, the ruler pays no cost if a coup occurs. Alternatively, the ruler can be assumed to pay a cost if a coup occurs without altering anything in the analysis except carrying another parameter across all calculations. The fact that a coup can depose her with positive probability is already an inducement for her to want to avoid it. Adding extra costs simply strengthens an incentive that is already present (and, as we shall see, quite strong). We do want to consider costs for the general, however, because he has to make a decision about executing a coup, and because these costs might represent institutional features of the existing regime that need to be taken into account.

Fourth, neither the ruler nor the general pay any costs when they fight the external threat. This assumption is consistent with the structure of the model, which allows for no choice to avoid that threat: the ruler simply must deal with it. Since the size of the threat already allows us to capture just how bad it could be for her, there is no need to introduce additional costs.Footnote ³

Fifth, both the ruler and the general are constrained in that they can only use the available military forces m to deal with the external threat (in effect, the ruler’s internal security designed to deal with coup attempts is not useful against external threats). This might appear too restrictive because it seems to disregard strategies the ruler could use to decrease the incentives for a coup. Such coup-proofing tactics could involve increasing the resources devoted to internal security, making it difficult for military units to coordinate and communicate without passing through centralized channels, dispersing units or staffing them with nonlocals, and others. These measures would decrease the probability of coup success at any level of military resources and increase the costs of launching one.

While our cost parameter can capture some aspects of these tactics, it cannot capture others. We could model the effect of such tactics on the probability of coup success with the resources available to the ruler’s internal security forces or her competence, but we have normalized them both. The results will not change if we were to use variables instead as long as we take them as given. In other words, if we think of the Guardianship Dilemma in the context of the ruler having done everything possible to minimize the internal dangers, our analysis follows without any changes. The only downside is that one could not take the model to data where these coup-proofing measures vary without some straightforward modifications that will not alter any of the substance of our argument.

This assumption might also be criticized on grounds that internal security forces may improve the state’s ability to defeat an external threat by augmenting the might of the regular military. We could account for this possibility by incorporating the ruler’s own internal security resources in the probability of success against T. Because this merely involves adding a constant, however, our analysis will not change. We are also doubtful about whether this addition would be appropriate. For instance, one might follow Svolik (Reference Svolik2012), who makes an empirical claim that the army is only generally useful for dealing with mass revolts or foreign forces. In most states—especially dictatorships—the day-to-day security is managed by another apparatus, whose personnel are generally not useful for large-scale operations. One could also point out that some coup-proofing measures (e.g., making it difficult for the commanders to coordinate) might actually have a detrimental effect on the state’s ability to defeat the external threat.

Sixth, the resources given to the military are equally useful for a coup and for fighting the external threat. One might question this on two grounds: it could be that resources are not fungible, and even if they are, they might be useful only in one of the two situations. For example, salaries, health and pension benefits, and payments to civilian contractors are certainly included in military budgets, but they are not likely to increase the fighting ability directly. Spending on some types of technologies could improve the fighting ability when it comes to the external threat without being very useful in a coup. Submarines and fighter jets might belong to that category.

Although both points are doubtless correct, they have only tangential bearing on the Guardianship Dilemma. Since the first type of spending will affect the incentive to launch a coup through the benefits derived from the existing regime, its effects can be approximated by the benefit parameter b_i . The only difference, of course, is that since these payments are part of the budget, they would be costly to the ruler. Under the no budget constraint assumption, this would merely result in another parameter being subtracted from the ruler’s payoff, necessitating further assumptions about the marginal costs of these funds, and perhaps restrictions that ensure an interior solution. That solution, however, is not going to produce any difference in the dynamics we study.

Finally, one might wonder about the assumption that more resources given to the military must necessarily increase its ability to prevail in a coup, as built into the functional form of p(·). From the perspective of any coup-plotters, there are some fundamental problems that they would need to overcome before having any chance of success: collective action and coordination problems that arise from incentives to renege on the plot and the necessity of conducting preparations in secrecy, as well as the absolutely critical question about securing the cooperation or at least neutralizing the units in the armed forces that were not privy to the coup (Luttwak Reference Luttwak1979). Very plausibly, these problems, and especially the latter, might be quite aggravated by the size and complexity of the armed forces. In other words, it could be that beyond some level, the larger and more organizationally complex the military, the harder it is for any general to organize a coup. (Such a dynamic could account for the political quiescence of the armies of the Soviet Union, North Korea, and China.) While this is certainly an intriguing possibility, we believe that such a “pacifying” dynamic would have to be quite exceptional as most countries do not have the population base to maintain large armies. Note also that an attempt to construct and maintain an army of sufficient size would probably run afoul of resource constraints.

