Stochastic Game with Interactive Information Acquisition: A Fixed-Point Alignment Principle

This paper studies a multi-player, general-sum stochastic game characterized by a dual-stage temporal structure per period. The agents face uncertainty regarding the time-evolving state that is realized at the beginning of each period. During the first stage, agents engage in information acquisition regarding the unknown state. Each agent strategically selects from multiple signaling options, each carrying a distinct cost. The selected signaling rule dispenses private information that determines the type of the agent. In the second stage, the agents play a Bayesian game by taking actions contingent on their private types. We introduce an equilibrium concept, Pipelined Perfect Markov Bayesian Equilibrium (PPME), which incorporates the Markov perfect equilibrium and the perfect Bayesian equilibrium. We propose a novel equilibrium characterization principle termed fixed-point alignment and deliver a set of verifiable necessary and sufficient conditions for any strategy profile to achieve PPME.