A duration estimator for a continuous time war of attrition game
Frederick J. Boehmke,
Douglas Dion and
Charles R. Shipan
Political Science Research and Methods, 2021, vol. 9, issue 4, 760-778
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.
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