Preventing Mass Mobilization:

Autocratic Responses to Revolutionary Threats∗

Jing-Yuan Chiou† Mark Dincecco‡ Trevor Johnston‡

March 11, 2015

Abstract

Revolutionary movements depend on mass mobilization. To prevent revolt, autocrats

can use domestic and foreign policy instruments. We model the autocrat’s policy choice

with a focus on the coordination problem that underlies revolutionary mobilization. We

show that the relationship between revolutionary threats and policy responses may be

non-monotonic. Smaller threats may actually provide stronger incentives for autocrats to

prevent mobilization, since policies are more cost-effective when threats are low. Further-

more, we show that domestic and foreign policies can serve as substitutes or complements.

We argue that these insights help resolve contradictory empirical results.

Keywords: autocracy, cooptation, repression, foreign diversion, revolution, global games

∗We thank Ethan Bueno de Mesquita, Allen Hicken, Pauline Jones Luong, James Melton, Iain Osgood, David

Rahman, Peter Rosendorff, Mark Tessler, Alon Yakter, and participants at the University of Michigan Compara-

tive Politics Workshop, the 2014 Midwest Political Science Association Conference, and the 2013 European Peace

Science Conference for helpful comments.†National Taipei University‡University of Michigan

1

1 Introduction

How do autocrats prevent revolution? This paper focuses on the coordination problem that

underlies mass mobilization. Coordination is at its core a problem of information (Chwe,

2001). Under incomplete information, citizens must decide whether to revolt, which only

succeeds if a sufficient number of citizens mobilize. Autocrats use various policy instruments

to prevent coordination and thereby deter mass mobilization. The conditions under which

these policies succeed is critical to understanding autocrat survival. To model this problem,

we take a global games approach.1 Using this framework, we analyze how autocrat policy

choice affects mass coordination and the likelihood of revolution.

Autocrats have two policy instruments in our model, one domestic and the other foreign.

The current literature generally studies each instrument in isolation. But focusing on a single

policy area may be problematic. Without considering the autocrat’s broader choice set, we

may ignore possible policy interactions. Our model addresses this problem by incorporating

both instruments. The domestic instrument represents cooptation or repression, which dis-

courage popular protest (Davenport, 2007), but at the cost of valuable state resources. The

second instrument concerns foreign affairs. The autocrat may adopt a provocative foreign

policy, which diverts attention away from domestic issues and toward a scapegoat foreign

government (Levy, 1989). This policy is costly in the sense that provocation may incite for-

eign military intervention. Thus, the autocrat must not only consider how his foreign policy

choice will influence the threat of revolt, but also whether the foreign government will decide

to intervene in response.

In our model, the autocrat faces a key choice: whether to fully eliminate a revolutionary

threat (at some cost), or to allow revolutions to occur with some positive probability. Depend-

ing on the cost of preventing mobilization, the autocrat may accept some risk of revolution

in equilibrium. This choice may be driven by resource constraints, or simply reflect a ratio-

nal gamble given the expected costs and benefits. If the autocrat decides to fully eliminate

the threat, then he will select a policy bundle that prevents successful coordination. Revolt

succeeds if and only if a sufficiently large number of citizens participate, reaching a critical

threshold or tipping point. Using some mix of domestic and foreign policies, the autocrat can

1In a global game, players must coordinate under incomplete information. A player’s private information in-forms her expectations about the true state of the world and other players’ beliefs and actions. These expec-tations drive equilibrium strategies and the probability of successful coordination. Morris and Shin (2003)provide an overview of the global games framework. Recent examples of global games include E. Bueno deMesquita (2010, 2011, 2014), Shadmehr and Bernhardt (2010, 2011), and Shadmehr (2014).

2

ensure that this threshold condition is not met, thus preventing mobilization and deterring

revolution.

Naive intuition may suggest that a higher revolution risk will always lead to more drastic

responses (e.g., greater domestic spending or a more provocative foreign policy). However,

we show that this relationship can actually be non-monotonic. Smaller revolutionary threats

may provide stronger incentives for the autocrat to respond more aggressively: preventing

revolt is simply more cost-effective when the threat is low. In this case, the autocrat can bet-

ter afford some mix of policies that fully eliminates nascent revolutionary movements. This

non-monotonic relationship may help resolve “contradictory” results found in the empirical

literature (Miller and Elgun, 2011). This literature suggests a strictly positive relationship

between domestic instability and the use of diversionary foreign policy: the greater the rev-

olutionary threat, the greater the diversion. A similar logic holds for greater cooptation or

repression in response to survival threats. Our model provides one explanation for why we

may not observe such a relationship in practice.

Similarly, the empirical literature that treats domestic and foreign policies as substitutes

generates mixed results (Enterline and Gleditsch, 2000). Our model considers conditions un-

der which these various policy instruments are substitutes or complements, which helps ex-

plain these mixed findings. Under certain conditions, the autocrat’s cost function will imply

substitutability between domestic and foreign policies. However, policy substitution does not

always hold. Moving from some positive probability of revolution to fully eliminating such a

threat induces complementarity.

The rest of the paper proceeds as follows. Section 2 reviews the current literature on au-

tocratic policy responses to revolutionary threats. Section 3 describes the global games ap-

proach and how it allows us to model coordination problems. Sections 4 to 7 present the

model. We first study the benchmark case without coordination problems, which is roughly

equivalent to a principal-agent setup. Next, we allow for coordination problems and con-

sider how this change alters the principal-agent results. Here we characterize the equilibrium

strategies for the autocrat, citizens, and the foreign government. Section 8 describes com-

parative statics. Section 9 discusses the model’s implications for the empirical literature. We

relegate all proofs to the appendix.

3

2 Revolutionary Threats and Policy Responses

All autocrats face some underlying threat of revolution. The severity of this threat differs

across regimes, with some autocrats more vulnerable than others. Why regimes differ in

this respect depends on structural factors (Skocpol, 1979, DeNardo, 1985) and economic con-

ditions (Haggard and Kaufman, 1995, Acemoglu and Robinson, 2001). Yet perhaps most im-

portant of all are differences across autocratic regime types (Geddes, 1999). The incidence and

spread of mass revolt greatly depends on the type of autocratic regime and its information

environment (Kuran, 1989, Lohmann, 1994).2

Autocrats have two basic policy instruments at their disposal. The first of these are do-

mestic measures, which can take one of two forms, cooptation or repression (Wintrobe, 1998,

Acemoglu and Robinson, 2000). Cooptation strategies range from broad policy concessions

(Desai et al., 2009, B. Bueno de Mesquita and Smith, 2009, B. Bueno and Smith, 2010, Malesky

and Schuler, 2010), to targeted distributive goods (Blaydes, 2006), to public sector jobs (Kim

and Gandhi, 2010). Such benefits are used to selectively purchase support which undermines

the opposition. This set of strategies helps prevent revolutions by raising the opportunity cost

of revolt.

Alternatively, autocrats may use repression to respond to revolutionary threats. All au-

tocratic societies are subject to some form of surveillance, which is used to monitor citizen

activities and ferret out nascent opposition movements. Complementing this more passive

form of repression, autocrats may also use selective violence (e.g., imprisonment, torture, ex-

ecutions) to physically and psychologically attack the opposition (Haber, 2008). Such tactics

are on display during periods of revolt, when the autocrat’s rule is in jeopardy. Repression

can also help prevent revolt by eliminating challenges before they mature.

In addition to these domestic measures, autocrats may respond through foreign policies.

Foreign policies can have reputational costs and may decrease the odds of leader survival.

Nonetheless, autocrats may pursue such policies in the hope that these actions will divert

attention away from domestic discontent and deter revolution.

2For some regimes (e.g., single-party autocracies), low-level protest may even be healthy, relieving tensions, re-vealing preferences, and providing information about opposition groups. Totalitarian regimes, by contrast, arefar less robust. These regimes depend on fear to craft popular and self-fulfilling perceptions of regime strength.By suppressing any form of public opposition, information becomes scarce and preference falsification intro-duces significant noise (Kuran, 1989). Consequently, these states are at a greater risk of rapid collapse, as smallprotests escalate and cascade into full-scale revolt (Lohmann, 1994). The collapse of the Eastern Bloc showshow quickly such regimes can fall when the masses mobilize (Kuran, 1991). While most pronounced for thesetypes of autocratic regimes, the challenge of revolutionary threats remains the same for all autocrats.

4

Chiozza and Goemans (2003) characterize three mechanisms through which diversionary

foreign policy may affect leader survival. The first two are psychological. Diversionary for-

eign policy either makes the foreign government a scapegoat for domestic failures or induces

an “us-versus-them” mentality that galvanizes popular support for the regime (Simmel, 1964,

Coser, 1956, Levy, 1989). Both of these mechanisms may depend on citizens being tricked.

The third mechanism derives from a rational choice context, where diversionary foreign poli-

cies are seen as a “rational gamble” (Downs and Rocke, 1994). If a leader’s odds of survival

are already low, then the opportunity cost of international conflict decreases. Furthermore, if

this provocation produces concessions by the foreign government, then this policy may even

be a net benefit for survival. Regardless of the specific mechanism, the logic of diversion-

ary foreign policy is clear: given domestic instability, this policy may help autocrats stay in

power.