In the end, ours is emphatically not a general model of coups. We do not study how coups are organized and how they succeed (Sutter Reference Sutter2000). Our interest is in the fundamental Guardianship Dilemma, which has to be analyzed prior to dealing with any strategies for ameliorating its effects. To this end, we have stripped the model of any factors that are not essential to the dilemma, and whose presence might obscure rather than clarify its logic.

KNOWN EXTERNAL THREAT

We shall begin our analysis with the case where T > 0 is common knowledge. If R does not hire a general, then there is no threat of a coup, so R’s payoff is p(m, T; 1) − m; i.e., she simply has to meet the threat with her own competence and the resources she has allocated. Maximizing this payoff yields $\widetilde{m}=\max (0,\sqrt{T}-T)$ . In any equilibrium in which G gets hired, R’s expected payoff must exceed the baseline of $p(\widetilde{m},T;1)-\widetilde{m}$ . This immediately implies that no coup can occur in equilibrium. In such an equilibrium, R’s expected payoff would be

which means that she would strictly prefer not to hire a general in the first place. The only equilibrium possibilities, then, are that either no coup occurs at all or one occurs with positive probability less than 1. The following result (all proofs are in Online Appendix A) shows, among other things, that a coup can never occur in equilibrium.

Lemma 1 In any equilibrium, G remains loyal if, and only if, T ⩾ T* _i (m, θ), where

with T* _i increasing in both parameters whenever it is non-negative.□

This immediately tells us that if G would remain loyal in the absence of an external threat, then he will remain loyal in the presence of such a threat irrespective of its size. If, on the other hand, G would be disloyal in the absence of an external threat, then he will execute a coup in the presence of an external threat only if this threat is not too large T < T* _i (m, θ). In this sense, sufficiently grave external threats can discipline even a potentially disloyal general and deter him from executing a coup, a sort of “circling the wagons” effect. This effect is due to the fact that the general only wants to take the risks and pay the costs of a coup when he is sufficiently confident about surviving the conflict with T, since survival is necessary to reap the benefits of ruling the state. In turn, as T increases, the loyalty-inducing effect of this external threat allows the ruler to pour additional resources into the military without triggering a coup.

Moreover, since R would not hire a general if a coup is certain, and Lemma 1 shows that G must remain loyal when indifferent, it follows that in equilibrium the probability of a coup must be zero. This leads to the following result.

Lemma 2 Fix any social group b_i . If R’s choices ensure G’s loyalty, then R always picks the most competent general from this group, $\overline{\theta }$ , and endows him with

where

is the maximum level of disloyalty that would not provoke a coup, and

is the level of disloyalty for the most competent G with resources optimally provided to deal with the external threat.□

This tells us how R would allocate military resources if doing so would preserve the loyalty of the general. We now show when R would prefer to hire a general given that she would have to ensure his loyalty.

Lemma 3 In equilibrium,

1. (i) R never hires G if the maximum competence is worse than her own: $\overline{\theta }<1$ ;

2. (ii) R always hires G with $\overline{\theta }>1$ when the external threat is sufficiently large: T ⩾ 1;

3. (iii) R may or may not hire G with $\overline{\theta }>1$ when T < 1, depending on the costs of a coup (c) and the benefits from the status quo (b_i). In particular, if both are sufficiently small, then R will not hire anyone.□

We have now established that the ruler will never hire anyone less competent than herself and that whenever she chooses to hire a general, she picks the most competent one she can find. Moreover, if the external threat is sufficiently serious, the ruler always hires a general although she might have to ensure his loyalty by providing him with fewer resources than what is optimal for dealing with that threat.

Cases (i) and (iii) of Lemma 3 are substantively unlikely. The former essentially means that no potential general is more competent than the ruler, a highly unlikely scenario (well, except perhaps if the ruler is Napoleon, but even then there might be a potential Wellington!). The latter requires that the external threat be negligible, in which case it is very easy to trigger the disloyalty of any general, which is why the decision to hire depends only on the benefits of the status quo and the costs of a coup. Since the ruler’s incentive to hire a general turns on a looming external threat and the need to get someone competent to deal with it, this case is irrelevant for our purposes. Consequently, we shall exclude these substantively unappealing scenarios from further consideration:

Assumption 2 (Preference for Hiring) There always exist generals more competent than the ruler ( $\overline{\theta }>1$ ), and the external threat is never negligible (T ⩾ 1).

