A duration estimator for a continuous time war of attrition game

Abstract

We developed a maximum likelihood estimator corresponding to the predicted hazard rate that emerges from a continuous time game of incomplete information with a fixed time horizon (i.e., Kreps and Wilson, 1982, Journal of Economic Theory 27, 253-279). Such games have been widely applied in economics and political science and involve two players engaged in a war of attrition contest over some prize that they both value. Each player can be either a strong or weak competitor. In the equilibrium of interest, strong players do not quit whereas weak players play a mixed strategy characterized by a hazard rate that increases up to an endogenous point in time, after which only strong players remain. The observed length of the contest can therefore be modeled as a mixture between two unobserved underlying durations: one that increases until it abruptly ends at an endogenous point in time and a second involving two strong players that continues indefinitely. We illustrate this estimator by studying the durations of Senate filibusters and international crises.