A Unified Approach to Dynamic Decision Problems with Asymmetric Information - Part II: Strategic Agents (1812.01132v1)

Abstract: We study a general class of dynamic games with asymmetric information where agents' beliefs are strategy dependent, i.e. signaling occurs. We show that the notion of sufficient information, introduced in the companion paper team, can be used to effectively compress the agents' information in a mutually consistent manner that is sufficient for decision-making purposes. We present instances of dynamic games with asymmetric information where we can characterize a time-invariant information state for each agent. Based on the notion of sufficient information, we define a class of equilibria for dynamic games called Sufficient Information Based Perfect Bayesian Equilibrium (SIB-PBE). Utilizing the notion of SIB-PBE, we provide a sequential decomposition of dynamic games with asymmetric information over time; this decomposition leads to a dynamic program that determines SIB-PBE of dynamic games. Furthermore, we provide conditions under which we can guarantee the existence of SIB-PBE.