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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 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.

Original languageEnglish (US)
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3676-3681
Number of pages6
ISBN (Electronic)9781509059928
DOIs
StatePublished - Jun 29 2017
Event2017 American Control Conference, ACC 2017 - Seattle, United States
Duration: May 24 2017May 26 2017

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period5/24/175/26/17

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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