Both the domestic and foreign policy literatures provide important insights into autocratic

rule and the menu of potential responses to revolutionary threats. These literatures have tra-

ditionally studied either the domestic or foreign sphere in isolation. However, restricting the

autocrat’s choice to only one policy instrument may generate incomplete, or even mislead-

ing, implications. Consider the varying empirical results on the effect of diversionary foreign

policy on the onset of war (Miller and Elgun, 2011). Scholars not only disagree on the magni-

tude of this effect, but also on its sign. Incorporating the autocrat’s domestic policy options

may help resolve these conflicting empirical results. In the next section, we introduce a mod-

eling framework that incorporates both domestic and foreign policy choices and allows for

interactions between them.

3 Global Games Approach

Having described the autocrat’s range of possible responses, we now discuss how to best

model this policy choice and its effect on revolutionary threats. The current literature gener-

ally draws on a principal-agent framework, focusing on the leader’s private information. A

single “principal,” such as a member of the selectorate in an autocracy (B. Bueno de Mesquita

et al., 2003), has the power to retain or replace his “agent,” the autocrat. The agent’s pri-

vate information creates room for opportunistic behavior, which may not be aligned with the

interests of the principal (Downs and Rocke, 1994). Within this framework, domestic and

foreign policies can help signal the leader’s type. For example, an international crisis may

5

provide the leader with the opportunity to showcase his ability (Richards et al., 1993, Hess

and Orphanides, 1995, Smith, 1996, 1998, Tarar, 2006, Gent, 2009).

This principal-agent dynamic is especially useful when we think about democracies or

hybrid regimes. In these systems, institutional rules and entrenched norms help define the

relevant actors and their relationships to one another. Given the selectorate’s power to re-

place the ruler, the principal-agent framework is attractive. This modeling approach, how-

ever, may be less applicable for other autocracies. Consider a totalitarian regime like Libya

under Muammar Qaddafi. Having captured the state, Qaddafi was able to dismantle inde-

pendent sources of power, build a ruling coalition from a small coterie of allies and family

members, and effectively purge the regime of any potential challengers (Davis, 1988). Once

such threats have been eliminated, an autocrat’s only real opposition comes from outside the

regime. Survival thus depends on preventing this opposition from coalescing. As the Libyan

opposition began to mobilize, Qaddafi quickly found himself under siege and facing mass

revolt. For such states, the central dynamic may better resemble a coordination problem: dis-

organized groups and latent opposition movements must overcome structural hurdles if they

are to challenge the autocrat.

Thus, in modeling the autocrat’s policy choice, we focus on the coordination problem

that underlies revolutions. In line with the “assurance game” perspective of revolutionary

participation (Taylor, 1987, Chong, 1991, Chwe, 2001), we assume that free-riding does not

fully deter the opposition (e.g., due to “selective incentives” provided to participants), but

that there are still coordination problems to overcome. Successful revolutions require joint

efforts from a group of heterogeneous citizens. The global games approach offers a natural

framework for modeling how distinct groups, which vary in their beliefs about the true state

of the world, coordinate.3 When deciding whether to revolt, citizens must evaluate their own

beliefs about the world and, critically, how the beliefs of others will influence the success or

failure of coordination efforts. By manipulating the information environment, the autocrat

can undermine coordination and thus prevent revolution.

The global games framework is flexible and has led to a growing and varied literature

that explores the effects of violence among a revolutionary vanguard (E. Bueno de Mesquita,

2010) and punishment after failed revolution attempts (Shadmehr and Bernhardt, 2011).4 Our

3Goemans and Fey (2009) and Baliga et al. (2011) consider heterogeneous citizens from which the ruler seekssupport to stay in power, but do not include strategic interactions among citizens themselves.

4Boix and Svolik (2013) examine the effect of political institutions on regime survival when an autocrat hasprivate information about national resources.

6

paper extends this logic to examine how an autocrat’s foreign and domestic policy choices

affect the threat of revolution. Within the broader global games literature, our model belongs

to the class of games with “one-sided limit dominance,” where only “not revolt” can be a

dominant strategy for citizens (E. Bueno de Mesquita, 2010, 2011, Shadmehr and Bernhardt,

2010, 2011).5 While global games with two-sided limit dominance, where both “revolt” and

“not revolt” can be dominant strategies, typically yield a unique equilibrium, we opt for a

framework of one-sided limit dominance to highlight the need for coordination.

4 Model of Autocratic Policy Choice

In this section, we develop a formal model of autocratic policy-making under the threat of

revolution. We first introduce the benchmark case, which treats the domestic population as a

unitary actor. This assumption excludes the possibility of coordination problems and roughly

approximates a principal-agent game. By solving this benchmark case, we largely recover the

standard results in the literature. In the next section, we relax this assumption and allow

for coordination problems. We show how this change is non-trivial, leading to new insights

about the effects of coordination problems on autocratic policy choice. First, however, let us

consider the basic model without coordination problems.

The model includes three players: an autocratic ruler, a domestic populace, and a foreign

government. The game has two stages. In the first stage, the autocrat publicly chooses a policy

bundle (c, µ), which consists of a domestic policy and foreign policy. This policy bundle is

observed by all players. For simplicity, assume that there is only one instrument for each

type of policy. The domestic policy instrument, c, determines the population’s cost of revolt.

Conceptually, we can think of this cost as a function of repression (i.e., punishment), or the

potential loss of benefits from cooptation (i.e., opportunity cost). The foreign policy choice is

represented by µ, capturing the degree to which the autocrat takes a provocative stance vis-a-

vis some foreign government. Provocations can take various forms, from bellicose language,

to troop movements, to missile tests. Such provocation increases the foreign government’s

incentive to intervene.

Note that these two instruments operate in distinct ways throughout the model. The do-

5E. Bueno de Mesquita (2010) reserves the term “global games” for settings with two-sided limit dominance. Hecalls his model, which exhibits one-sided limit dominance, a game of regime change. Morris and Shin (2003)provide a discussion of limit dominance.

7

mestic policy must be financed and thus costs resources, whereas the foreign policy is in this

sense “free” but raises the risk of foreign intervention. As we show later, these instruments

further differ in their strategic implications and how they influence the likelihood of revolt

or intervention in equilibrium. With these policy instruments, the autocrat’s objective func-

tion (described in detail ahead) resembles that of a simple loss-minimization problem. This

function has two parts: spending costs from domestic measures and the expected loss from

revolution and foreign intervention. When choosing a policy bundle, the autocrat looks to

minimize this total loss.

After the policy bundle is announced, we arrive at the second stage of the game. At this

point, the foreign government and populace move simultaneously, deciding whether to inter-

vene or revolt, respectively. First consider the foreign government and its choice to intervene.

Foreign intervention can take various forms, from economic sanctions and targeted strikes, to

full-scale war. We are agnostic about the specific type of intervention, which may be oppor-

tunistic (e.g., Iraq’s invasion of post-revolution Iran in 1980) or humanitarian (e.g., airstrikes

during the Libyan civil war in 2011). In the model, citizens do not receive any benefits or costs

from intervention.6

Drawing on the conventional global games framework, the foreign government will inter-

vene if θ exceeds a threshold f − α · A. Here θ represents the foreign government’s type, or

its willingness to go to war. The form of this threshold is standard for global games models

and has a straightforward interpretation. Both f and α are exogenous parameters, with α ≥ 0.

We can think of f as the baseline threshold: as it increases, intervention becomes less likely.

The variable A ∈ [0, 1] captures domestic instability, more precisely, the expected threat to

the ruler’s survival, and is an equilibrium outcome of the game. When α > 0, a higher A

(i.e., greater instability) reduces the decision threshold of the foreign government and makes

military intervention more likely.7 By contrast, when α = 0, the threshold is simply f , which

implies that domestic instability does not affect the foreign government’s choice to intervene.

Only the foreign government knows the true value of θ. Ex ante, it is common knowledge

that θ is normally distributed with mean µ and variance σ2θ . A more provocative foreign policy

(i.e., higher µ) increases the probability that the foreign government will be more willing

to intervene. Let M denote the set of foreign policies available to the autocrat, and define

6An extension of this model could allow for positive or negative payoffs from intervention. While incorporatingsuch payoffs is not difficult, it would only complicate the model without qualitatively changing the results.

7Alternatively, θ and f − α · A can be the foreign government’s benefit and cost of military intervention, respec-tively.

8

µ > −∞ and µ < ∞ as the minimal and maximal elements, respectively.

At the same time, the domestic population observes some private information about θ

and then decides whether to revolt at a cost c > 0. A successful revolution provides a benefit,

b > 0, for those who participate. In the benchmark case, we assume that the population is

a unitary actor, which effectively precludes any free-riding problem. In subsequent sections,

however, we relax this assumption, which opens up the possibility of free-riding. Free-riding

can be a problem when individual citizens must decide whether to participate in some costly

collective action. While this problem is important, it is not the focus of this paper, which con-

centrates on the problem of mass coordination under incomplete information. By assuming

that the benefit, b, only goes to participants, the problem of free-riding disappears.8 We fur-

ther assume that participants only receive b if there is no foreign intervention. If the foreign

government intervenes, then the benefits from a successful revolution disappear.

