Specification

The baseline model has three players: a patron (P), a prospective ally (A), and a common rival (R). There are two stages, each of which entails a bargaining interaction with R. In stage 1 A bargains with R on its own, while in stage 2 P and R bargain, with A potentially weighing in on P’s side. Here, we study how observing A’s bargaining interaction with R in stage 1 allows P to draw inferences about A’s preferences and future behavior in stage 2.

A and P share a preference over the distribution of the assets in dispute with R, but place different values on them. P (and R) value them at 1, while A values them at $\alpha \lt 1$ , which is private information to A. In other words, A holds a “bias” in favor of P’s bargaining position, capturing the intuition that A’s preferences over the issue(s) at stake are closer to P’s than to R’s, but not identical to P’s.Footnote ²² $\alpha $ can take on one of two values, $\underline \alpha $ or $\overline \alpha $ , where $\underline \alpha \lt \overline \alpha $ . When $\alpha = \underline \alpha $ , A is defined as an abandoner (denoted $\underline A $ ) that will not support P against R even with an alliance, whereas when $\alpha = \overline \alpha $ , A is a supporter (denoted $\overline A$ ) that will honor its alliance obligations to P. P is initially uncertain of A’s type, holding prior beliefs that $\alpha = \overline \alpha $ with probability $q$ and $\alpha = \underline \alpha $ with probability $1 - q$ . Similarly, R holds priors that $\alpha = \overline \alpha $ with probability $\rho $ and $\alpha = \underline \alpha $ with probability $1 - \rho $ .Footnote ²³ Figure 1 illustrates the configuration of the actors’ goals.

Figure 1. Spatial graph of actors’ preferences and types

Figure 2 presents the game tree. Stage 1 begins with A choosing whether to accept or reject an offer, $x$ , from R. Acceptance results in peaceful settlement at $x$ . Rejection results in winner-take-all conflict that imposes costs ${k_{\rm{R}}}$ on R and ${k_{\rm{A}}}$ on A, and which A wins with probability $w$ , its share of the bilateral distribution of power with R. Payoffs from the first-stage settlement are weighted by a factor, $\phi $ , which can be greater than or less than 1. This captures the relative value of the different assets at stake across the two stages (including discount rate). Conflict thus yields expected payoffs of $\phi w\alpha - {k_{\rm{A}}}$ for A and $\phi \left( {1 - w} \right) - {k_{\rm{R}}}$ for R, while a peaceful settlement yields payoffs of $\phi \alpha x$ for A and $\phi \left( {1 - x} \right)$ for R.Footnote ²⁴

Figure 2. Extensive form of the baseline model (R’s payoffs omitted for legibility)

Between stages, P chooses whether to ally with A. Alliance transfers utility $u$ from P to A, whereas nonalignment is payoff-neutral.Footnote ²⁵ $u$ captures two benefits to A at P’s expense.Footnote ²⁶ First is the investment P makes to enhance A’s military capabilities and coordinate them with P’s own. Second, by accepting some degree of dependence on A for operational effectiveness—such as basing, logistics, or local force deployments—P becomes obligated to defend A from third-party threats in general. In turn, P’s investment in and commitment to its allies reduce their defense spending needs,Footnote ²⁷ amounting to a direct transfer captured by $u$ . Thus, we model P’s prospective abandonment concerns during the alliance-formation process as the risk that its costly investment in A will yield no strategic payoff.

The second-stage asset is again valued at 1 by P and $\alpha $ by A, with the actors holding identical ideal points.Footnote ²⁸ How stage 2 proceeds depends on whether P has allied with A. Without an alliance, P reaches a peaceful settlement according to the bilateral distribution of power, $\pi $ . This yields second-stage payoffs of $\pi $ for P, $\alpha \pi $ for A, and $1 - \pi $ for R.

Conversely, if P has allied with A, stage 2 begins with A choosing whether to support P against R or to abandon its alliance commitment. Support carries cost $c$ , which represents the effort A must expend to actually bring its military power to bear on P’s side.Footnote ²⁹ Whereas abandonment entails pocketing the security resources bestowed by P, support, even short of war, requires A to invest in and mobilize its military capacity to enhance P’s bargaining leverage against R.Footnote ³⁰ Thus, support occurs when $\alpha $ is above a particular threshold, ${\alpha ^{\rm{*}}} \equiv {{c} \over {w}}$ , while abandonment occurs when $\alpha \lt {\alpha ^{\rm{*}}}$ . As mentioned, we assume that $\underline \alpha \lt {\alpha ^{\rm{*}}}$ and that $\overline \alpha \ge {\alpha ^{\rm{*}}}$ , such that A is an abandoner when $\alpha = \underline \alpha $ and a supporter when $\alpha = \overline \alpha $ .

If A abandons, the second-stage payoffs follow just as they did with no alliance. However, sustaining the alliance adds A’s capabilities to P’s in the bargaining interaction with R. With A’s support, the coalition of P and A holds capabilities of $\pi + w$ , raising the settlement to that point. P’s second-stage payoff is then $\pi + w$ , while A’s is $\alpha \left( {\pi + w} \right) - c$ and R’s is $1 - \pi - w$ .