Under Assumption 2, Lemma 3 implies that R will always hire a general in equilibrium. The following result shows that, generally speaking, the ruler will give preference to the privileged groups when it comes to selecting a general.

Lemma 4 Let b* be the unique solution to S* _i (T) = S(T). If $\overline{b}\le b^*$ , then R strictly prefers to pick G from $\overline{b}$ ; otherwise R is indifferent among any $b_i\in (b^*,\overline{b}]$ , and strictly prefers any of them to any b_i < b*.□

Thus, R will either choose from the most privileged group or from among the few most privileged (when each of them provides enough benefits to ensure the loyalty of generals drawn from them). Moreover, R will always pick the most competent G she can although she might have to handicap the general resource-wise in order to ensure his loyalty. We can state the main result somewhat loosely as follows:

Proposition 1 If the extent of the external threat is common knowledge and Assumptions 1 and 2 are satisfied, then in any subgame-perfect equilibrium, the ruler picks the most competent general. If there are groups that derive sufficient benefits from the status quo to ensure the loyalty of a general selected from them at the allocation that is militarily optimal to deal with the external threat, then the ruler chooses from any among them, and endows the general with the optimal resources (the equilibria are payoff-equivalent). If no such group exists, the ruler selects the general from the most privileged group, and endows him with just enough resources to ensure his loyalty. No coups occur in equilibrium, but the external threat is not properly met when the ruler is forced to handicap the general.□

We have thus established that when the size of the threat is known, the Guardianship Dilemma is, in principle, solvable: militaries remain loyal in equilibrium, and the ruler’s strategy always privileges domestic political survival over dealing with the external threat. The government hires competent generals, but controls resource flows to the armed forces in order to ensure military loyalty. The more privileged the groups from which the generals are selected, the less biting the trade-off between stability (risk of a coup) and security (risk from the external threat). Since the costs of the coup act as a substitute for benefits, the more effective anticoup measures, the less biting the trade-off becomes and the less pressing the need to privilege the military. In this way, “coup-proofing” works much as previous studies suggest.

The very solvability of the dilemma and especially the fact that whenever the trade-off between stability and security exists it is always resolved in favor of stability are puzzling given the frequency of military interventions in politics. If rulers have levers for controlling their armed forces, why are defections by military forces such a regular occurrence?

ASYMMETRIC INFORMATION ABOUT THE EXTERNAL THREAT

Let us now assume that only G observes the actual external threat T, whereas R is only imperfectly informed about it. As before, subgame perfection implies that given an allocation m, a general of competence θ who obtains status quo benefits b_i will execute a coup if, and only if, the condition in Lemma 1 is not satisfied; i.e., if the threat T is not sufficiently large to deter him. This suggests that it will be sufficient to analyze the case with two types of threats: small and large, with $1<T_{\text{S}}<T_{\text{L}}$ (notice that we are maintaining Assumption 2). The ruler believes that the threat is $T_{\text{S}}$ with probability q ∈ (1, 0) and $T_{\text{L}}$ with complementary probability.

From the comparative statics on T, we know that when threats become sufficiently large, the marginal costs of military allocations begin to outweigh their usefulness, so R responds by decreasing m even though there is no danger of a coup. We consider it highly implausible that a ruler will be so hampered by these marginal costs that she would respond to more serious threats by reducing her spending on security. Instead of introducing a parameter for marginal costs and requiring it to be sufficiently small given the maximum threat magnitude, we shall simply restrict the threat to ensure that the optimal allocation is strictly increasing in its size. This is already true when R constrains G, so this really only affects the unconstrained allocation.

Assumption 3 (Reasonable Costs of Security) The marginal costs of security are not so high as to cause larger threats to require smaller countermeasures under complete information: $m_i^*(T_{\text{L}})>m_i^*(T_{\text{S}})>0$ .

If R does not hire a general, her expected payoff is

which has a unique optimal allocation that results in a strictly positive payoff.

When R hires a general, any allocation can result in one of three outcomes: a certain coup, no coup, and a coup only if the threat is small. To see this, fix some m and observe that if G stays loyal under T_S given that allocation, he must certainly do so under T_L as well. Conversely, if he executes a coup under T_L , then he must also do so under T_S as well. The sole remaining possibility is that he executes a coup under T_S but remains loyal under T_L .

We begin by ruling out the possibility that the ruler will hire anyone when she believes that doing so would result in an inevitable coup (this parallels the complete-information case).

