turkmath.org

In this talk, I will present a general theory for discrete-time mean-field games. I will cover both perfect state and partial state information structures. In mean-field games, the players are coupled through the empirical distribution of their states, which affects both the players individual costs as well as their state transition probabilities. In such dynamic games with decentralized information, obtaining the exact Nash equilibrium is quite difficult with a finite number of players. The mean-field approach offers a way out of this difficulty. First focusing on the perfect state information, I will show existence of a mean-field equilibrium in the infinite population limit. I will then show that the policy obtained from the mean-field equilibrium is approximately Nash when the number of players is sufficiently large. Following this, I will turn to the class of discrete-time partially observed mean-field games. By converting the original partially observed problem to a fully observed one on the belief space and the dynamic programming principle, I will establish the existence of Nash equilibria. I will again show, as in the perfect state information case, that the mean-field equilibrium policy, when adopted by each player, forms an approximate Nash equilibrium for games with sufficiently many players. Based on joint works with Tamer Başar and Maxim Raginsky.