Recall that the autocrat can raise the cost of revolt by increasing c. We assume that c is

bounded, such that c ∈ C ⊂ (0, b), and the expense to the autocrat, E(c), is strictly increasing

in c. Let c and c be the minimal and maximal feasible domestic policies, respectively, and,

without loss of generality, let E(c) = 0. We further assume that c < b for all c ∈ C. Under this

assumption, the benefit of replacing the ruler is always greater than the cost, ensuring that

the populace has some interest in deposing the ruler.

Before solving the game, let us note a crucial premise in our model. The population’s

uncertainty is not about the autocrat’s type but rather, the foreign government’s. In many to-

talitarian regimes, a population is isolated from the outside world and left only with state pro-

paganda. Under these conditions, the population is often better informed about the regime

and its domestic policies than it is about some foreign government and its willingness to

intervene.9 By introducing this uncertainty around the foreign government’s type, we can

explore how the threat of intervention informs the population’s choice to revolt. This setup

helps explain the logic behind diversionary foreign policy and the conditions under which it

succeeds.

In solving the benchmark case without coordination problems, let us begin by considering

the population’s choice of whether to revolt. The populace, believing that foreign intervention

8We can relax this assumption and still maintain the equilibrium. So long as participation provides some addi-tional benefit, then free-riding will not qualitatively alter our results.

9Take, for example, North Korea. However opaque their state institutions, the North Korean populace is cer-tainly aware of the regime’s vast repressive and security apparatus. Less clear to the North Korean populace ishow Japan or the US would respond to the regime’s latest rhetoric or saber-rattling.

9

occurs with probability wP, decides to revolt if10

b · (1 − wP) > c ⇒ 1 − wP >c

b. (1)

The populace receives some private signal, θP, that is positively, but imperfectly, correlated

with θ. The private signal is defined as follows: θP = θ + εP, where the noise term εP is

normally distributed with mean zero and variance σ2ε and is independent of θ. By standard

Bayesian updating, conditional on the private signal, θ is normally distributed with mean

λθP + (1 − λ)µ and variance λσ2ε , where λ ≡ σ2

θ /(σ2θ + σ2

ε ). This information helps the pop-

ulation assess the likelihood of foreign intervention: a larger θP implies a larger θ in expecta-

tion.

Throughout the paper, we assume that the domestic audience and foreign government

adopt a “switching strategy:” a party switches from one action to the other when its private

information exceeds some threshold level. Suppose that the foreign government intervenes

when its willingness, θ, is greater than a cut-off value I. Given I, the populace’s private signal,

θP, helps determine the likelihood of foreign intervention as follows:

wP = Pr(θ > I|θP) = 1 − Φ

(I − λθP − (1 − λ)µ√

λσε

)

(2)

where Φ is the CDF of the standard normal distribution. The likelihood of intervention is

higher when: (i) I is lower, indicating that the foreign government will intervene over a

broader range of θ; and (ii) θP is higher, implying a greater expected willingness to intervene.

For all finite µ and c/b ∈ (0, 1), there exists a θP such that the likelihood of intervention, wP,

is sufficiently small and condition (1) holds. This implies that the autocrat always faces a

non-zero probability of revolt.

For the benchmark case, let A represent the probability that the population revolts. Sup-

pose that the population revolts if the private signal θP is smaller than a cut-off value P. Since

θP is normally distributed with mean θ and variance σε, given θ and P, the foreign government

believes that the ruler will be replaced with probability A = Pr(θP < P|θ) = Φ((P − θ)/σε),

and intervenes when θ > f − α · A = f − α · Φ((P − θ)/σε), or, equivalently, when

f < θ + α · Φ

(P − θ

σε

)

. (3)

10We assume that upon indifference the principal will not replace the ruler and the foreign country will notintervene. Since we consider normal distributions, which are continuous, this assumption does not affect ourresults. The same is true for our assumption that the ruler falls when A = T, which we will introduce laterwhen coordination problems are present.

10

On the right-hand side, a higher θ directly boosts the incentive to intervene. But it also im-

plies that the domestic population is more likely to receive a higher private signal, and thus

less likely to revolt. When α > 0, this updating negatively affects the foreign government’s

decision to intervene; we consider these implications in Section 7.

We further impose Assumption 1 to constrain the magnitude of α. This assumption en-

sures that foreign intervention is strictly increasing in θ, whereby the foreign government will

optimally adopt a switching strategy.11

Assumption 1. 0 ≤ α ≤ σε

√2π.

Lemma 1. (Monotonic intervention decision) Given Assumption 1, for each finite P, there exists a

unique I ∈ ( f − α, f ] such that the foreign government intervenes for θ > I.

Slightly abusing notation, an equilibrium (I, P) simultaneously satisfies:

I + α · Φ

(P − I

σε

)

≡ f and Φ

(I − λP − (1 − λ)µ√

λσε

)

≡ c

b. (4)

In the former condition, given P, the foreign government is indifferent between intervention

or not when θ = I. In the latter condition, given I, the domestic populace is indifferent

between revolting or not when observing θP = P. In this case, a higher µ always raises

the equilibrium probability of foreign intervention Pr(θ > I) = 1 − Φ((I − µ)/σθ). These

conditions imply the following proposition.

Proposition 1. (No coordination) When a single principal can replace the ruler, the ruler cannot fully

eliminate domestic survival risks, and a more provocative foreign policy always raises the likelihood of

foreign military intervention.

This proposition captures the basic insights from our benchmark case. As a unitary actor,

the domestic population resembles the principal in a principal-agent game. Absent coordi-

nation problems, the population always has the capacity to revolt against (i.e., replace) the

autocrat (i.e., the agent). Given such a threat, a provocative foreign policy increases the like-

lihood of intervention. This result is particularly instructive when compared to the next sec-

tion. The simple relationship between provocative foreign policy and military intervention

depends on the absence of coordination problems, which makes revolt a constant threat. In

the next section, we consider how coordination problems may diminish this threat and thus

alter the relationship between autocratic policy-making and leader survival.

11If α > σε

√2π, then the foreign government’s intervention decision may not be monotonic in θ, even when the

domestic audience sticks to the switching strategy.

11

5 Coordination Problems

We now allow for coordination problems by relaxing the assumption of a unitary domestic

populace. Successful revolutions depend on the coordination of a continuum of mass one

citizens. The regime falls if and only if the number of citizens that revolt, A ∈ [0, 1], exceeds

some threshold T ∈ (0, 1).

Citizens are ex ante identical. At the second stage, a citizen j observes a private signal

θj = θ + ε j, where ε j is normally distributed with mean zero and variance σ2ε and independent

of θ. The noise term is also independent across citizens. We only consider pure and symmetric

strategies (i.e., citizens that receive the same private signal will behave in the same way).

If there is no foreign intervention, a citizen receives a benefit b only when she participates

in a successful revolution that brings down the regime. Otherwise she receives a payoff of

zero. As described in the last section, benefit b mitigates the free-riding problem of revo-

lutions. When there is foreign military intervention, all citizens receive the same expected

payoff. We thus assume that the fates of citizens are bound together by foreign interven-

tion, without necessarily imposing a “rally around the flag” effect against the foreign enemy

(Simmel, 1964).

The global games approach uses private information about a common parameter as the

key modeling device to analyze coordination. By private signals, we do not assume that

citizens know very much about the true θ. The variance of the noise term σ2ε can be large

and so the signal can be very coarse, as can be the case in a highly repressive regime. In fact,

Assumption 1 puts a lower bound on σ2ε . The crucial feature is that citizens have different, yet

correlated, information upon which they evaluate both θ and the expected actions of other

citizens.

Given this private information and the expectations that it generates, we can begin to solve

for the typical citizen’s optimal strategy. Since there is only a benefit from revolution when

the foreign government does not intervene, at the second stage, citizen j revolts when

(1 − wj) · Sj · b > c ⇒ ln (1 − wj) + ln Sj > ln( c

b

)

, (5)

where wj and Sj are the expected likelihoods of intervention and revolution, respectively. The

expression on the left-hand side of the arrow states that the expected benefit of revolt must be

greater than the costs. The right-hand side expression is simply a log-transformation to ease

our analysis. By comparing this expression to the analogous condition (1), we can begin to

12

see the consequences of coordination problems. In condition (1), the unitary population will

replace the ruler whenever the belief 1 − wj is higher than the cost-benefit ratio (c/b). The

introduction of coordination problems brings in the additional element Sj, which raises the

bar for revolt. As a probability, Sj must be bounded between zero and one, making ln Sj neg-

ative. This implies that the addition of Sj decreases the right-hand side for both expressions

in condition (5), reducing the likelihood of revolt from the benchmark case.

Beyond simply decreasing the probability of revolt, coordination problems also introduce

a strategic dilemma for citizens, producing an equilibrium of “pure coordination failure.”

Having relaxed the assumption of a unitary population, there now exists an equilibrium

where no citizen revolts because of the expectation that no one else will revolt, which im-

plies ln Sj = −∞ for all j (E. Bueno de Mesquita, 2010, 2011, Shadmehr and Bernhardt, 2010,

2011). This result leads to the following lemma.

