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

摘要

We formulate and analyze a general class of stochastic dynamic games withasymmetric information arising in dynamic systems. In such games, multiplestrategic agents control the system dynamics and have different informationabout 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 strategiesis 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 andbelief system. In a PBE, every agent's strategy should be a best response underthe belief system, and the belief system depends on agents' strategy profilewhen there is signaling among agents. Therefore, the circular dependencebetween strategy profile and belief system makes it difficult to compute PBE.Using the common information among agents, we introduce a subclass of PBEcalled common information based perfect Bayesian equilibria (CIB-PBE), andprovide a sequential decomposition of the dynamic game. Such decompositionleads to a backward induction algorithm to compute CIB-PBE. We illustrate thesequential decomposition with an example of a multiple access broadcast game.We prove the existence of CIB-PBE for a subclass of dynamic games.