A Unified Approach to Dynamic Decision Problems With Asymmetric Information: Nonstrategic Agents

Abstract

We study a general class of dynamic multi-agent decision problems with asymmetric information and non-strategic agents, which includes dynamic teams as a special case. When agents are non-strategic, an agent's strategy is known to the other agents. Nevertheless, the agents strategy choices and beliefs are interdependent over times, a phenomenon known as signaling. We introduce the notion of sufficient information that effectively compresses the agents information in a mutually consistent manner. Accordingly, we propose an information state for each agent that is sufficient for decision making purposes. We present instances where we can determine an information state with a time-invariant domain for each agent. We present a generalization of the policy-independence property of belief in Partially Observed Markov Decision Processes to dynamic multi-agent decision problems. Furthermore, we propose a sequential decomposition that decouples the interdependence between the agents strategies and beliefs over time, and enables us to formulate a dynamic program to determine a globally optimal policy in dynamic teams via backward induction.