Lemma 2. (Coordination failure) There is always an equilibrium where no citizen revolts.

This equilibrium may not be unique. Static global games often yield a unique equilibrium

(Morris and Shin, 2003), but these conditions may not hold for all forms of uncertainty (E.

Bueno de Mesquita, 2014) or in dynamic contexts (Angeletos et al., 2007). Our model exhibits

multiple equilibria under certain conditions. Specifically, when revolt is possible (i.e., there

exists a cutoff rule such that some citizens participate in revolution), there are multiple equi-

librium strategies, one with zero participation and one with positive participation. In the

spirit of E. Bueno de Mesquita (2010), we impose the following equilibrium selection rule:

when multiple equilibria exist, all citizens choose the same strategy.

Having specified our equilibrium selection rule, we now consider the conditions under

which revolt can emerge in equilibrium. We begin with the case of α = 0. When α = 0, the

citizens’ collective action, A, does not affect the foreign government’s decision. Hence, the

foreign government intervenes when θ > f . Since citizen j’s private signal θj is generated by

the same stochastic process as the principal in the benchmark case, we can use condition (2)

to obtain her assessment of foreign intervention. By incorporating the foreign government’s

intervention threshold I = f and using her private signal θj (instead of θP), citizen j believes

that foreign intervention occurs with probability

wj ≡ Pr(θ > f |θj) = 1 − Φ

(f − λθj − (1 − λ)µ√

λσε

)

. (6)

Citizen j must also evaluate the likelihood of revolt from condition (5). Her private signal

θj similarly informs this belief. Let all other citizens adopt the switching strategy, choosing

13

to revolt when their private signal is smaller than some threshold J. Given J and θj, citizen j

believes that revolutions occur with probability12

Sj ≡ Pr(A ≥ T∣∣θj) = Φ

(

J − σεΦ−1(T)− λθj − (1 − λ)µ√

λσε

)

. (7)

This expectation is decreasing in θj and increasing in J. Given correlated signals, a higher

θj implies that the other citizens are also more likely to receive higher private signals. In

expectation, then, citizens should be less willing to revolt, given the threat of intervention.

Conversely, a higher threshold means that citizens will revolt over a wider range of private

signals, thus raising the likelihood of revolution.

A threshold J is an equilibrium threshold if the marginal citizen (i.e., whose private signal

is equal to J), is indifferent between revolting or not:

ln

[

Φ

(f − λJ − (1 − λ)µ√

λσε

)]

︸ ︷︷ ︸

≡ ln (1 − wJ)

+ ln

[

Φ

((1 − λ)(J − µ)− σεΦ

−1(T)√λσε

)]

︸ ︷︷ ︸

≡ ln SJ

= ln( c

b

)

, (8)

where wJ and SJ are the marginal citizen’s expectations of foreign intervention and regime

collapse, respectively. We further denote L(J) ≡ ln (1 − wJ) + ln SJ , which incorporates the

marginal citizen’s overall evaluation of obtaining reward b. This expression, L(J), includes

all of the probability terms in the equilibrium determination, allowing us to focus on the

information part of the problem.

A higher J reduces 1 − wJ but raises SJ , as evident in the following comparative statics:

∂(1 − wJ)

∂J=

−λ√λσε

φ

(f − λJ − (1 − λ)µ√

λσε

)

< 0, (9)

and

∂SJ

∂J=

1 − λ√λσε

φ

((1 − λ)(J − µ)− σεΦ

−1(T)√λσε

)

> 0, (10)

where φ(·) is the density function of the standard normal distribution. The equilibrium

threshold, by equating L(J) to the cost-benefit ratio of revolt, ln (c/b), strikes a balance be-

tween higher intervention risk and broader revolt participation. Figure 1 illustrates the key

12 We derive equation (7) in the proof of Lemma 3. The no-revolt equilibrium has the equilibrium thresholdJ = −∞. Shadmehr and Bernhardt (2011) show the existence of an equilibrium with a non-switching strategy,where citizens revolt if and only if their private signals fall in an interval bounded on both sides. Intuitively,“no revolt” for low private signals is “self-enforcing” similar to pure coordination failure. Despite the impli-cation of the low likelihood of foreign intervention, if all other citizens do not revolt for low private signals,then no citizen will revolt when observing low signals. We omit this case.

14

JJ

L L

J J J∗J∗∗

(a) (Unique) No-revolt equilibrium (b) Equilibrium with revolt

ln(c/b)

ln(c/b)

LL

Figure 1: Equilibria Across Revolt Thresholds

feature of L as a function of J and equilibrium revolt outcomes. The following lemma pro-

vides a formal characterization.

Lemma 3. (Tipping point) Suppose that α = 0. L(J) has a unique maximizer J ≡ arg maxJ L, and a

finite maximal value L ≡ maxJ L that is strictly decreasing in µ. Given c/b ∈ (0, 1), there exists a

unique µ such that L(µ) ≡ ln (c/b), and µ is strictly decreasing in c.

If ln (c/b) > L, or, equivalently, µ > µ(c), then “no revolt” is the unique equilibrium.

If ln (c/b) ≤ L, or, equivalently, µ ≤ µ(c), then there also exists another equilibrium with

equilibrium threshold J∗ ≥ J (and when µ = µ, J∗ = J). When J∗ > J, both dJ∗/dc and dJ∗/∂µ < 0.

Lemma 3 implies that any equilibrium threshold that leads to revolt cannot take extreme

values. When J is too high, the marginal citizen would find the likelihood of foreign interven-

tion too great to be worth the cost of revolt. Formally, as J → ∞, ln (1 − wJ) → −∞. In this

case, there is no equilibrium where all citizens revolt, regardless of the value of their private

signal. On the other hand, a very low threshold J means that few citizens will have private

signals smaller than the threshold, and with few participants the revolution is doomed to fail.

Formally, as J → −∞, ln SJ → −∞. Note that, in the benchmark case, since the domestic

populace is a unitary actor, there is no need for coordination and revolution occurs whenever

foreign military intervention is highly unlikely.

Panels (a) and (b) of Figure 1 illustrate this existence condition for a finite equilibrium

threshold (i.e., an equilibrium threshold −∞ < J < ∞ such that some citizens will revolt). In

Panel (a), we let L represent the maximal value of L, where L < ln (c/b). In this case, no J

can satisfy condition (8). The autocrat does not face a threat of revolution because no revolt

is the unique equilibrium outcome. If, however, L ≥ ln (c/b), as in Panel (b), then revolt

15

c c

µ

µ

RD

No-revolution zone

Revolution zoneDomestic policy

Foreign policy

(c1, µ1)

(c2, µ2)

(c1, µ1)

Figure 2: Policy Choice Across Parameter Spaces

can emerge in equilibrium. Under this condition, there is an equilibrium threshold J∗ ≥ J

(where J ∈ (−∞, ∞) that attains the maximal value L).13 Panels (a) and (b) illustrate the

existence condition for J, and effectively represent distinct parameter spaces, characterizing

the conditions under which revolt may occur in equilibrium.

Figure 2 further illustrates these conditions on the domain of policy space (c, µ). Given

some c, µ is the maximal level of foreign provocation under which revolt can emerge. Alter-

natively, we can define a “revolution-deterrence frontier,” RD ≡ min{µ : µ ∈ M, µ > µ}, as

the minimal foreign policy that is strictly greater than µ. This value is the minimally provoca-

tive foreign policy that can deter revolutions.14 As shown in Figure 2, RD has a negative

slope and separates the policy space into two zones. A policy bundle (c, µ) falls in the “no-

revolution zone” when it satisfies µ ≥ RD(c) and so fully prevents domestic revolt from

arising. Otherwise, the policy bundle falls in the “revolution zone” and, with an equilibrium

13The value of the maximizer J may vary with µ. The sign of dJ/dµ is the same as the sign of ∂2L/∂µ∂J,

evaluated at J. When ln (c/b) < L, another equilibrium exists with threshold J∗∗. This equilibrium exhibitscounterintuitive comparative statics: a higher c or µ raises J∗∗ and invites more protesters. It is also unstable(Shadmehr and Bernhardt, 2010, E. Bueno de Mesquita, 2011). If a small perturbation occurs such that domesticaudiences adopt a slightly lower threshold J < J∗∗, then by L(J) < ln (c/b) the audience with private signal Jwill not revolt. The equilibrium threshold will thus be set further away from J∗∗. In addition to the selectionrule from before, we exclude this equilibrium from our analysis.

14If RD is not well-defined, e.g., when M = [µ, µ] is an internal, we let RD = µ + ǫ, where ǫ > 0 but arbitrarily

close to zero while keeping RD ∈ M.

