TY - GEN

T1 - Markov-Nash equilibria in mean-field games with discounted cost

AU - Saldi, Naci

AU - Basar, Tamer

AU - Raginsky, Maxim

N1 - Publisher Copyright:
© 2017 American Automatic Control Council (AACC).

PY - 2017/6/29

Y1 - 2017/6/29

N2 - 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 locally compact 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 the solution concept of 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 → 1, 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.

AB - 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 locally compact 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 the solution concept of 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 → 1, 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.

UR - http://www.scopus.com/inward/record.url?scp=85026996218&partnerID=8YFLogxK

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U2 - 10.23919/ACC.2017.7963516

DO - 10.23919/ACC.2017.7963516

M3 - Conference contribution

AN - SCOPUS:85026996218

T3 - Proceedings of the American Control Conference

SP - 3676

EP - 3681

BT - 2017 American Control Conference, ACC 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2017 American Control Conference, ACC 2017

Y2 - 24 May 2017 through 26 May 2017

ER -