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We develop two extensions of the traditional deterrence game to examine the influence of third players, called Assassin and Donor, upon the behavior of a Challenger. The results present the optimal behavior of Challenger when Assassin and Donor are included in the traditional deterrence game. The key result is that Challengers who back down, and thereby activate Assassin or Donor, are more prone to initiate conflict in the first place than are Challengers who escalate, and thereby avoid Assassin or Donor.

The model developed in this paper provides a formal prospect theory account of Challenger's behavior in the traditional deterrence game played under sequential decision analysis. The model is used to analyze two basic claims commonly made in the international relations literature regarding the importation of prospect theory into the analysis of crisis games. These claims pertain to Challenger's behavior when the valuation of the status quo is positive and Challenger's behavior when the valuation of the status quo is negative. We model the traditional deterrence game between Challenger and Defender as a one-sided incomplete information game where Challenger is uncertain about Defender's preference ordering. We examine the behavior of Challenger under the condition that the status quo is declining, using a von Neumann—Morgenstern decision rule as specified by expected utility theory, and a Kahneman—Tverksy decision rule as specified by prospect theory. The formal results show that these claims do not hold unconditionally and must be stated more precisely. Furthermore, there exist conditions under which the claims are false. We show that in addition to specifying the valuation of the status quo and the value of the probability of loss, as per the claims, a fuller understanding of Challenger's behavior also requires a specification of Challenger's valuation of the status quo vis-à-vis the valuations of other major payoffs in the game. In so doing, we capture many of the details relevant to a more complete analysis of Challenger's behavior in the deterrence game.

The poliheuristic theory of foreign policy decision making posits a two-stage process wherein the decision maker first employs a noncompensatory decision rule to eliminate politically unacceptable alternatives and then employs a (perhaps) traditional decision procedure to select from the remaining set of acceptable alternatives. Ageneral decision analysis is used to provide a structured account of the elimination process of the first stage of the poliheuristic theory by displaying a noncompensatory decision rule for eliminating unacceptable policy alternatives. The results show how general decision analysis can be used to specify when an alternative is unacceptable to a political decision maker who is sensitive to public opinion.