Modeling Deterrence and International Crises

Abstract

The continuous Prisoner's Dilemma is a reasonable model for nuclear crises (usually represented by “Chicken”), and for the arms race. This article addresses the existence of credible deterrence strategies that promote cooperation as a dynamically stable steady state. Decisions made repeatedly in time are the selection by each side of a level of hostility. Assessment of the resulting situation is represented by a utility function for each player. As the game proceeds, players are concerned with the current situation as well as with the future consequences of their present decisions. Thus each side must formulate intentions and expectations of each other's future behavior and use them to infer their own present optimal decisions. A formal concept of deterrence strategy is introduced: It promises the other side retaliation in kind to prevent any gain from aggressive play, and it inflicts increasing losses as a result of escalation. If one side adopts such a deterrence strategy, the other side cannot do better than acting similarly, and when both sides adopt it, they both enjoy optimal decision rules that confirm intentions and expectations. The resulting dynamical system endows cooperation with asymptotic stability provided the threats of retaliation contain a fair mix of firmness and restraint.