We develop an empirical estimator directly from an extensive-form crisis bargaining game with incomplete information and discuss its features and limitations. The estimator makes it possible to draw inferences about states' payoffs from observational data on crisis outcomes while remaining faithful to the theorized strategic and informational structure. We compare this estimator to one based on a symmetric information version of the same game, using the quantal response equilibrium proposed in this context by Signorino (1999, American Political Science Review 93:279–298). We then address issues of identification that arise in trying to learn about actors' utilities by observing their play of a strategic game. In general, a number of identifying restrictions are needed in order to pin down the distribution of payoffs and the effects of covariates on those payoffs.
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