Results

Equilibrium analysis

We solve the model using the perfect Bayesian equilibrium solution concept.Footnote ³¹ There are three “classes” of equilibria across all parameter spaces, depicted in Figure 3: (1) separating equilibria (SE) in which abandoners accept R’s offer and supporters reject it; (2) pooling equilibria (PE) in which both types accept; and (3) a PE where both types reject.Footnote ³² Our main results concern a comparison of the SE and the acceptance PE, so we begin by describing those equilibria before returning to the rejection PE.

Figure 3. A’s equilibrium response for the baseline model. Arrows indicate the effect of having alliance at stake

The acceptance PE occur when R is sufficiently confident A is a supporter that it issues the minimum offer, $x_{\overline A}^{\rm{*}}$ , that supporters (and thus both types) accept.Footnote ³³ In response to acceptance, P retains its prior beliefs, allying if and only if it holds sufficiently confident priors that A is a supporter ( $q \gt {u} \over {w}$ ).Footnote ³⁴

Conversely, the SE occur when R is sufficiently confident that A is an abandoner that it issues the minimum offer, $x_{\underline A }^*$ , that only abandoners would accept. Supporters, being the more resolved type, necessarily reject this offer. P therefore forms posterior beliefs that A is a supporter with certainty in response to rejection, and an abandoner with certainty in response to acceptance. In the latter case P never allies, while in the former case P allies if and only if $w \ge u$ .Footnote ³⁵

Our key results rest on a comparison of A’s incentives to fight in the equilibria where alliance is at stake versus those where it is not. Alliance is defined to be at stake when P would ally if and only if A rejects R’s offer.Footnote ³⁶ Thus, in terms of the exogenous game parameters, alliance is at stake in the SE if and only if $w \ge u$ , whereas in the PE it also depends on P’s prior and off-path beliefs.Footnote ³⁷ Since these formal definitions are cumbersome and unintuitive, we use “alliance at stake” as a more substantively meaningful shorthand hereafter.

Empirical Applications

To establish the generality of our argument before presenting a detailed empirical illustration, we first provide a brief, nonsystematic survey of historical cases that appear to exhibit our theoretical logic.Footnote ⁴⁷ Naturally, the range of the examples that follow is constrained by the limits of our own knowledge, and there are likely many additional manifestations of the theory.

There are numerous instances of military confrontations that were motivated in part by reassurance of a prospective security partner. Many occur under US hegemony, with other states attempting to secure or maintain a beneficial security relationship with the US as patron. In a cross-national study that corroborates one aspect of our mechanism, Gannon and Kent find a correlation between a state’s need for a US alliance commitment and the costliness of its contribution to the 2001–2014 war in Afghanistan,Footnote ⁴⁸ suggesting that our causal logic motivated US security partners in this period. The same was true of the Korean War. In Thailand, for example, the “mere prospect of military aid had sparked a revolution in postwar Thai foreign policy amenable to American interests.”Footnote ⁴⁹ The Thais knew the US sought a “definite confirmation regarding the policy of the Thai government in defending against communist aggression,”Footnote ⁵⁰ and acknowledged that by deploying troops with UN forces in Korea “we will get various things in return,” ultimately resulting in membership in the US-led SEATO alliance.Footnote ⁵¹

A more speculative example is China’s attempt to achieve rapprochement with the US in what would become a “tacit alliance” against the USSR. Margaret MacMillan suggests that Mao Zedong may have provoked the 1969 Sino–Soviet border war in part as a means of “sending a signal to the Americans that the rupture between the People’s Republic and the Soviet Union was permanent,” and marks this as “the moment when [Henry] Kissinger finally accepted that … the time was favorable for an American move toward China.”Footnote ⁵²

Our argument is equally applicable in contexts where reassurance is needed to maintain existing alliance benefits or resuscitate a lapsed or fraying alliance. In recent years, Denmark’s “will to actively maintain its status as a contributing and constructive ally through participation in [US-led] military operations [was] driven by a perception of the United States as crucial to Denmark’s national security.”Footnote ⁵³ Denmark has been “happy to fight … to secure the alliance commitments that not so long ago seemed unchallenged.”Footnote ⁵⁴ Similarly, Austria made a deliberate decision in 1914 to provoke war with Serbia, in part to assure Germany of Austrian reliability and sustain its alliance commitment. Austrian diplomats fretted that “our decision should be influenced strongly by the fact that … by a weak and hesitating policy we might risk not being so certain of German support at some future time.”Footnote ⁵⁵ Austria’s foreign minister wrote that “in Germany it would not be understood if we were to neglect this opportunity” to provoke war with Serbia. That is, “Germany would consider further negotiating with Serbia a confession of weakness on our part,” which would have serious “repercussions for our position in the Triple Alliance and Germany’s future policy” toward Austria.Footnote ⁵⁶ Germany’s urging “had a great influence on the firm attitude of the [Austrian] Emperor” Franz Joseph, resulting in an ultimatum to Serbia “composed so that the possibility of its acceptance is practically excluded.”Footnote ⁵⁷

