Multiplayer Performative Prediction Games with Incomplete Information

This paper investigates multiplayer performative prediction games in settings with incomplete information. We formalize these games as *performative Bayesian games*, in which players strategically choose their decisions (or predictions) that jointly shape the resulting data distributions, while each player possesses private information unknown to others. A natural adaptive strategy for players is to iteratively (1) optimize their decisions based on current posterior beliefs about others' private information under the data distribution induced by the joint decision, and (2) update those beliefs upon observing others' realized decisions. We introduce the concept of a performatively stable Bayesian equilibrium as a desirable outcome: a decision profile and associated belief system such that the deployed decisions are mutually optimal given the data distributions they induce and the converged beliefs, eliminating the need for further update of either decisions or beliefs. Our main contributions are threefold. First, we provide a formal game-theoretic definition of performative Bayesian games. Second, we derive theoretical conditions under which the natural alternating best-response-and-belief-update dynamics converge to a performatively stable Bayesian equilibrium. Third, leveraging these theoretical results, we design an algorithm that guarantees convergence to such an equilibrium and minimizes the maximum deviation from the original equilibrium when the convergence conditions are violated. Experimental evaluations on crude oil trading and ride-sharing market validate our theoretical results and demonstrate the effectiveness of the proposed algorithm.