Signaling games are central to political science but often have multiple equilibria, leading to no definitive prediction. We demonstrate that these indeterminacies create substantial problems when fitting theory to data: they lead to ill-defined and discontinuous likelihoods even if the game generating the data has a unique equilibrium. In our experiments, currently used techniques frequently fail to uncover the parameters of the canonical crisis-signaling game, regardless of sample size and number of equilibria in the data generating process. We propose three estimators that remedy these problems, outperforming current best practices. We fit the signaling model to data on economic sanctions. Our solutions find a novel U-shaped relationship between audience costs and the propensity for leaders to threaten sanctions, which current best practices fail to uncover.