This last illustration highlights the applicability of our argument to contexts without a hegemonic US patron, and to relatively symmetrical great-power security relationships. An example under the former condition is the intervention of the Kingdom of Piedmont-Sardinia (“Piedmont”) in the Crimean War. Piedmont joined the anti-Russia coalition in part to “insinuate [itself] into the West’s good graces ahead of Austria, and, if possible, to gain Western support for [Piedmont]’s ambitions in Italy.”Footnote ⁵⁸ Thus, Piedmont fought to signal that it would be a more reliable partner to the British and French in securing the European status quo than the Austrians would be. Historians conclude that as a result of its involvement in the Crimean War, Piedmont “came to the [diplomatic] understanding which led ultimately to the independence of Italy,” with a Franco–Italian coalition defeating Austria at Solferino in 1859.Footnote ⁵⁹

Another pre-1945 manifestation of our mechanism was the formation of the Anglo–Japanese Alliance. In 1894, “Russian penetration into northern China … culminated in the Sino-Japanese War,” wherein Japan sought to wrest Korea from a crumbling Qing Empire to prevent it from falling to the Russians. Thus, “Japan emerged as a rival with Russia”—which was also Britain’s chief rival—making clear that “Britain and Japan shared a common interest in opposing further Russian expansion.”Footnote ⁶⁰ In light of Japan’s war to obstruct Russia, Britain’s foreign secretary considered “a Russo-Japanese clash over Korea … inevitable in the long run,” deeming Japan “our natural ally… [Japan] will be a counterpoise to the Russians & so far a distinct advantage to us. Our policy must be to make her our ally.”Footnote ⁶¹ Similar dynamics played out more intentionally in the Boxer Rebellion during 1901. Tokyo dispatched 10,000 soldiers to help defend joint Japanese–British interests and contest expansion of Russian influence in China, in hopes of making “Britain willing to allot Japan a role as its principal partner in Asia.”Footnote ⁶² The interventions were ultimately successful in this endeavor, as “Japan finally achieved its goal of concluding a new treaty with Britain” in 1902.Footnote ⁶³ Ian Nish concludes that “Japan’s behavior helped in steering British opinion towards recognizing Japan as a useful ally against Russia in Asia.”Footnote ⁶⁴

Furthermore, although our argument applies most clearly to asymmetric cases in which a powerful patron confers security rents on a relatively weak ally, it can also obtain among relatively equal powers when one transfers net resources to the other. Once such instance is the “diplomatic revolution” of 1756, during the Seven Years’ War, in which long-time rivals France and Austria aligned with each other against their previous allies, Prussia and Britain, respectively.Footnote ⁶⁵ Key to the realignment was the burgeoning Austro–British commercial and colonial rivalry, as well as Britain’s overtures toward Austria’s main rival, Prussia.Footnote ⁶⁶ As Britain moved increasingly toward Prussia, the Austrians looked to France, Britain’s adversary in the North American theater, as a potential alternative. Recognizing that they “held in prospect a substantial alliance with Austria,” the French launched maritime operations against Britain and a 15,000-troop landing at Minorca to attract Vienna further. Subsequently, the Austrians were “impressed by France’s performance in the war, and believed … Versailles would deal with her more honestly than had their counterparts in London.”Footnote ⁶⁷ Thus, France’s demonstrated willingness to fight the British in Europe helped persuade the Austrians that France would also be a reliable ally against Prussia.Footnote ⁶⁸

A final empirical implication is that if taking a hard line and demonstrating a willingness to fight a common adversary can promote alliance formation, then a prospective ally’s concessions and refusal to fight should forestall it. This is seen in the effect that British and French appeasement of Nazi Germany had on alliance negotiations with the Soviet Union. Although the British “saw Soviet policy as a ruse to get Britain and France into a war with Germany while the USSR sat aside … the Soviet side saw it the other way around, convinced by various Anglo-French attempts to come to terms with Hitler.”Footnote ⁶⁹ Indeed, “after the Munich conference, Soviet confidence in Britain and France hit rock bottom.”Footnote ⁷⁰

This brief historical survey demonstrates that our logic generalizes across several different contexts. Whereas smaller states have often fought to garner patronage from a hegemonic US since 1945, we can also identify several cases with a non-US patron, one with symmetrical alliance partners (the Seven Years’ War), and another (Allied appeasement of Germany) exhibiting the negative implication of our argument that failure to stand firm can subvert alliance formation that otherwise seemed likely.

Sino–Soviet Reassurance in the Korean War

We illustrate results 1 to 3 with China’s entry into the Korean War in 1950. This case captures the SE with alliance at stake, casting China as the prospective ally, the USSR as patron, and the United States as third-party rival. We argue that China’s involvement in the war helped Chinese leader Mao Zedong demonstrate to Soviet dictator Josef Stalin China’s reliability as an ally. This allowed Mao to garner a Soviet alliance commitment and corresponding economic aid vital to the survival of the fledgling PRC. Initially skeptical of China’s intentions, Stalin demanded that the Chinese demonstrate their resolve to fight in support of Soviet aims by intervening in Korea. This conditional promise of Soviet security cooperation played an important role in Mao’s authorization of North Korea’s initial invasion, his decision to enter the war, and the manner in which he conducted it, informing both the timing of the intervention and the costly and prolonged military strategy China employed. But our primary purpose is to show how Mao used his entry into the war and tough bargaining posture during its course to credibly reassure Stalin and secure alliance benefits, rather than showing that war would not have occurred counterfactually. We will discuss later how our argument complements Mao’s other main motivation for intervention, to counter the threat of US troops approaching the Chinese border.

