The Sensitivity of Critical Risk Values to Small Changes in the Value of the Status Quo

This paper reports on a technical result that we have derived from various formal models that support a prospect-theoretic account of the traditional deterrence game. The result is as follows. In sequential prospect-theoretic play of the traditional deterrence game, under both one-sided and two-sided incomplete information, Challenger's decision over whether or not to threaten Defender can be remarkably sensitive to the specification of the model's parameter values, including very small changes in the valuation of the status quo.This result supports the intuition commonly advanced in the International Relations literature: a loss averse decision maker will choose the risk averse act if the sure-thing is perceived to be acceptable, and will choose the risk preferring act if the sure-thing is perceived to be unacceptable. The foregoing intuitive explanation for a decision maker's risk-related behavior relies, in general, on only two variables: the presence of loss aversion and the valuation of the status quo. Here we show that this explanation is under-specified in that the degree of sensitivity also depends on the quality of Challenger's probability assessment and on the relative size of the value of the status quo vis-à-vis the size of the other payoffs in the game.