Markov-Nash equilibria in mean-field games with discounted cost
Type :
Article
Publication Status :
Published
Access :
restrictedAccess
Abstract
In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov--Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptions, we demonstrate the existence of a mean-field equilibrium in the infinite-population limit $N \to \infty$, and then show that the policy obtained from the mean-field equilibrium is approximately Markov--Nash when the number of agents $N$ is sufficiently large.
Source :
SIAM Journal on Control and Optimization
Date :
2018
Volume :
56
Issue :
6
Publisher :
Society for Industrial and Applied Mathematics Publications
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