16

threshold J∗ ≥ J, the citizens successfully revolt with probability

S∗ ≡ Φ

(J∗ − µ − σεΦ

−1(T)

σθ

)

. (11)

The size of the equilibrium threshold, J∗, affects the scale of revolt. When citizens adopt a

higher equilibrium threshold, revolting across a larger range of private signals, in expectation

there will be a larger scale of revolt and a higher likelihood, S∗, of successful revolution. The

condition J∗ ≥ J further implies that the expected scale of citizen revolt, should it occur, can-

not be too small. If too small, then the chance of success would be extremely low, providing

no citizen with an incentive to participate. Successful revolt thus depends on a critical tipping

point: either there is no revolt at all, or citizen revolt emerges with an expected scale that is

no smaller than when citizens adopt the threshold J.

Proposition 2. (Coordination and prevention) Given the need to coordinate, revolution depends on

reaching the tipping point, such that no revolt occurs when µ ≥ RD(c).

6 Optimal Policy Choice

To this point, we have focused on the citizens and the foreign government. We now consider

the autocrat’s optimal policy decision, completing the model by discussing his objective func-

tion. We begin by considering two possible cases. In the first case, citizens are trapped in an

equilibrium of coordination failure. In the second case, revolution is possible but only if a suf-

ficient number of citizens coordinate and reach the tipping point. We explore the autocrat’s

policy response in each case, evaluating the conditions under which he will choose to fully

deter or to “accommodate” (i.e., not fully eliminate) revolutionary threats. By accommodate,

we simply allow for the possibility that the cost of deterring revolt may be so high that the

autocrat chooses some policy response that does not fully eliminate the threat. Accommoda-

tion does not imply doing nothing; only that given the autocrat’s loss function, he chooses a

policy bundle that allows for some threat of revolt to remain.

The autocrat’s loss function comprises multiple parts. The ruler incurs a loss dw(S) ≥0 when the foreign government intervenes (the superscript w stands for “war”) and a loss

dp(S) ≥ 0 otherwise (the superscript p stands for “peace”). Both loss functions are strictly

increasing in S, the probability of revolt. Without loss of generality, we normalize dp(0) = 0,

setting the autocrat’s loss to zero when neither revolt nor intervention occur. This outcome

17

is obviously best for the autocrat. We further denote d ≡ dw(0) − dp(0) = dw(0) as the loss

purely due to foreign intervention (i.e., when S = 0).

Using these terms, we can define the autocrat’s expected loss as

D(w, S) ≡ w · [dw(S)− d] + (1 − w) · dp(S), (12)

which is strictly positive if and only if both S and w are strictly positive. Given this loss

function, the ruler then chooses a policy bundle (c, µ) ∈ C × M to minimize

w(µ) · d + D(w, S) + E(c), where w(µ) ≡ 1 − Φ[( f − µ)/σθ ]. (13)

Finally, we make the assumption that intervention is costly to the autocrat, even when

there is no revolution threat.

Assumption 2. (Costly Intervention) d > 0.

If there is no threat of revolution (i.e., S = 0), then the autocrat chooses the least provoca-

tive foreign policy µ to minimize the likelihood of foreign intervention. The autocrat’s optimal

choice is the minimal policy (c, µ), which minimizes his objective function. There is no need

to enact additional domestic measures (i.e., a higher c) or provocative foreign policy (i.e., a

higher µ).

Alternatively, now suppose that revolution is possible given some critical tipping point.

Citizens may now revolt so long as they reach a sufficient threshold. Under this condition,

the minimal policy bundle, (c, µ), by assumption, cannot prevent revolt. Instead, it results in

a non-zero probability S∗(c, µ) of revolt and a loss w(µ)d + D(w(µ), S∗(c, µ)) to the ruler. The

ruler may raise c at an expense of a higher E(c), or raise µ at a cost of a higher w(µ), or both,

to reduce the threat of revolution. The ruler prefers a policy bundle (c, µ) in the no-revolution

zone to (c, µ) when

D(w(µ), S∗(c, µ)) > d · [w(µ)− w(µ)] + E(c), (14)

where w(µ) ≥ w(µ). This condition holds when D is sufficiently large under (c, µ). For exam-

ple, the ruler may extract large rents from staying in power, so that the loss from intensified

foreign relations is less important.

These challenges to coordination may help explain why we do not observe open revolt

or unrest in many autocratic regimes. In some cases, coordination failure is the equilibrium

18

outcome. When this condition obtains, the autocrat does not need to resort to repressive mea-

sures or expensive cooptation, nor provoke international tensions. In other cases, however,

coordination may be possible but revolt fails to meet some critical threshold. In countries like

Iran and North Korea, we may think that some combination of repression/cooptation and

diversionary foreign policy frustrate collective action by preventing successful coordination.

Under such conditions, autocrats will deter revolt at the cheapest cost possible. Rulers look to

minimize loss w(µ) · d + E(c) subject to condition µ ≥ RD(c). The optimal policy must be lo-

cated on the revolution-deterrence frontier. Once reaching this frontier, further provocations

would only encourage foreign intervention, and more expansive domestic measures would

only consume more resources; neither would bring any additional benefit for the ruler. And,

since RD(c) is decreasing in c, diversionary foreign policy has an upper bound RD(c).15

On this frontier, µ and c are strategic substitutes. Consider two cost functions, E1 and E2.

Suppose that dE1/dc > dE2/dc for all c (i.e., E1 entails a higher marginal cost of implementing

domestic measures). The optimal policy under Et can be defined as (ct, µt), which satisfies

µt = RD(ct), for t = 1 and 2, where c1 ≤ c2 and µ1 ≥ µ2 (see Figure 2). When domestic policy

becomes more expensive (i.e., when the cost function increases from E2 to E1), the autocrat

will substitute it with foreign policy by increasing µ from µ2 to µ1 and reducing c from c2 to

c1.

Substitution effects allow regimes to trade-off between policy instruments as marginal

costs change. If some shock to the international or domestic system alters the marginal costs,

then the autocrat can respond by substituting the more expensive or risky policy for the other.

This policy choice over multiple instruments provides the autocrat with flexibility when mass

revolt is possible.

Finally, let us consider the condition under which the autocrat chooses accommodation

over deterrence. After all, if the cost of deterrence is prohibitive, then he may instead choose

to accommodate threats. The ruler chooses a policy bundle (c, µ) ∈ C × M to minimize the

loss function{

w(µ) · d + E(c) if µ = RD(c),

w(µ) · d + D(w(µ), S∗) + E(c) if µ < RD(c),(15)

15The opposite of Assumption 2, i.e., d < 0, may capture a “hawkish” ruler that would prefer internationalcrisis for reasons unrelated to domestic survival risks. In this case, unless there is a direct cost of raising µ, theruler will choose the more provocative foreign policy µ regardless of the constraint facing citizens. And sinceforeign policy alone can prevent revolt, the ruler will choose the minimal c = c. This opposite assumptionleads to an autocracy that is characterized by an extremely provocative stance in the international arena, butlax domestic control.

19

where S∗ and w(µ) are determined by conditions (11) and (13), respectively. The optimal

policy bundle solves this minimization problem. When the ruler moves from the revolution-

deterrence frontier to the revolution zone, the loss function exhibits an upward jump with

a size of D. By this discontinuity, policy bundles in the revolution zone that are “too close”

to the revolution-deterrence frontier, namely, the grey area in Figure 2, cannot be optimal.

A policy bundle (c, RD(c)) on the deterrence frontier dominates a bundle (c′, µ′), with µ′<

RD(c′), when

[w(RD(c))d + E(c)] − [w(µ′)d + E(c′)] < D(c′, µ′), (16)

where D(c′, µ′) = D(w(µ′), S∗(c′, µ′)).

This discontinuity is critical, because it leads to a potential complementarity between do-

mestic and foreign policies. Returning to Figure 2, suppose that there are two domestic cost

functions E1 and E2 (with dE1/dc > dE2/dc). Further suppose that under the high cost func-

tion E1, the ruler finds it too costly to deter revolutions. Under this condition, the ruler would

prefer accommodation, choosing the optimal policy (c1, µ1) in the revolution zone. If, how-

ever, the cost of domestic policy were to fall (i.e., a shift from E1 to E2), then the ruler would

respond by raising the repression/cooptation level to c2, where c2 > c1.16 Even if more re-

pressive measures per se cannot prevent revolt (i.e., µ1 < RD(c2)), they can reduce the level

of foreign policy provocations necessary to decrease revolutionary threats. To capitalize on

the gain of suppressing domestic survival risks, the ruler may now find it worthwhile to raise

µ until it reaches the revolution-deterrence frontier, i.e., µ2 = RD(c2). In this case, domestic

policies and foreign provocation become complementary.

Proposition 3. (Optimal policy choice) Given Assumption 2, the autocrat’s optimal policy choice is as

follows: If there is no threat of revolution, then the autocrat selects the minimal policy bundle (c, µ).

If there is a threat of revolution (i.e., there exists some sufficient tipping point), then the autocrat will

select some policy bundle (c, µ) that solves Expression (15); this bundle will be on the deterrence fron-

tier if (c, µ) satisfies Expression (16); otherwise, the autocrat will accommodate the threat by selecting

some policy in the revolution zone.

16This result can be established by the same “revealed preference” reasoning as in the proof of Proposition 3.

