An Approach to Stochastic Dynamic Games with Asymmetric Information and Hidden Actions

We consider in discrete time, a general class of sequential stochastic dynamic games with asymmetric information with the following features. The underlying system has Markovian dynamics controlled by the agents’ joint actions. Each agent’s instantaneous utility depends on the current system state and the agents’ joint actions. At each time instant each agent makes a private noisy observation of the current system state and the agents’ actions in the previous time instant. In addition, at each time instant all agents have a common noisy observation of the current system state and their actions in the previous time instant. Each agent’s actions are part of his private information. The objective is to determine Bayesian Nash Equilibrium (BNE) strategy profiles that are based on a compressed version of the agents’ information and can be sequentially computed. We present an approach/methodology that achieves the above-stated objective. We show by example that, according to the methodology proposed in the paper, BNE strategy profiles with the above characteristics do not exist in general. We also present an instance of a game where BNE strategy profiles with the above features exist. We show that the methodology also works for the case where the agents have no common observations.