Finite State Dynamic Games with Asymmetric Information: A Framework for Applied Work

We present a framework for the applied analysis of dynamic games with asymmetric information. The framework consists of a definition of equilibrium, and an algorithm to compute it. Our definition of Applied Markov Perfect equilibrium is an extension of the definition of Markov Perfect equilibrium for games with asymmetric information; an extension chosen for its usefulness to applied research. Each agent conditions its strategy on the payoff or informationally relevant variables that are observed by that particular agent. The strategies are optimal given the beliefs on the evolution of these observed variables, and the rules governing the evolution of the observables are consistent with the equilibrium strategies. We then provide a simple algorithm for computing this equilibrium. The algorithm is easy to program and does not require computation of posterior distributions, explicit integration over possible future states, or information from all possible points in the state space. For specificity, we present our results in the context of a dynamic oligopoly game with collusion in which the outcome of firms? investments are random and only observed by the investing agent. We then use this example to illustrate the computational properties of the algorithm.