20

7 Effects of Revolt on Foreign Intervention

So far, we have assumed that α = 0 and showed how domestic and foreign policies could

prevent coordination by simply raising the cost of revolt and lowering the expected bene-

fits. We now conclude our analysis by exploring the case when α > 0, which allows for

the possibility that the foreign government’s choice depends on the citizens’ actions. As α

increases, domestic instability has a greater effect on the foreign government’s incentive to

intervene. Thus, citizens must consider how their choice to revolt will influence the foreign

government’s action.

To begin, assume α > 0 and suppose that the citizens face the tipping point constraint,

adopting a threshold Jα.17 By Lemma 1, there is a unique threshold Iα such that the foreign

government intervenes when θ > Iα. Given a citizen’s private signal θj, the likelihood of

foreign intervention is then 1 − Φ[(Iα − λθj − (1 − λ)µ)/√

λσε].18 An equilibrium threshold

for the citizen now solves

ln

[

Φ

(Iα(Jα)− λJα − (1 − λ)µ√

λσε

)]

+ ln

[

Φ

((1 − λ)(Jα − µ)− σεΦ

−1(T)√λσε

)]

︸ ︷︷ ︸

≡ Lα(Jα)

= ln (c

b). (17)

The left-hand side, denoted as Lα, shares similar properties with L, as shown in the following

lemma.19

Lemma 4. (New tipping point) Suppose α > 0 but Assumption 1 holds. The maximal value of the

function Lα, maxJα Lα ≡ Lα, is strictly decreasing in µ. Given c/b ∈ (0, 1), there exists a unique µα

such that Lα(µα) ≡ ln (c/b), and µα< µ.

Lemma 4 suggests that deterrence is easier when α > 0. Figure 3 illustrates this point. The

revolution-deterrence frontier exhibits a downward shift, µα(c) < µ(c) for all c, because now

17The parameter α is irrelevant when pure coordination failure prevails. On the other hand, since the foreigngovernment has a dominant strategy to intervene when θ > f , the assessment of foreign intervention is strictlypositive, Pr(θ > f |θj) > 0, for all θj. Again, there is no equilibrium where every citizen revolts.

18 Conditional on θ, the scale of revolt is Aα = Pr(θj ≤ Jα|θ) = Φ[(Jα − θ)/σε]. Assumption 1 still ensures that itis mutually compatible for both the citizens and the foreign government to adopt switching strategies. But, asin Shadmehr and Bernhardt (2010, 2011), revolt decisions may no longer be globally strategic complementarywhen α > 0. The positive impact of Aα on foreign intervention may cause the revolt incentive of a citizen tobe (locally) decreasing in Aα.

19The strict concavity of Lα may require additional conditions, e.g., Jα< Iα. If the function Lα is not strictly

concave in Jα, then for µ ≤ µα there may be more than two finite equilibrium thresholds, some of which are

local maxima like J in Figure 1 and some of which resemble J∗ or J∗∗ depending on the slope of Lα aroundthese solutions. The results in this section are based on the possibility of deterrence and are thus valid whenany of these finite equilibrium thresholds is selected.

21

RD

Domestic policy

Foreign policy

RDα

µH

µL

Figure 3: Shifting the Deterrence Frontier

the marginal citizen recognizes that a larger scale of revolt (i.e., a higher threshold Jα) encour-

ages foreign intervention. Let RDα be the corresponding revolution-deterrence frontier. As

shown in Figure 3, for all c, RDα is always lower than RD.

We can also show that, contrary to conventional wisdom, provoking international ten-

sions may actually lower the probability of foreign intervention in equilibrium. For illustra-

tion, return to Figure 3. Here, we fix domestic policy c and consider two foreign policies

µL and µH, such that µL < µα(c) < µH . This assumption implies that only µH, but not µL,

prevents revolt. Let IαL < f be the equilibrium intervention threshold of the foreign govern-

ment. The foreign policy µL gives rise to an equilibrium probability of foreign intervention

1−Φ[(IαL − µL)/σθ ]. By contrast, the more provocative policy, µH induces the foreign govern-

ment to choose a threshold f , resulting in an equilibrium probability of foreign intervention

1 − Φ(( f − µH)/σθ). Taking these two probabilities and re-arranging terms, we reach the

following condition

f − µH > IαL − µL ⇔ α · Φ

(Jα∗L − Iα

L

σε

)

> µH − µL. (18)

If this condition is met, then the more provocative foreign policy, µH , causes a lower likeli-

hood of foreign intervention. In this case, foreign policy becomes a more attractive instrument

than domestic policy because it no longer entails a trade-off between internal and external

threats.

This result is significant in the sense that foreign policy is now strictly preferred to do-

mestic measures. When revolt makes the foreign government more willing to intervene, a

more provocative foreign policy not only prevents revolt, but also reduces the likelihood of

22

intervention. If condition (18) holds, then autocrats should pursue diversionary foreign pol-

icy whenever facing domestic challenges. Such policies are cheaper than domestic measures

and do not include the risk normally associated with international provocations. This result

is summarized in the following proposition.

Proposition 4. (Foreign policy dominance) Suppose that α > 0 but satisfies Assumption 1. Diversion-

ary foreign policy may cause a lower probability of foreign military intervention in equilibrium.

Proposition 4 depends on the assumption of coordination problems. Recall that in the

benchmark model, we assumed that α satisfies Assumption 1, and further assumed a unitary

population. Under these conditions, the likelihood of foreign intervention was strictly in-

creasing in provocative foreign policy, as specified in Proposition 1. The negative relationship

characterized in Proposition 4 departs significantly from the previous result. By incorporat-

ing coordination problems, we show that provocative foreign policy may have the opposite

effect on intervention.

This result has implications for what we should observe in the real world. Namely, the

presence or absence of coordination problems implies opposite responses to provocative for-

eign policy. These different responses may help us understand why an autocrat’s foreign

provocations will make international conflict more likely in some cases, but not in others.

This variation can help explain contradictory findings in the empirical literature, which often

overlooks the potential role of coordination problems.

8 Comparative Statics

Having solved the game and characterized the equilibrium behavior, we now take stock with

a brief discussion of comparative statics. At the outset, it is important to note that many of

the model’s key insights derive from the discontinuity separating the no-revolution and rev-

olution zones. This discontinuity drives some of the implications that have already been dis-

cussed, like the conditions under which policy instruments are substitutes or complements.

Policy instruments interact differently across these zones, which are separated by the dis-

continuity that renders marginal changes largely irrelevant. Moreover, within these zones,

marginal changes are often less significant than the induced effects of the discontinuous jump.

Furthermore, as the last section made clear by comparing Proposition 1 and Proposition 4,

the introduction of coordination problems significantly changes the effects of foreign provo-

23

cation on intervention. Underlying this result is our assumption on the parameter α, which

captures the degree to which domestic revolt influences the foreign government’s choice to

intervene. By moving from α = 0 to α > 0, we were able to show the potential importance of

revolt and coordination problems on the likelihood of intervention. With α > 0, the citizens

have to worry that by revolting, they may increase the risk of intervention. When α = 0,

this concern does not figure into the population’s calculus, revealing the significance of this

parameter and its effect on the game’s strategic logic. Ultimately, it is a discrete but critical

change in α, from zero to positive, that is most noteworthy, rather than a marginal change in

some already positive α.

One parameter that we have not yet discussed in depth is b, which represents the pop-

ulation’s expected benefits from revolution. These benefits loosely relate to the underlying

grievances or level of discontent within the population. As discontent or grievances increase,

citizens will be more willing to revolt, expecting a greater benefit from successful revolution.

The empirical literature typically suggests that growing domestic discontent encourages au-

tocrats to pursue diversionary foreign policy. The possibility of preventing revolt, however,

points to a more subtle relationship. It is easier to prevent revolt at lower levels of discontent,

creating the possibility of a non-monotonic relationship between domestic grievances and the

autocrat’s policy response.

Consider two discontent levels bH and bL, with bH> bL

> c. Suppose that the status quo

policy bundle (c0, µ0) cannot deter revolt at either level (i.e., µ0 < RD(c0) for both bH and bL).

A higher level of discontent implies a greater threat of revolution: fixing the policy bundle, J∗

and so S∗ and D are all increasing in b.

The ruler decides whether to implement a more aggressive policy bundle (c0 +△c, µ0 +

△µ), where △µ ≥ 0 or △c ≥ 0 and at least one is strictly positive. Suppose that (c0 +

△c, µ0 +△µ) can only prevent revolt under the low discontent level, but fails under the high

discontent level. Facing high discontent, the ruler chooses (c0 +△c, µ0 +△µ) if

D(c0, µ0, bH)− D(c0 +△c, µ0 +△µ, bH)

> [w(µ0 +△µ)− w(µ0)]d + E(c0 +△c)− E(c0).(19)

In words, the ruler chooses a more aggressive policy bundle if the reduction in domestic sur-

vival risks can offset the cost of intensified international relations or more repressive domes-

tic measures (or both). By a similar calculation, low discontent prompts the ruler to choose

24

(c0 +△c, µ0 +△µ) if

D(c0, µ0, bL)− 0 > [w(µ0 +△µ)− w(µ0)]d + E(c0 +△c)− E(c0). (20)

In both situations, switching to the more aggressive policy bundle has the same cost, as seen

on the right-hand side of expressions (19) and (20). The difference is driven by the benefit,

which is found on the left-hand side of each expression. There is less survival risk under

low discontent, even when the ruler maintains the status quo, D(c0, µ0, bL) < D(c0, µ0, bH).

