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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: <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-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.<\/jats:p>","DOI":"10.1007\/s13235-024-00567-6","type":"journal-article","created":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T13:01:45Z","timestamp":1716814905000},"page":"997-1026","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: The Existence of Equilibria"],"prefix":"10.1007","volume":"14","author":[{"given":"Piotr","family":"Wi\u0119cek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,27]]},"reference":[{"issue":"1","key":"567_CR1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1142\/S0218202517400036","volume":"27","author":"Y Achdou","year":"2017","unstructured":"Achdou Y, Bardi M, Cirant M (2017) Mean field games models of segregation. 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