Decentralized Bayesian learning in dynamic games

We study the problem of Bayesian learning in a dynamical system involving strategic agents with asymmetric information. In a series of seminal papers in the literature, this problem has been studied under a simplifying model where selfish players appear sequentially and act once in the game, based on private noisy observations of the system state and public observation of past players' actions. It is shown that there exist information cascades where users discard their private information and mimic the action of their predecessor. In this paper, we provide a framework for studying Bayesian learning dynamics in a more general setting than the one described above. In particular, our model incorporates cases where players participate for the whole duration of the game, and cases where an endogenous process selects which subset of players will act at each time instance. The proposed methodology hinges on a sequential decomposition for finding perfect Bayesian equilibria (PBE) of a general class of dynamic games with asymmetric information, where user-specific states evolve as conditionally independent Markov processes and users make independent noisy observations of their states. Using our methodology, we study a specific dynamic learning model where players make decisions about investing in the team, based on their estimates of everyone's types. We characterize a set of informational cascades for this problem where learning stops for the team as a whole.