Dynamic Games with Asymmetric Information: Common Information Based Perfect Bayesian Equilibria and Sequential Decomposition
For researchers in dynamic games and multi-agent systems, this work provides a tractable equilibrium concept and computational method for asymmetric information settings, though it is incremental as it builds on existing PBE and common information ideas.
This paper formulates stochastic dynamic games with asymmetric information and introduces common information based perfect Bayesian equilibria (CIB-PBE) to address the circular dependence between strategy and beliefs. A sequential decomposition is provided, leading to a backward induction algorithm for computing CIB-PBE, with existence proven for a subclass.
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.