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Abstract
This essay explores a deterrence relationship between one defender and two challengers that are interconnected game-theoretically but are otherwise acting independently. In the double deterrence game model, the primary challenger makes the first move, defender, the second, and the secondary challenger makes its move only after the defender and the primary challenger have made their choices. In other words, the threat of the secondary challenger is both latent and contingent. There are four types of defenders, and three types of the two challengers. These preference assumptions define 36 distinct strategic environments, or games. These games are analyzed under both complete and incomplete information. The results are highly sensitive to the specific combination of player types. Deterrence is most likely to succeed when a defender's threat is highly credible, and to fail when it is low. The secondary challenger is most likely to have an impact on play only at intermediate levels of the defender's and the primary challenger's credibility. Assuming a rising challenger, or a declining defender, or both, a danger zone will exist just prior to, or immediately after, the primary challenger has achieved parity with the defender, that is, when a balance of capabilities exists. The principal aim of a defender of the status quo facing two challengers acting independently should be on preventing a challenge by its primary opponent. This conclusion is robust no matter what configuration of player types one assumes.

Alexander J. Field (2014, 54) argues that game theory "offers little guidance, normatively or predictively, in thinking about behavior or strategy in a world of potential conflict." He makes this claim by attributing to John von Neumann a view of the superpower relationship during the Cold War period that has no basis in fact and inferring policy prescriptions to that view that are simply not there. Field also suggests that Thomas Schelling's explanation of the "event that didn't occur" leads to the conclusion that "deterrence works because we are human, not because we are entirely rational" (Field 2014, 86). In this essay I show that there is at least one logically consistent game-theoretic explanation of the absence of a nuclear war during the long-peace of the 1950s and early 1960s. I also demonstrate that Field's assumptions lead to exactly the opposite conclusions; that is, that mutual deterrence can in fact be reconciled with rationality and that game theory is a powerful tool for understanding interstate conflict.

"Perfect Deterrence Theory" published on by Oxford University Press.

AbstractThis paper interprets the Moroccan crisis of 1905–1906 in the context of an incomplete information game model, the Tripartite Crisis game, and one of its proper subgames, the Defender-Protégé subgame. In the early stages of the crisis the action choices of the players were shown to be consistent with the players' beliefs, but their beliefs were not tested. In the final phase, beliefs and action choices were brought into harmony. British support of France during the conference that ended the crisis, the firm stand that France took at the conference, and the German decision to press for a conference is explained in terms of the model's principal variables. The explanation derived from the model is not necessarily at odds with consensus historical interpretations of the Moroccan crisis. Nonetheless, it offers several advantages over standard, largely atheoretical or ad hoc descriptions. One clear advantage is the convenient framework the model provides for organizing information about the crisis around a common set of assumptions and concepts and for the clear way the most salient causal variables are highlighted. Another is the model's ability to point to a logically consistent set of expectations about the connections between certain action choices and the beliefs that drive them. Finally, the model's straightforward applicability to an important and complicated watershed event is suggestive of its potential generality.

This essay constructs a theoretically rigorous explanation of the 1914 European war that involved Austria—Hungary, Germany, Russia, and France. It also serves to confirm Trachtenberg's contention that `one does not have to take a particularly dark view of German intentions' to explain the onset of war in 1914 and `question the ``inadvertent war'' theory'. A number of related questions about the Great War are also addressed within the context of a generic game-theoretic escalation model with incomplete information. The analysis suggests that general war broke out in Europe in 1914 because both Austria— Hungary and Germany believed that, when push came to shove, Russia would stand aside if Austria moved aggressively against Serbia. There is a sense in which the war can be said to be unintended but there is no sense in which it should be understood as accidental.