  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.