In late 1949, the Chinese communists faced a litany of problems that made securing a Soviet alliance immensely valuable. The task of rebuilding and governing a backward, war-torn country stood before them, and US-backed threats still loomed from Taiwan and Japan. A Soviet alliance was China’s best hope of bolstering itself against these formidable security challenges, while also promising desperately needed economic assistance.Footnote ⁷¹ As Westad notes, “virtually all Chinese Communist leaders believed that the construction and survival of [a Chinese socialist] state would depend on Soviet support.”Footnote ⁷² Thus, through 1949 Mao bombarded Stalin with pleas for an alliance accompanied by aid. Yet Stalin repeatedly declined to hear Mao’s requests.Footnote ⁷³

The fundamental barrier to an alliance was a daunting reassurance problem. Stalin was skeptical that the PRC was sufficiently reliable to warrant the massive investment in China’s reconstruction Mao hoped would accompany a formal alliance.Footnote ⁷⁴ As the CCP emerged victorious in its civil war, “Stalin could not shake his doubts about Mao’s long-term intentions toward the Soviet Union and the West,”Footnote ⁷⁵ concluding from Mao’s ambivalent diplomatic posture toward the US that if push came to shove the Chinese would not “want to quarrel with the Americans.”Footnote ⁷⁶ Ideologically, “Stalin remained very concerned about Mao’s loyalty to Soviet leadership” and his commitment to Stalin’s vision for world communism.Footnote ⁷⁷ As Goncharov, Lewis, and Xue emphasize, “Stalin did not consider Mao a true Marxist and always suspected that the Chinese revolution sooner or later would mutate into something else, meaning something anti-Marxist and anti-Soviet.”Footnote ⁷⁸ Moreover, “Mao was aware of Moscow’s apprehensions about Chinese ‘Titoism’ and was determined to prove China’s loyalty to the world revolutionary movement.”Footnote ⁷⁹ To overcome these concerns and achieve a mutually beneficial alliance, credible reassurance signals were needed.

Mao’s key reassurance signal was his willingness to confront the US over Korea once it became clear the Soviet alliance was at stake. North Korean leader Kim Il Sung badly needed Soviet and Chinese support in his pending civil war, but initially found both Stalin and Mao unenthusiastic.Footnote ⁸⁰ Mao twice turned down Kim’s early requests for Chinese intervention in Korea, and Chinese leaders even agreed in October 1949 that a North Korean attack on the South should be avoided entirely.Footnote ⁸¹

Once Stalin agreed to discuss a potential alliance with Mao in January 1950, however, Mao’s position on Korea changed dramatically. In one exchange, Stalin (who himself had leverage to restrain Kim Il-Sung) “clearly placed the last chance at stopping [North Korea’s initiation of] the war on Mao’s shoulders by giving him veto power over Kim’s final decision.”Footnote ⁸² Stalin’s reason for doing so was “to test Mao’s dedication to ‘proletarian internationalism.”’Footnote ⁸³ Christensen concurs that “the outbreak of the Korean War was the first ‘great test’ of the Sino-Soviet alliance, and the process leading up to it exemplified Stalin’s pre-war lack of trust in Mao.”Footnote ⁸⁴ This clearly shows that Stalin saw China’s behavior in the looming Korean conflict as a critically informative signal of Mao’s commitment to Soviet aims. In terms of our model, an alliance was at stake.

Crucially, Mao fully recognized Stalin’s “great test” and responded as we hypothesize. Once he had been “put on the spot by Stalin, Mao Zedong had no alternative but to confirm his support for the North Korean plans” in order to maximize alliance benefits from the USSR.Footnote ⁸⁵ Thereafter, as Westad notes, Mao was quite genuinely “fighting for friendship.”Footnote ⁸⁶ Mao himself recalled that “Stalin did not fully trust him to be a real revolutionary until after China’s massive intervention in the Korean War.”Footnote ⁸⁷ To demonstrate his revolutionary credentials, in January 1950 Mao sent 50,000 to 70,000 troops to North Korea, a move he had previously refused to make.Footnote ⁸⁸ Thus, having ensured war was imminent by granting support for Kim’s invasion, Mao then committed to covert intervention by preemptively deploying Chinese troops.Footnote ⁸⁹ These were key signals of Mao’s resolve that coincided precisely with the initiation of Sino–Soviet alliance discussions.

Furthermore, as US forces approached the Chinese border in October, Mao responded to Stalin’s request that he officially enter the war with five to six additional divisions by instead sending nine, despite his awareness that the initial lack of Soviet air support would leave his troops immensely vulnerable.Footnote ⁹⁰ For Shen and Xia, “China’s dispatch of troops, therefore, was a key step in turning the Sino-Soviet alliance from a paper alliance to a real one.”Footnote ⁹¹

Consistent with result 3, the Soviets deemed China’s entry into the Korean War a credible signal of its reliability and responded accordingly. Chinese intervention served to “convince Stalin that Mao and his government would not compromise with the United States and would stand by the Communist cause even against staggering odds… The Korean conflict strengthened Stalin’s trust in Mao.”Footnote ⁹² Mao himself confirmed that until China’s intervention in Korea, the Soviets “doubted that ours was a real revolution.”Footnote ⁹³ Thus, “only because of the outbreak of the Korean War and Mao’s decision to send troops to aid Korea under extremely difficult circumstances was the Sino-Soviet relationship strengthened… The political, military, diplomatic, and economic dimensions of the Sino-Soviet alliance were transformed by the war.”Footnote ⁹⁴ As mentioned (see note 71), Soviet assistance to China dramatically increased thereafter.

