D. Marc Kilgour

Credibility, Uncertainty, and Deterrence

In this paper the connection between deterrence stability and threat credibility is examined conceptually and theoretically. We formulate as a model of bilateral deterrence a game of incomplete information in which each player is uncertain about its opponents preferences should it unilaterally alter the status quo. Uncertainty about the preferences of ones opponent leads to uncertainty about the opponents willingness to retaliate. By identifying the credibility of each players retaliatory threat with the probability that a player prefers retaliation to capitulation, we maintain consistency with both the traditional strategic literature, where credibility usually means believability, and with game theory, where credibility is usually synonymous with sequential rationality (i.e., subgame perfect equilibrium). We analyze formally the strategic implications of this conception of credibility and thus explore the critical role played by uncertainty in deterrence. By explicitly modeling uncertainty, we are able to understand the role of threats in contributing to, or detracting from, the robustness of a deterrence relationship.

Domestic Political Structure and War Behavior

A natural approach to understanding the tendencies of nations to enter or avoid wars is through the study of national decision making in international crises. Recent game-theoretic models of national crisis behavior can be used to generate research hypotheses about how specific features of national political structures and political culture are related to war-proneness. To illustrate, propositions about the relationships of several national characteristics to crisis involvement and war initiation are derived from two such models. Empirical testing of these hypotheses can help shed new light on Kants thesis that democracies are less war-prone than other states.

Modeling 'Massive Retaliation'

A generic asymmetric two-stage escalation model of incomplete information is used to examine strategic relationships in which one player adopts a defense posture akin to the “Massive Retaliation” policy of the Eisenhower administration that relies only on the threat of escalation to deter aggression. In the model, a challenger must decide whether to contest the status quo and a defender must choose between capitulation and escalation. Each player has probabilistic knowledge of the others preference between conceding and fighting an all-out war. All perfect Bayesian equilibria of the Incomplete Information Escalation game are identified and interpreted. Unlike two-stage games of complete information, war and escalation may be rational outcomes under incomplete information. At certain times, these outcomes may be inevitable. Challengers preferring conflict to capitulation always initiate conflict, whatever the information state of the game. But when information is incomplete, even challengers with an aversion to all-out war may rationally precipitate a crisis. Similarly, when it is unsure of a challengers preferences, even a defender preferring not to wage war may rationally choose to escalate a conflict. The conditions associated with a stable status quo, a successful challenge, an escalated conflict, and war are discussed.

How Democracy Resolves Conflict in Difficult Games

Democracy resolves conflicts in difficult games like prisoners’ dilemma and chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative outcome. In the transformed game, it is always rational for voters to vote for the cooperative outcome, because cooperation is a weakly dominant strategy independent of the decision rule and the number of voters who choose it. Such games are illustrated by 2-person and n-person public-goods games, in which it is optimal to be a free rider, and a biblical story from the book of Exodus.

Are Crises Rational? A Game-Theoretic Analysis

A crisis occurs when countries, by escalating a conflict, increase the probability that a war will occur (Snyder, 1972: 218). The crisis may be precipitated by threats, force deployments or mobilization, a change in government, a costly arms race that can no longer be tolerated, or any of a number of other factors that may rapidly alter a country’s strategic assessment of its relationship with another country. Whatever the precipitating factors, we assume that a country that escalates a conflict does so because it — or, more accurately, its leaders — think that, despite the greater likelihood of war, escalation will be to its benefit.

Game Theory and National Security

Arms races deterrence winding down star wars optimal threats crisis instability verification national security and war, political scientists and mathematicians.