Deterrent Threats

The fundamental idea of deterrence is simple enough. A party is deterred from some action when it decides against the action to avoid a response threatened by a second party. Note the two conditions: (1) the threat by the second party must be explicit and contingent on the initial action and (2) absent the threat, the first party must prefer to carry out the action. Deterrence has long played a role in human life—for instance in law enforcement systems designed to deter crime, in the efforts of parents to deter children from misbehaving, and in policies of empires aimed at deterring attacks on their possessions and client states. Also common is the two-sided variant of deterrence, in which two sides reciprocally deter each other, as in an armed standoff.

Deterrence has always been a fundamental component of international politics. But at the end of World War II, the demonstrated power of nuclear weapons persuaded many thinkers that the success of deterrence was now of ultimate priority: the proper aim of deterrence based on the threat of nuclear retaliation seemed to be to ensure that the threat never had to be implemented. Success in deterrence was declared to be the keystone of U.S. foreign policy, and U.S. military strategist Bernard Brodie famously suggested that the main purpose of the military had been to win wars, but from now on its main purpose is to avert them.

But deterrence based on a threat that cannot be carried out seemed problematic. The debate about rationality and deterrence began in the decade immediately following World War II when the rapidly developing field of game theory was exploring the concept of rational choice, defined as choosing alternatives that are most in the chooser's own interest. To see the terms of the debate, represent unilateral deterrence as an extensive-form game shown in Figure 1, where the first party is called Initiator and the second Defender. Deterrence occurs when the Initiator chooses Do Not Act, and the outcome is Status Quo (SQ). Other possible outcomes are Revision (Rev), if Initiator acts but Defender does not respond, and Confrontation (Conf), if Initiator acts and then Defender responds. To understand deterrence, one must understand when each possible sequence of actions will be selected.

Before addressing the conditions for the success of deterrence, we make the assumptions that

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Figure 1 Unilateral Deterrence.

Without (A1), there is nothing to deter. Without (A2), there is no reason to deter it. Consistent with these assumptions, Initiator is a revisionist state and Defender a status-quo power.

For games such as unilateral deterrence, game theory recommends a solution concept called subgame perfect equilibrium, which models each player (party) as making choices to achieve its most preferred available outcome, on the assumption that any subsequent choices will be made according to this same principle. Assuming rationality and full information, choices depend solely on each player's relative preferences over the three possible outcomes: barring ties, Initiator has three preference orderings consistent with (A1), and Defender has three consistent with (A2). As it happens, there is always a unique subgame perfect equilibrium, which is shown in Table 1. In particular, the outcome is Status Quo when Defender prefers Confrontation to Revision and Initiator prefers Status Quo to Confrontation. Thus, for deterrence to succeed, Defender's threat must satisfy two

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