The direct quotes and historical literature we have cited show that the actors were motivated at least in part by our hypothesized mechanism. However, this is not intended to refute the leading alternative hypothesis for why China entered the war—the threat from the US advance on the Korean Peninsula—which operated alongside ours. Christensen, among others, argues that “Mao’s decision to enter Korea in force was triggered by the American decision to send US forces north of the 38th parallel… Mao did not intend to allow American troops to remain permanently behind a buffer in North Korea, regardless of the buffer’s width.”Footnote ⁹⁵ Yet many of these scholars have also acknowledged the salience of Mao’s desire to secure Soviet support. Christensen himself notes that the aggressive military strategy and “tough posturing” Mao adopted were at least partly “designed to influence the Soviets.”Footnote ⁹⁶ Hao and Zhai similarly identify “several Chinese interests and goals, including the improvement in Sino-Soviet relations [that] were considered by the Chinese leaders in making their decision.”Footnote ⁹⁷ Likewise, for Chen Jian, Rosemary Foot, and Allen Whiting, defending China against US forces and strengthening ties to the Soviets were both significant elements of Mao’s calculus.Footnote ⁹⁸

Furthermore, while the arguments are not mutually exclusive, ours helps account for several aspects of China’s entry into and conduct in the war that are otherwise anomalous. The first is the timing of Mao’s authorization of, preparation for, and initial intervention in the conflict. As we have seen, Mao invited the US threat by signing off on Kim’s invasion in the first place, in order to impress Stalin. Likewise, the deployment of combat-ready troops to North Korea in January occurred immediately after Stalin revealed the conditional possibility of an alliance, but nine months before US forces entered North Korean territory and threatened China’s border. Second, as Christensen observes in his later work, once China intervened its military strategy “of course ran directly against the goal of deterring the United States from sending its forces across the 38th parallel in the first place and reduced the likelihood that Sino-American conflict would remain limited after escalation.”Footnote ⁹⁹ Thus, while “Mao’s decision to enter Korea in force” may have been “triggered by the American decision to send US forces north of the 38th parallel,” as Christensen argues,Footnote ¹⁰⁰ our mechanism helps explain the earlier Chinese diplomatic and military policies that helped precipitate this threatening US behavior.

Finally, our argument sheds light on the intransigent bargaining position Mao adopted even as the US sought a settlement that could eliminate the threat to China. As Oriana Mastro notes, after entering the war China “maintained a closed diplomatic posture for the next eight months, refusing all third-party proposals for direct talks and not making any offers itself.”Footnote ¹⁰¹ This bargaining posture is puzzling if Mao’s only goal was to eliminate the US threat on the Korean Peninsula. However, it fits very well with Mao’s goal of securing an alliance by reassuring the Soviets of his resolve to incur high costs in opposing the Americans. Our argument thus works in tandem with Mao’s defensive motivations to explain China’s entry into the Korean War, and adds value in explaining crucial aspects of Mao’s strategy.

In sum, China’s entry into the Korean War nicely illustrates the model’s first three results. A state might harden its bargaining position and even incur costs of war with a common rival to reassure a prospective patron and secure a valuable alliance. Although China’s costs of fighting the US were immense, once Stalin made clear that authorization of and intervention in the Korean War would be seen as credible signals of China’s reliability, Mao jumped in with both feet. He endorsed Kim’s invasion, committed thousands of his best troops to fighting well before the war began, and then adopted a military strategy and bargaining position that guaranteed much higher costs than were necessary to defend China’s border. The gamble was successful, helping to nail down the Soviet alliance commitment and economic aid China so desperately needed.

Specification

This extension adds a new actor, P’s existing client, C, who shares P’s ideal point and valuation of the asset.Footnote ¹⁰³ Stage 1 parallels the baseline model, except that instead of bargaining with R, A bargains with C over an asset orthogonal to the one at stake with R in stage 2.Footnote ¹⁰⁴ This first-stage asset carries a value of $\beta $ to A. As above, C makes an offer, $x$ , regarding the first-stage asset, which A accepts or rejects. In stage 2 P then bargains with R, either alone or in conjunction with A, depending on P’s and A’s previous choices.

Two departures from the baseline model more realistically capture bargaining with P’s existing client.Footnote ¹⁰⁵ First, because C reliably supports P against R, first-stage conflict between A and C reduces P’s second-stage bargaining leverage against R by quantity $f$ , from $\pi $ to $\pi - f$ . Second, we no longer assume A’s power relative to C is the precise degree of power that it adds in coalition with P against R. Instead, we attach coefficient $z \ge 1$ to A’s first-stage share of power, giving A a $zw$ probability of winning a first-stage conflict with C. Thus, C receives a first-stage payoff of $\phi \left( {1 - x} \right)$ following acceptance and of $\phi \left( {1 - zw} \right) - {k_C}$ following rejection. C’s second-stage payoffs are identical to P’s.

Results

The equilibrium profile of this extension is identical to the baseline model, except that there is no pooling on rejection.Footnote ¹⁰⁶ This leaves two equilibrium classes, separating and pooling on acceptance.Footnote ¹⁰⁷ Section 2 of the appendix contains a full equilibrium analysis of the extension.

