Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: The Existence of Equilibria

TL;DR

This paper establishes the first existence theorems for stationary and Markov equilibria in discrete-time mean-field games with multiple populations, considering both discounted and total payoffs, under general assumptions.

Contribution

It introduces the first stationary and Markov equilibrium existence results for discrete-time multi-population mean-field games with broad assumptions.

Findings

Existence of stationary and Markov equilibria proven for discrete-time multi-population MFGs.

Results extend to single population case, relaxing previous strong assumptions.

Applicable to both discounted and total payoff criteria.

Abstract

In the paper we present a model of discrete-time mean-field game with several populations of players. Mean-field games with multiple populations of the players have only been studied in the literature in the continuous-time setting. The main results of this article are the first stationary and Markov mean-field equilibrium existence theorems for discrete-time mean-field games of this type. We consider two payoff criteria: discounted payoff and total payoff. The results are provided under some rather general assumptions on one-step reward functions and individual transition kernels of the players. In addition, the results for total payoff case, when applied to a single population, extend the theory of mean-field games also by relaxing some strong assumptions used in the existing literature.