Nash Equilibria for Stochastic Games with Asymmetric Information-Part 1: Finite Games

TL;DR

This paper introduces a method to compute Nash equilibria in stochastic games with asymmetric information by transforming them into symmetric information games using common information, enabling a backward induction algorithm for equilibrium analysis.

Contribution

It presents a novel approach to characterize and compute Nash equilibria in asymmetric information stochastic games via common information and Markov perfect equilibria.

Findings

Equivalent symmetric information game formulation

Backward induction algorithm for Nash equilibrium computation

Characterization of common information based Markov perfect equilibria

Abstract

A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information among the controllers makes it difficult to compute or characterize Nash equilibria. Using common information among the controllers, the game with asymmetric information is shown to be equivalent to another game with symmetric information. Further, under certain conditions, a Markov state is identified for the equivalent symmetric information game and its Markov perfect equilibria are characterized. This characterization provides a backward induction algorithm to find Nash equilibria of the original game with asymmetric information in pure or behavioral strategies. Each step of this algorithm involves finding Bayesian Nash equilibria of a one-stage Bayesian game. The class of Nash equilibria of the original game that can be characterized in this backward manner are named common information based Markov perfect equilibria.