The PE occur when C is sufficiently confident A is an abandoner that it issues the minimum offer, $x_{\underline A }^*$ , that both types accept. In response to acceptance, P retains its prior beliefs, allying if and only if it holds sufficiently confident priors that A is a supporter ( $q \gt {u \over w}$ ). Alliance is at stake in the PE if and only if P’s priors dictate alliance in response to pooling ( $q \ge{u \over w}$ ) and P forms off-path beliefs $q' \le {{\rm{u}} \over {\rm{w}}}$ . These conditions imply that P would ally in response to pooling on acceptance, but not off path in response to rejection.Footnote ¹⁰⁸

The SE occur when C is sufficiently confident A is a supporter that it issues the minimum offer, $x_{\overline A}^{\rm{*}}$ , that only supporters would accept. P therefore forms perfectly accurate posterior beliefs. P never allies in response to rejection, and allies in response to acceptance if and only if $w \ge u$ . Thus, alliance is at stake in the SE if and only if $w \ge u$ .Footnote ¹⁰⁹

As before, we compare A’s incentives to fight in the equilibria where alliance is at stake to those where it is not. Figure 4 shows how the minimum offers each type will accept— $x_{\overline A}^{\rm{*}}$ for the supporter and $x_{\underline A }^*$ for the abandoner—shift with and without alliance at stake, and the ranges of offers (including out-of-equilibrium offers) each type accepts and rejects under each condition. In the SE without alliance at stake, $x_{\overline A}^{\rm{*}} = zw - {{{k_{\rm{A}}} + f\overline \alpha } \over {\phi \beta }}$ . But this threshold decreases to $x_{\overline A}^{\rm{*}} = zw - {{{k_{\rm{A}}} + f\overline \alpha } \over {\phi \beta }} - {{u - c + w\overline \alpha } \over {\phi \beta }}$ in the SE with alliance at stake. Likewise, in the PE without alliance at stake, $x_{\underline A }^* = zw - {{{k_{\rm{A}}} + f\underline \alpha } \over {\phi \beta }}$ , but this decreases to $x_{\underline A }^* = zw - {{{k_{\rm{A}}} + f\underline \alpha } \over {\phi \beta }} - {u \over {\phi \beta }}$ in the PE with alliance at stake.Footnote ¹¹⁰

Figure 4. A’s equilibrium response for the model extension. Arrows indicate the effect of having alliance at stake

These results are the mirror image of the baseline model’s. As before, the prospect of an alliance incentivizes both abandoners and supporters to reassure P. In contrast, however, reassurance entails accepting the offer from the patron’s existing client, rather than rejecting an offer from its rival. Thus, accepting C’s offer signals compatibility with P, whereas rejection signals incompatibility.

This implies that whereas the prospect of alliance can generate conflict between a prospective ally and the patron’s rival, it can avert conflict that counterfactually might have occurred between the ally and the patron’s existing client (due, for example, to exogenous incomplete information or commitment problems that are not included in our model). Proposition 6 (in the appendix) shows that when the alliance is sufficiently valuable, supporters accept all offers. In this case, even if C were overoptimistic about its likelihood of victory or underestimated A’s valuation of the first-stage asset, war with the supporter would still be avoided no matter how severe these information problems.Footnote ¹¹¹ In short, a patron’s abandonment concerns can facilitate rapprochement between its prospective and existing clients, as a means for the former to reassure the skeptical patron of its reliability.

Result 4. When P’s alliance decision is conditional on A’s bargaining behavior toward an existing client that shares P’s preferences, both supporters and abandoners are more likely to accept the client’s offer. If alliance is sufficiently valuable, supporters accept all offers.^{Footnote 112}

Empirical Applications

As we did for the baseline model, we preface our full-length case study of the formation of the ANZUS Alliance with several other real-world manifestations of result 4 to establish that it generalizes beyond a single example.

In 1972, Egypt sought substantial US military and economic aid, if not an alliance, yet “American economic aid was largely contingent upon [Egypt] pursuing a USA-sponsored peace with Israel.”Footnote ¹¹³ Consequently, reducing hostilities with Israel loomed large in Egyptian strategy: “The Egyptian-Israeli peace process … was intimately linked to … Egypt’s transition from a Soviet ally to a nation in the American orbit.”Footnote ¹¹⁴ Egyptian President Anwar Sadat’s unprecedented concessions to achieve peace with Israel “aimed at changing the attitudes of the US public, Congress and the USA’s Jewish community.”Footnote ¹¹⁵ Indeed, Sadat saw the “framework for the agreement he was seeking with the Israelis” as part of a wider plan to “restore diplomatic relations between Egypt and the United States.”Footnote ¹¹⁶

This mechanism also operates in the absence of a hegemonic US. When considering expansion of the Austro–German Dual Alliance to include Italy, Germany made its commitment conditional on Italian concessions to Vienna. The Germans required Italy’s “abandonment of irredentism”—that is, of “the enlargement of the Italian state by the conquest of Austria’s subject nationalities.” But although “acceptance of the status quo in Central Europe and the Balkans must have been a bitter pill,”Footnote ¹¹⁷ the Italians recognized it as a worthwhile trade-off on the grounds that “as soon as we have removed the causes of distrust existing towards us in Austria, the accomplishment of an alliance with Germany will meet with no obstacle.”Footnote ¹¹⁸ Bismarck himself acknowledged that for Italy “the key to the German door was to be found in Vienna.”Footnote ¹¹⁹

