Dynamic Games with Asymmetric Information: Common Information Based Perfect Bayesian Equilibria and Sequential Decomposition

TL;DR

This paper introduces a new equilibrium concept called common information based perfect Bayesian equilibrium (CIB-PBE) for dynamic games with asymmetric information, providing a sequential decomposition method for computation and demonstrating its existence.

Contribution

It develops a novel equilibrium framework (CIB-PBE) for asymmetric information dynamic games and offers a backward induction algorithm for its computation.

Findings

CIB-PBE exists for a subclass of dynamic games.

Sequential decomposition simplifies equilibrium computation.

Application to a multiple access broadcast game demonstrates practicality.

Abstract

We formulate and analyze a general class of stochastic dynamic games with asymmetric information arising in dynamic systems. In such games, multiple strategic agents control the system dynamics and have different information about the system over time. Because of the presence of asymmetric information, each agent needs to form beliefs about other agents' private information. Therefore, the specification of the agents' beliefs along with their strategies is necessary to study the dynamic game. We use Perfect Bayesian equilibrium (PBE) as our solution concept. A PBE consists of a pair of strategy profile and belief system. In a PBE, every agent's strategy should be a best response under the belief system, and the belief system depends on agents' strategy profile when there is signaling among agents. Therefore, the circular dependence between strategy profile and belief system makes it difficult to compute PBE. Using the common information among agents, we introduce a subclass of PBE called common information based perfect Bayesian equilibria (CIB-PBE), and provide a sequential decomposition of the dynamic game. Such decomposition leads to a backward induction algorithm to compute CIB-PBE. We illustrate the sequential decomposition with an example of a multiple access broadcast game. We prove the existence of CIB-PBE for a subclass of dynamic games.