Nevertheless, the ruler can have a stronger incentive to choose (c0 +△c, µ0 +△µ) under bL

than under bH . In other words, we can have

D(c0, µ0, bL) > D(c0, µ0, bH)− D(c0 +△c, µ0 +△µ, bH), (21)

because revolt can only be deterred under low discontent. The possibility of deterrence cre-

ates a strong incentive to pursue diversionary foreign policy. This incentive can be important

for understanding the mixed empirical literature on domestic instability and diversionary for-

eign policy. Given this strategic environment and the autocrat’s choice over multiple policy

instruments, the conventional wisdom regarding the linear and strictly increasing relation-

ship between domestic instability and provocative foreign policy may not hold.

Proposition 5. (Benefits from revolution) For policy bundles in the revolution zone, the ruler may have

stronger incentives to provoke international tensions at a lower level of domestic discontent.

9 Conclusion

For totalitarian regimes in particular, avoiding revolutions is largely about preventing the

opposition from mobilizing. As such, we have focused our attention on this most basic of

coordination problems within autocracies. We depart from the current literature and develop

a formal model that introduces two key changes. First, we draw on a global games framework

to fully explore the role of coordination problems in autocratic policy choice. Second, we

incorporate both domestic and foreign policies within a single theoretical framework. These

changes lead to new insights on the likelihood of revolutions and the conditional effects of

multiple policy instruments.

Our model shows that the policy space is split into two distinct zones, one in which revolu-

tion can occur, and one in which it cannot. A policy bundle in the no-revolution zone contains

25

some mix of domestic and foreign policy choices such that the tipping point for revolution

is never reached. By contrast, a policy bundle in the revolution zone leads to some strictly

positive probability of revolution. Thus, moving from this zone into the no-revolution zone

results in a discontinuous decline in the risk of revolution, from strictly positive to zero. At

a more conceptual level, we can think of these zones as representing two states of the world:

one in which revolution is possible, and the other where it is not. Depending on which world

best characterizes a given regime, we should expect different outcomes to obtain.

Moreover, these different zones lead to distinct empirical implications, which may help

explain why the literature on diversionary foreign policy has produced “contradictory” find-

ings (Miller and Elgun, 2011). This literature typically suggests a strictly positive relationship

between domestic threats and the use of diversionary foreign policy: the greater this threat,

the greater the diversion. The discontinuous jump between these two zones provides one ex-

planation for why we may not observe such a relationship in practice. The autocrat’s optimal

policy bundle may “jump” from allowing some positive threat of revolt to fully eliminat-

ing it. Furthermore, there is a possible negative relationship between discontent and policy

response. The autocrat may respond more forcefully to lower levels of threat since these chal-

lenges can be fully deterred, while higher levels make a similar response prohibitively costly

or infeasible. Our results suggest that the empirical literature has not adequately accounted

for this discontinuity and the potential non-monotonicity in autocrat responses.

The revolution and no-revolution zones further determine how the autocrat’s domestic

and foreign policy choices interact. If the autocrat wants to eliminate all revolution risk, then

the optimal choice is the most cost-efficient policy bundle in the no-revolution zone, which

will be found on the zone’s frontier. This frontier has a negative slope, implying policy sub-

stitutability. Thus, if the autocrat increases the strength of the domestic policy response, then

he does not need to maintain the same level of diversionary foreign policy (or vice versa).

The substitution effect, however, does not hold for policy bundles off the frontier. If total

prevention proves to be too costly, then the autocrat may be willing to accept some positive

revolution risk, thereby placing the optimal policy bundle in the revolution zone. The discon-

tinuous change in the threat of revolution that occurs by moving from this zone to the frontier

implies that, under some conditions, domestic and foreign policies may reinforce each other.

Even if a stronger domestic policy response cannot by itself deter revolution, it reduces this

risk when coupled with the foreign policy instrument. Thus, a change in the autocrat’s pre-

ferred position – from accepting some positive revolution risk, to fully eliminating it – induces

26

policy complementarity.

Our model thus leads to new predictions on policy choices and how they interact. The

empirical literature that treats domestic and foreign policies as substitutes has only produced

mixed results (Enterline and Gleditsch, 2000). Our model suggests that, depending on where

a policy bundle is located (i.e., on or off of the deterrence frontier), domestic and foreign

policies may be substitutes or complements. The conditional nature of policy interactions

may have significant empirical implications.

27

Appendix: Proofs

� Lemma 1

Proof. When α = 0, then I = f for all P. Suppose that α > 0 and fix P. Define R(θ; P) ≡ θ + α · Φ[(P −θ)/σε ]. Since R is continuous in θ and R( f ; P) > f > R( f − α; P), by the intermediate value theorem,

there exists I ∈ ( f − α, f ) such that R(I; P) ≡ f . The standard normal density φ(·) is bounded above

by 1/√

2π. If α ≤ σε

√2π, then

∂R

∂θ= 1 − α

σεφ

(P − θ

σε

)

≥ 0. (22)

The equality holds only when α = σε

√2π and θ = P. Since R is strictly increasing except possibly at

one point, I must be unique. Q.E.D.

� Proposition 1

Proof. The comparative static with respect to µ is

[

1 − ασε

φPασε

φP

1 −λ

] [

dI/dµ

dP/dµ

]

=

[

0

1 − λ

]

, (23)

where φP ≡ φ[(P − I)/σε]. Therefore,

dI

dµ=

(1 − λ)(α/σε)φP

λ[1 − (α/σε)φP] + (α/σε)φP< 1, (24)

and so d(I − µ)/dµ < 0. Q.E.D.

� Lemma 3

Proof. Given J and θ, citizen j joins the revolt when θj = θ + ε j ≤ J, which occurs with probability

Pr(ε j < J − θ) = Φ((J − θ)/σε). By the law of large numbers, it also measures the number of protesters

A. Regime collapse occurs when A ≥ T, or, equivalently, θ ≤ J − σεΦ−1(T). We then obtain equation

(7).

Let φ be the pdf of standard normal distribution. Since the standard normal distribution is log-

concave, d2 ln [Φ(z)]/dz2 = d(φ/Φ)/dz < 0, the function (φ/Φ)(z) is strictly decreasing in z. In addi-

tion, φ/Φ → 0 as z → ∞, and, by l’Hopital’s rule, limz→−∞

φΦ(z) = limz→−∞

φ′

φ (z) = limz→−∞

−zφφ =

∞. Let x ≡ [ f − λJ − (1− λ)µ]/(√

λσε) and y ≡ [(1 − λ)(J − µ)− σεΦ−1(T)]/(

√λσε). Strict concavity

holds:

∂L

∂J= −

√λ

σε

φ

Φ(x) +

1 − λ√λσε

φ

Φ(y) and

∂2L

∂J2= (

√λ

σε)2 d(φ/Φ)

dx+ (

1 − λ√λσε

)2 d(φ/Φ)

dy< 0. (25)

28

As J → −∞, x → ∞ and y → −∞, and so ∂L/∂J → ∞. Similarly, ∂L/∂J → −∞ for J → ∞. The

maximizer J, determined by ∂L/∂J ≡ 0, is unique and takes a finite value, and L is strictly increasing

in J for J < J and strictly decreasing for J > J. Since J is finite, L < 0.

For µ < µ′, L(µ) = L( J(µ), µ) ≥ L( J(µ′), µ) > L( J(µ′), µ′) = L(µ′), where the strictly inequality

comes from, fixing J,

∂L

∂µ= −1 − λ√

λσε

[φ

Φ(x) +

φ

Φ(y)

]

< 0. (26)

For all J, a higher µ reduces L(J). Given ln (c/b) < 0, any µ such that L(µ) = ln (c/b) must be unique.

The existence of µ comes from L → 0− for µ → −∞ and L → −∞ for µ → ∞. For all J, L(J, µ) → 0−

when µ → −∞. Since, by the definition of L, 0 > L(µ) ≥ L(J, µ), it implies that L → 0− for µ → −∞.

Suppose that µ → ∞. Since L is strictly decreasing in µ, if L 9 −∞, then L is bounded below (and

converges to a finite number). Consider a strictly increasing sequence {µn} such that µn → ∞. For

each n, define δn ≡ J(µn) − µn, where J(µn) is the maximizer corresponding to µn. For each n, the

maximal value is

Ln = ln Φ

(f − µn − λδn

√λσε

)

+ ln Φ

((1 − λ)δn − σεΦ

−1(T)√λσε

)

. (27)

If δn → −∞, then the second term, and so the whole Ln → −∞, for the first term is bounded above

by zero. But if δn9 −∞, then for each real number, there is a subsequence δk(n) whose elements are

larger than this number. For this subsequence, µk(n) + λδk(n) → ∞. The first term, and so Lk(n) → −∞,

which contradicts the requirement that L is bounded below.

