Sequential Analysis of Deterrence Games with a Declining Status Quo

Abstract

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.

Confusions of Loss Aversion and Risk Attitude in International Relations and Peace Science

“…This research note was an attempt to resolve a puzzle that began with the intuition advanced by a prospect-theoretic account of behavior in international relations and peace science, and ended with a set of formal results that ran counter to that intuition (Carlson and Dacey 2004, 2006a, 2006b. That puzzle was explained via a mechanism that identified when a loss averse decision maker, with a negative valuation of the sure-thing payoff, would choose the risk averse act (Jervis, 2004).…”

“…In a series of papers, we developed a model that supported a formal prospect-theoretic account of decision making and the results derived from the model clearly and consistently showed that the foregoing intuition often fails to hold (Carlson and Dacey 2004, 2006a, 2006b. Indeed, there are several cases wherein loss aversion, and specifically a high level of loss aversion, induces risk aversion, not risk seeking, over losses.…”

Social norms and the traditional deterrence game

“…These claims have been examined within the context of a prospect-theoretic account of the traditional deterrence game (Carlson and Dacey 2006a). In this section, we examine the degree to which a declining status quo affects Challenger's risk-related behavior.…”

The Emerging Fourth Wave of Deterrence Theory-Toward a New Research Agenda

“…This is closely related to another problem: in contrast to the implied assertion of most classical approaches to deterrence, actors do not always prefer preserving the status‐quo (Zagare 2004:128; Quackenbush and Zagare 2005:101; Langlois and Langlois 2006:161–162). In fact, formal models scholars demonstrate that interactions among opponents are much more complicated than envisioned by classical deterrence approaches (for example, Powell 1990:70; Werner 2000:721–722, 729–730; Danilovic 2001:102–103, 2002; Fearon 2002:20–22; Carlson and Dacey 2006).…”

“…For a more limited view of the influences of costly signals on deterrence outcomes, see Danilovic (2002:130-40). 721-722, 729-730;Danilovic 2001Danilovic :102-103, 2002Fearon 2002:20-22;Carlson and Dacey 2006). A further difficulty is that although third wave scholars have acknowledged the importance of studying threat formation and how deterrence is affected by the policymaker's interpretation of reality, from a constructivist point of view it would seem that they have generally considered the interest as given (Luke 1989:212;Carlsnaes 1992:251;Wendt 1999:36;Guzzini 2000:149;Tannenwald 2007:33-34).…”