Continuous-Time Games with Imperfect Public Information

Résumé

We study n-player continuous-time repeated and stochastic games with imperfect monitoring in which the publicly observable state vector follows a jointly controlled Markov diffusion process. By extending the analysis of Sannikov (2007) to allow for more than two players and payoff-relevant state variables, we characterize the correspondence of (perfect public) equilibria and attainable payoffs. We introduce two types of optimality equations: an elliptic partial differential equation, and a parabolic one. Under an identifiability condition on the monitoring technology, the support function of the equilibrium payoff correspondence is the greatest viscosity solution of the elliptic equation, but it may not be the unique solution. The parabolic equation has a unique viscosity solution, and we develop a numerical method to compute it. The solution of the parabolic equation converges (as the time parameter goes to infinity) to the support function of the equilibrium payoff correspondence. Relative to the two-player repeated games of Sannikov (2007), the optimal equilibria of the games that we study have new features, such as absorbing regimes that do not correspond to static Nash or Markov equilibria. Most of the talk will concentrate on results for n-player repeated games. If time permits, results for stochastic differential games will also be discussed. joint work with Yuliy Sannikov (Stanford GSB)