α-Rank-Collections: Analyzing Expected Strategic Behavior with Uncertain Utilities

We introduce a new game-theoretical solution concept for settings where players have probabilistic information about preferences described as distributions about von Neumann–Morgenstern utility functions. This solution concept extends the Markov-Conley-Chains (MCCs) and α-Rank algorithm to Bayesian games, providing a tractable method for analyzing strategic interactions without requiring precise knowledge of players’ utility functions. The approach avoids the limitations of Nash equilibrium, such as multiple equilibria, by ranking strategies based on their probabilities of success. We apply the method to well-known bimatrix games and the Boston matching mechanism, offering a novel framework for analyzing the outcomes of games with probabilistic preferences.