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

Piotr Więcek ()
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Piotr Więcek: Wrocław University of Science and Technology

Dynamic Games and Applications, 2024, vol. 14, issue 4, No 10, 997-1026

Abstract: 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: $$\beta $$ β -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.

Keywords: Mean-field game; Discrete time; Multiple-population game; Stationary mean-field equilibrium; Markov mean-field equilibrium; Discounted payoff; Total payoff; 91A15; 91A13; 91A10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-024-00567-6

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