Limitations to the Direct Testing of Extensive Form Crisis Bargaining Games

This paper investigates the possibility of embedding extensive-form crisis bargaining games directly into empirical tests of these interactions. Given a game structure and data on the relative frequency of the possible outcomes, what can we infer about the distribution of payoffs and, by extension, the effect of covariates (e.g., military capabilities, regime types, etc.) on those payoffs? We show that even with a very simple game structure, such inferences are plagued by under-identi£cation and are highly sensitive to the assumed information structure. We present maximum likelihood estimators for inferring the payoffs of a basic three-move con¤ict game from the observed distribution of outcomes. Separate estimators are developed for quantal response (QRE), complete information Nash (NE), and perfect Bayesian equilibrium (PBE) solutions to the game. We develop two main results. First, the distribution of payoffs implied by a given set of outcome data strongly depends upon an untestable assumption about the structure of information. As a result, two analysts with the same model and the same data but different beliefs about the information structure can arrive at very different estimates of the payoffs — and have no way to determine empirically which is better. Second, regardless of the solution concept employed, non-innocuous identifying restrictions must be made that limit the generality of the results and make them dif£cult to interpret substantively. Researchers interested in testing strategic choice models of international con¤ict should focus on testing their models’ comparative-static predictions, while keeping in mind the limitations we identify.