Finally, this causal logic again manifested between symmetrical allies during the “diplomatic revolution” early in the Seven Years’ War. With the Anglo–Austrian alliance breaking down in 1755, the British attempted to resurrect it by offering a massive subsidy to Russia, which had been allied with Austria since 1746. Although this gambit was unsuccessful for the reasons discussed earlier, Britain’s extension of aid to Russia was a direct response to an Austrian suggestion and implies that reassuring Austria was a key British motive.Footnote ¹²⁰

Australia’s Bid for a US Alliance

We illustrate result 4 through Australia’s post-World War II bargaining position regarding its rival, Japan, which the US was nurturing as a bulwark against communist expansion. In terms of our model, this case again captures the SE with alliance at stake, with the US as P, Australia as A, Japan as C, and the USSR/China as R. Despite profound fear of renewed Japanese aggression, Australia made substantial concessions concerning Japan’s economic revival to demonstrate that it shared US anti-communist priorities—actions that were sufficiently credible to American decision makers that the US granted the ANZUS alliance by mid-1951. To be clear, we do not claim that war between Australia and Japan would have counterfactually occurred, only that Australia took a softer line toward Japan to signal compatibility with the US, which captures our core argument.

Although the US and Australia now seem like natural and inevitable allies, the overlap in their interests and regional visions was quite unclear following World War II. Australia initially seemed far less committed than the US to containing communism. Tensions between Canberra and Washington centered on, among other things, Australian efforts to develop a neutral camp between the US and USSR that would include London and Ottawa,Footnote ¹²¹ and the American perception that the Australians were simply “unrealistic as regards Communist designs and methods.”Footnote ¹²² US concerns about “initial efforts by Australia to lead a third force in the growing conflict between East and West” persisted into 1950, as reflected in a US embargo on sharing classified intelligence with Canberra.Footnote ¹²³ Due to this US skepticism, Australia’s initial efforts to “extract some sort of post-war security guarantee … proved unsuccessful.”Footnote ¹²⁴

Abandonment concerns underpinned US alliance hesitancy.Footnote ¹²⁵ NSC 48/2 emphasized in 1949 that Asia-Pacific countries, including Australia, must show themselves willing to contain communism collectively before the US would become involved.Footnote ¹²⁶ Prominent in the minds of American policymakers was the cost of sinking resources into Australia’s defense capabilities, represented in the model by the direct utility transfer, $u$ , from P to A. Assistant Secretary of State William Butterworth opposed allying with Australia, largely because US security provision would reduce Australia’s incentives to pay for its own defense.Footnote ¹²⁷ Thus, as Australia’s Department of External Affairs noted, “Between the end of 1947 and mid-1950 the Americans showed little inclination [toward a multilateral] Japanese peace settlement or a Pacific Pact.”Footnote ¹²⁸

Crucially, US anti-communist strategy in Asia centered on a rehabilitated Japan as the United States’ key ally. As Secretary of State Dean Acheson put it, the US needed to “push ahead with the reconstruction of those two great workshops,” Japan and Germany.Footnote ¹²⁹ Thereafter, “the new [US] priority was to make provisions for Japan’s security from outside aggression. Punitive efforts were replaced by regenerative efforts.”Footnote ¹³⁰

However, Australia still perceived Japan as a profound threat.Footnote ¹³¹ Indeed, “one legacy of the war shared by the overwhelming majority of Australians was this realised fear of Japan.”Footnote ¹³² In February 1951 Minister of External Affairs Percy Spender decried US plans to include Japan in a Pacific Pact that would transform it “from an enemy into an ally over-night… We would clearly find it most difficult to accept… We cannot, in common prudence, dismiss Japan as a threat to Australian security, remote as this may seem at the moment.”Footnote ¹³³ In short, as Spender stated, “we did not trust Japan.”Footnote ¹³⁴

Spender reiterated to Truman advisor John Foster Dulles many times Australia’s resistance to cooperating with Japan, and the Americans were well aware that they could not resolve these Australian insecurities.Footnote ¹³⁵ Indeed, Dulles and Acheson were convinced that a multilateral alliance including Japan would be a nonstarter with Australia.Footnote ¹³⁶ Acheson bemoaned that Australian behavior at the Far Eastern Commission overseeing the Japanese occupation threatened to “jeopardize [Japan’s] stabilization program” and “seriously weaken [authority] of occupation,” from which “only Sovs and their Jap Commie Party minions will reap any advantage.”Footnote ¹³⁷ Furthermore, he expressed deep concern that “Australia has clung to the belief that the principal threat to its security comes from a revived Japan rather than from a Communist Asia backed by the Soviet Union.”Footnote ¹³⁸ Thus, American leaders held pessimistic prior beliefs about Australia’s support for a US containment strategy centered on a powerful Japan.