Lemma 5 There is no equilibrium in which R hires G when she expects a coup to occur with certainty.□

Thus, in any equilibrium in which R hires a general, the general’s loyalty is either certain or else only in doubt conditional on the actual size of the threat. The following result shows two things. First, the ruler will never hire anyone less competent than herself. Second, the ruler’s strategy depends on her prior belief about the magnitude of the threat. If she is sufficiently convinced that the threat is large (i.e., q is small), then she allocates more resources to G even though she knows that G will execute a coup if the threat is, in fact, small. The allocation is not, however, optimal for meeting $T_{\text{L}}$ either because the possibility that it will be used in a coup against her forces the ruler to curtail it a bit. In this situation, the ruler faces a positive probability of a coup and does not have enough forces to deal with the large threat. If R is sufficiently convinced that the threat is small (i.e., q is high), then she plays it safe: she allocates just enough resources to ensure the loyalty of G under the assumption that the threat is small. While this does ensure that no coup takes place, the ruler will find herself severely handicapped if the threat turns out to be large.

Lemma 6 Fix a social group b_i and a level of competence θ. In any equilibrium, R hires G only if $\theta >\max (1,T_{\text{S}})$ . In the unique equilibrium in which R hires G, there exists a unique q* ∈ (0, 1) such that

• • if q ⩽ q*, then R allocates $\min (m_{\text{C}}(q),m_i^*(T_{\text{L}}))$ , where $m_{\text{C}}(q)$ is the unique unconstrained maximizer of R’s expected payoff, and G executes a coup if the threat is $T_{\text{S}}$ but remains loyal otherwise (risky strategy);

• • if q > q*, then R allocates $m_i^*(T_{\text{S}})$ , and G remains loyal (safe strategy).

When R plays the risky strategy, she not only faces a positive probability of a coup from a general with substantial resources, but may also fail to provide adequate resources to deal with the large threat. When R plays the safe strategy, she certainly fails to provide adequate resources for the large threat.□

Having established what resources R will allocate once she has chosen G with some competence θ from some class b_i , we now ask how she makes these selections. Since Lemma 6 shows that hiring can only occur if $\theta >\max (1,T_{\text{S}})$ , we shall assume that $\overline{\theta }$ satisfies this condition.

Lemma 7 Fix a social group b_i . In any equilibrium, R hires the most competent G she can ( $\overline{\theta }$ ).□

Finally, we need to consider the social group from which R selects the general. We first show that R’s payoff is nondecreasing in b_i if she pursues the riskless strategy. In particular, it is constant in b_i if the complete-allocation optimum against $T_{\text{S}}$ is unconstrained, and strictly increasing otherwise. Thus, starting with a very low b_i the payoff will not change, and increasing b_i eventually causes it to start increasing.

Lemma 8 Let b*(T) denote the unique solution to S(T) = S* _i (T). And let $b_1=\min (b^*(T_{\text{S}}),b^*(T_{\text{L}}))$ and $b_2=\max (b^*(T_{\text{S}}),b^*(T_{\text{L}}))$ . If $\overline{b}\le b_1$ , then R strictly prefers to pick G from $\overline{b}$ . If $\overline{b}\in (b_1,b_2)$ , then R strictly prefers to pick G from $\overline{b}$ for q > q* if $b_1=b^*(T_{\text{S}})$ , and for q ⩽ q* if $b_1=b^*(T_{\text{L}})$ , and is indifferent among any $b_i\in [b_1,\overline{b}]$ for any other q (but strictly prefers any of them to b_i < b ₁). If $\overline{b}\ge b_2$ , then R is indifferent among any $b_i\in [b_2,\overline{b}]$ (but strictly prefers any of them to b_i < b ₂).□

We can now state the main result under asymmetric information.

Proposition 2 If only the general knows the extent of the external threat, then in the essentially unique equilibrium the ruler picks the most competent general from the most privileged strata in society. If the ruler is sufficiently sure that the threat is small, she provides the general with only enough resources to meet that threat (even these might be constrained), and the general remains loyal regardless of the extent of the threat. If the ruler is sufficiently sure that the threat is large, she provides the general with resources that balance the risk of a coup with the risk of failing to meet the large threat with adequate resources (even these might be insufficient for the large threat). The general remains loyal if the threat is large but executes a coup if the threat is small.□

Proof The result follows immediately from lemmata 6, 7, and 8. The equilibrium is essentially unique because R might be indifferent among many values of b_i as long as they are sufficiently high. Each of these corresponds to a different equilibrium but they are all payoff-equivalent.■

Supplementary Materials

To view supplementary material for this article, please visit http://dx.doi.org/10.1017/10.1017/S0003055415000131