Justin Esarey and Will H. Moore Florida State University

1. * A Crisis Bargaining Game with Private Information Capabilities/Resolve Bumba Mukherjee University of Notre Dame Justin Esarey and Will H. Moore Florida State University Strategic Interaction and Interstate Crises: A Fixed-Effects Bayesian Quantal Response Estimator for Incomplete Information Games Methodological Question: When data are generated from an incomplete information game, how can the influence of private information types be econometrically captured? Step 1: Derive a likelihood from the game using Quantal Response Equilibrium solution concept Our model assumes that all states play this game separately with all other states in directed dyads. The game is played at every time period. A panel thus contains 2t(nC2) many games. Our project considers the game at right, a crisis bargaining game adapted from Lewis and Schultz (2003). The μ parameters capture a state’s private resolve, its taste for war. The equations at left show QRE solutions for a state’s probability of action at each of the three decision nodes. These equations (particularly Pr(Resist)) incorporate Bayesian updating where possible. The last line at right incorporates these solutions into a likelihood. States update their beliefs about opponents’ μ using Bayes’ rule both (i) within a game, and also (ii) by observing the outcomes of all games involving all other states at the end of a time period. This feature allows states to learn about each other over time. Step 2: Estimate using Bayesian methods (for panel data, estimate each year sequentially) In a panel data set, the prior is the posterior from last year’s estimation. The estimator mimics the state’s learning process, allowing the researcher to draw inferences about μand about how states are learning about each other’s μ over time. The figure at left displays this process for one state in a 6 year panel with 19 other states playing the crisis bargaining game (in directed dyads). The data set is simulated from the FE-BQRE model using randomly-selected true values of βandμ. Estimation was performed using a single-block random walk Metropolis-Hastings sampler written in R by Justin Esarey. Values of the likelihood were calculated using a 4-processor workstation, the snow package (Tierney et al.), and the rlecuyer random number generator (Sevikova and Rossini). Monte Carlo simulation reveals that private information can be recovered, even from reasonably small datasets. The figure at right shows FE-BQRE estimates of μ against its true value for 1,000 Monte Carlo cross-sectional datasets with 20 countries each (total of 20,000 μ estimates, n = 760 for each set). Estimates were obtained by approximating the posterior mode for μ using the optim package in R. Quasi-informative priors were assumed (prior mean = true mean + normal(mean=0, standard deviation=1), prior variance = inverse gamma(shape=1).)