A Framework for Studying Decentralized Bayesian Learning with Strategic Agents

Abstract

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 investigated under a simplifying model where selfish players appear sequentially and act once in the game. It has been 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 just described. In particular, our model incorporates cases where players can act repeatedly and there is strategic interaction in that each agent’s payoff may also depend on other players’ actions. The proposed framework hinges on a sequential decomposition methodology for finding structured perfect Bayesian equilibria of a general class of dynamic games with asymmetric information. Using this methodology, we study a specific dynamic learning model where players make decisions about public investment based on their estimates of everyone’s states. We characterize a set of informational cascades for this problem where learning stops for the team as a whole. Moreover, we show that such cascades occur almost surely.