When L > ln (c/b), since L → ln 0 + ln 1 = −∞ for J → ±∞, there exist unique J∗ and J∗∗ such

that J∗ > J > J∗∗ and L(J∗) = L(J∗∗) = ln (c/b). The equilibrium threshold J = −∞ does not depend

on c, b, or µ. The implicit function theorem fails at J for ∂L/∂J = 0 at this point; comparative static

results are not well-defined. When c increases, for example, the equilibrium threshold jumps from J to

−∞, and when c decreases, it goes to either J∗ or J∗∗. At J∗, the comparative static results are

dJ∗

dc=

1

c · (∂L/∂J)|J∗,

dJ∗

db=

−1

b · (∂L/∂J)|J∗, and

dJ∗

dµ=

−(∂L/∂µ)

(∂L/∂J)|J∗, (28)

where ∂L/∂J < 0 at J∗. The results for J∗∗ are obtained by evaluating ∂L/∂J at J∗∗ and thus have

opposite signs. Q.E.D.

� Proposition 3

Proof. The optimality of policy (ct, µt), t = 1 and 2, implies that

w(µt)d + Et(ct) ≤ w(µ−i)d + Et(c−i), where − i 6= i

⇒E1(c1)− E1(c2) ≤ d[w(µ2)− w(µ1)] ≤ E2(c1)− E2(c2).(29)

29

If dE1/dc > dE2/dc but c1 > c2, then

∫ c1

c2

dE1

dcdc = E1(c1)− E1(c2) >

∫ c1

c2

dE2

dcdc = E2(c1)− E2(c2); (30)

a contradiction. Q.E.D.

� Lemma 4

Proof. Since Iα< f , for all finite Jα, Lα(Jα) < L(Jα). For all µ, the maximal value Lα

< L < 0. By

Iα> f − α, for finite µ, the maximal value Lα

9 −∞. The same arguments in Lemma 3 apply here to

show that Lα is strictly decreasing in µ, and that Lα → 0− as µ → −∞. When µ → ∞, the property

of Lα< L ensures that Lα → −∞. We then obtain the existence and uniqueness of µα. By Lα

< L for

finite µ, µα< µ. Q.E.D.

30

References

Acemoglu, D and J. Robinson (2000). “Democratization or Repression?” European Economic

Review, 44: 683–93.

Acemoglu, D. and J. Robinson (2001). “A Theory of Political Transitions.” American Economic

Review, 91: 938–63.

Angeletos, G., C. Hellwig, and A. Pavan (2007). “Dynamic Global Games of Regime Change:

Learning, Multiplicity, and the Timing of Attacks.” Econometrica, 75: 711–56.

Baliga, S., D. Lucca, and T. Sjostrom (2011). “Domestic Political Survival and International

Conflict: Is Democracy Good for Peace?” Review of Economic Studies, 78: 458–86.

Blaydes, L. (2006). “Electoral Budget Cycles under Authoritarianism: Economic Opportunism

in Mubarak’s Egypt.” Working paper, Stanford University.

Boix, C. and M. Svolik (2013). “The Foundations of Limited Authoritarian Government: Insti-

tutions, Commitment, and Power-Sharing in Dictatorships.” Journal of Politics, 75: 300–16.

Bueno de Mesquita, B., A. Smith, R. Silverson, and J. Morrow (2003). The Logic of Political

Survival. Cambridge, MA: MIT Press.

Bueno de Mesquita, B. and A. Smith (2009). “Political Survival and Endogenous Institutional

Change.” Comparative Political Studies, 42: 167–97.

Bueno De Mesquita. B. and A. Smith (2010). “Leader Survival, Revolutions, and the Nature

of Government Finance.” American Journal of Political Science, 54: 936-50.

Bueno de Mesquita, E. (2010). “Regime Change and Revolutionary Entrepreneurs.” American

Political Science Review, 104: 446–65.

Bueno de Mesquita, E. (2011). “Regime Change with One-Sided Limit Dominance.” Working

paper, University of Chicago.

Bueno de Mesquita, E. (2014). “Regime Change and Equilibrium Multiplicity.” Working pa-

per, University of Chicago.

Chiozza, G. and H. Goemans (2003). “Peace Through Insecurity: Tenure and International

Conflict.” Journal of Conlfict Resolution, 47: 443–67.

Chong, D. (1991). Collective Action and the Civil Rights Movement. Chicago: University of

Chicago Press.

31

Chwe, M. (2001). Rational Ritual: Culture, Coordination, and Common Knowledge. Princeton:

Princeton University Press.

Coser, L. (1956). The Functions of Social Conflict, New York: Free Press.

Davenport, C. (2007). “State Repression and Political Order.” Annual Review of Political Science,

10: 1–23.

Davis, J. (1988). Libyan Politics Tribe and Revolution. Los Angeles: University of California Press.

DeNardo, J. (1985). Power in Numbers. Princeton: Princeton University Press.

Desai, R., Olofsgard, A. and T. Yousef (2009). “The Logic of Authoritarian Bargains.” Eco-

nomics & Politics, 21: 93–125.

Downs, G. and D. Rocke. (1994). “Conflict, Agency, and Gambling for Resurrection: The

Principal-Agent Problem Goes to War.” American Journal of Political Science, 38: 362–80.

Enterline, A. and K. Gleditsch (2000). “Threats, Opportunity, and Force: Repression and Di-

version of Domestic Pressure, 1948-1982.” International Interactions: Empirical and Theoretical

Research in International Relations, 26: 21–53.

Geddes, B. (1999). “What Do We Know About Democratization After Twenty Years?” Annual

Review of Political Science, 2: 115–44.

Gent, S. (2009). “Scapegoating Strategically: Reselection, Strategic Interaction, and the Di-

versionary Theory of War.” Interactional Interactions: Empirical and Theoretical Research in

International Relations, 35: 1–29.

Goemans, H. and M. Fey (2009). “Risky but Rational: War as an Institutionally-Induced Gam-

ble.” Journal of Politics, 71: 35–54.

Haber, S. (2008). “Authoritarian Government.” In B. Weingast and D. Wittman, eds., The Ox-

ford Handbook of Political Economy, Oxford: Oxford University Press.

Haggard, S. and R. Kaufman (1995). The Political Economy of Democratic Transitions. Princeton:

Princeton University Press.

Hess, G. and A. Orphanides (1995). “War Politics: An Economic, Rational-Voter Framework.”

American Economic Review, 85: 828–46.

Kim, W. and J. Gandhi (2010). “Coopting Workers under Dictatorship.” The Journal of Politics,

72: 646–58.

32

Kuran, T. (1989). “Sparks and Prairie Fires: A Theory of Unanticipated Political Revolution.”

Public Choice, 61: 41–74.

Kuran, T. (1991). “Now Out of Never: The Element of Surprise in the East European Revolu-

tion of 1989.” World Politics, 44: 7–48.

Levy, J. (1989). “The Diversionary Theory of War: A Critique.” In M. Midlarsky, ed., Handbook

of War Studies, Ann Arbor: University of Michigan Press.

Lohmann, S. (1994). “The dynamics of informational cascades: the Monday demonstrations

in Leipzig, East Germany, 1989-91.” World Politics, 47: 42–101.

Malesky, E. and P. Schuler (2010). “Nodding or Needling: Analyzing Delegate Responsive-

ness in an Authoritarian Parliament.” American Political Science Review, 104: 482–502.

Miller, R. and O. Elgun (2011). “Diversion and Political Survival in Latin America.” Journal of

Conflict Resolution, 55: 192–219.

Morris, S. and H. Shin (2003). “Global Games: Theory and Applications.” In M. Dewatripont,

L. Hansen, and S. Turnovsky, eds., Advances in Economics and Econometrics, Cambridge:

Cambridge University Press.

Richards, D., T. Morgan, R. Wilson, V. Schwebach, and G. Young (1993). “Good Times, Bad

Times, and the Diversionary Use of Force: A Tale of Some Not-So-Free Agents.” Journal of

Conflict Resolution, 37: 504–35.

Shadmehr, M. (2014). “Mobilization, Repression, and Revolution: Grievances and Opportu-

nities in Contentious Politics.” Journal of Politics, 76: 621–35.

Shadmehr, M. and D. Bernhardt (2010). “Coordination Games with Common Values.” Work-

ing paper, University of Miami.

Shadmehr, M. and D. Bernhardt (2011). “Collective Action with Uncertain Payoffs: Coordi-

nation, Public Signals, and Punishment Dilemmas.” American Political Science Review, 105:

829–51.

Simmel, G. (1964). Conflict and the Web of Group Affliations, New York: Free Press.

Skocpol, T (1979). States and Social Revolutions. Cambridge: Cambridge University Press.

Smith, A. (1996). “Diversionary Foreign Policy in Democratic Systems.” International Studies

Quarterly, 40: 133–53.

33

Smith, A. (1998). “International Crises and Domestic Politics.” American Political Science Re-

view, 92: 623–38.

Tarar, A. (2006). “Diversionary Incentives and the Bargaining Approach to War.” International

Studies Quarterly, 50: 169–88.

Taylor, M. (1987). The Possibility of Cooperation. Cambridge: Cambridge University Press.

Wintrobe, R. (1998). The Political Economy of Dictatorship. Cambridge: Cambridge University

Press.

34