Counterfactual prediction in complete information games: Point prediction under partial identification

We study the problem of counterfactual prediction in discrete decision games with complete information, pure strategies, and Nash equilibria: the presence of multiple equilibria poses unique challenges. We introduce multiple types of counterfactuals to establish sharp identified bounds for their prediction probabilities. We propose and compare various point prediction methods, namely midpoint prediction, an approach using a Dirichlet-based prior, a maximum entropy method, and minmax with an entropy constraint. On balance, we conclude that the maximum-entropy approach is the least of several evils. Our results have implications for counterfactual prediction in other models with partial identification.