However, as result 4 implies, Australia’s apprehensions about Japanese aggression also made its willingness to support Japanese rehabilitation an informative signal of whether it shared US anti-communist priorities. The US therefore made alliance with Australia conditional on Australia’s policies toward Japan. According to Dulles’ chief advisor, Marshall Green, the key question was whether, given that an alliance was at stake, “Australia could be expected to moderate its previous position demanding that Japan remain completely disarmed and demilitarized for decades hence.”Footnote ¹³⁹ Truman was adamant that he would commit to a “mutual assistance arrangement among the Pacific island nations” only on the strict condition that potential alliance partners “accept the general basis on which the United States is prepared to conclude a peace settlement with Japan.”Footnote ¹⁴⁰ Dulles likewise wrote in January 1951 that “in view of the inter-dependence of the Pact and the proposed Japanese peace, the United States should not become committed to the Pact unless it is assured that the other Parties will agree to the kind of a Japanese peace that the United States feels is necessary.”Footnote ¹⁴¹

By early 1951, the Australians came to realize that a US alliance commitment was conditional on Australia’s acquiescence to a revived and integrated Japan: “The American interest in guaranteeing Australia and New Zealand appears to be linked with their desire to ensure that Japan … is protected against Communist aggression.”Footnote ¹⁴² An External Affairs memo confirmed that to consummate a US alliance “we should be required to identify ourselves with the policy that … Australia is committed to support Japan.”Footnote ¹⁴³ This was the first time the Australians had explicitly linked “some substantial guarantee of our security” from the US to “a form of peace treaty with Japan which we dislike.”Footnote ¹⁴⁴

Having come to understand that a US alliance was at stake, Australian policy-makers deemed it sufficiently valuable that they tolerated much looser restrictions on Japan than they preferred, ultimately accepting Tokyo’s economic and military resurgence as a counterweight to Chinese and Soviet expansionism. As Spender noted in February 1951, he had “taken the utmost care during the past few months to maintain a common front with the United States.”Footnote ¹⁴⁵ Consequently, the multilateral Japanese peace settlement Australia signed in 1951 was historically unprecedented in its generosity to a defeated adversary. Japanese reparations were satisfied by mandatory purchases of Japanese goods that gave Tokyo privileged access to its former victims’ markets.Footnote ¹⁴⁶ Economically, the currency that flowed into Japan enabled “the Japanese to re-equip and modernize their plants” and “to expand in an amazing way.”Footnote ¹⁴⁷ Purged wartime elites were reintegrated into government. Crucially, despite Japan’s Article 9 peace constitution and immediate US control over Japan’s Self-Defense Forces, binding restrictions on Japanese rearmament were perceived as slight to nonexistent, subject only to ad hoc enforcement by the US. In terms of the model, Australian concessions to support Japan’s economic recovery and inclusion in Pacific defense arrangements were costly signals that Australia shared US anti-communist security preferences and would serve as a reliable ally.

US observers recognized these signals. Acheson, Dulles, and their colleagues were impressed by Prime Minister Robert Menzies’s vow of “assistance in swinging [Australian] public opinion around to realities of Japanese situation, with special emphasis upon … denying Japan and its industrial complex to Soviets.”Footnote ¹⁴⁸ The Americans acknowledged “a greater measure of [Australian] support than in the past for our Far Eastern policies in general and particularly as they relate to Japan,”Footnote ¹⁴⁹ concluding that “the views Mr. Menzies expressed when he was in Washington were [regarding the Japanese treaty] in large measure close to ours.”Footnote ¹⁵⁰ Assistant Secretary of State Dean Rusk wrote Acheson that Australia had, “in connection with negotiation of the Japanese peace treaty, now accepted the principle of eventual Japanese contribution to its own defense.”Footnote ¹⁵¹ National Intelligence Estimate 19 (of April 1951) noted that Canberra was “reconciled to the necessity of Japanese defensive rearmament” and “desire[d] safeguards against both Communist expansionism and resurgent Japanese militarism.”Footnote ¹⁵²

In response, American leaders updated their beliefs about the compatibility of Australian and US security preferences. In March 1950 the US ambassador to Australia emphasized the “sincerity of [Spender’s] intention and [the] importance [the] new Australian Government attaches to [the] US phase of its foreign relations,” noting that “every known act of [Menzies’] government since taking office indicates it really means business” in combating communism, and that it “has gone out of its way to strengthen [the] US-Australian relationship. In particular, it is endeavoring to meet our position re … [the] Communist problem.” The State Department soon updated as well, noting the “marked change in the orientation and direction of Australian foreign policy” since 1950, and that “Spender is desirous of establishing the closest and most cooperative relations with the United States and has in effect made this objective a cardinal point of his foreign policy.”Footnote ¹⁵³ The Joint Chiefs of Staff affirmed in December 1950 that Australia could be trusted to “contribute … to the security of the [Asia-Pacific] area.”Footnote ¹⁵⁴ Dulles thereafter deemed Australia perhaps the most loyal US ally, with Canberra having “stoutly faced up to [the] situation” and served as “our strong supporters” in combating communism.Footnote ¹⁵⁵

These updated US beliefs culminated in the ANZUS alliance in the summer of 1951, within days of the Japan peace settlement. Although the Japan treaty was “a signal [that the US] expected the Japanese to rearm soon,”Footnote ¹⁵⁶ which the Australians deplored, its signing generated credible assurances that Australia would support the US anti-communist strategy in Asia even when it conflicted with Australia’s other perceived interests. This allowed Spender to overcome US abandonment concerns and secure the alliance that had been an elusive holy grail for Australian governments for decades.