Author
Saldı, Naci, Başar, T., Raginsky, M.
Publication Date
2018
Publication Place
-
Society for Industrial and Applied Mathematics Publications
Subject
Mean-field games, Nash equilibrium, Discounted cost
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0363-0129
Record ID
850d6fcb-41fc-4ddc-8d5b-a4778924351c
Library Location
Natural and Mathematical Sciences
Date
2018
Notes
Air Force Office of Scientific Research ; Office of Naval Research
Sample Text
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.
DOI
10.1137/17M1112583
Cilt
56
