Stochastic Graphon Games: I. The Static Case

Ren'e Carmona, Daniel B. Cooney, Christy V. Graves, Mathieu Lauriére

Research output: Contribution to journalArticlepeer-review

Abstract

We consider static finite-player network games and their continuum analogs graphon games. Existence and uniqueness results are provided as well as convergence of the finite-player network game optimal strategy profiles to their analogs for the graphon games.We also showthat equilibriumstrategy profiles of a graphon game provide approximate Nash equilibria for the finite-player games. Connections with mean field games are discussed. Amotivating application of Cournot competition is presented, and explicit computation of its Nash equilibrium is provided.

Original languageEnglish (US)
Pages (from-to)750-778
Number of pages29
JournalMathematics of Operations Research
Volume47
Issue number1
DOIs
StatePublished - Feb 2022

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

Keywords

  • Graphon games
  • Mean field games
  • Networks

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