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Stochastic Graphon Games: I. The Static Case

Author

Listed:
  • René Carmona

    (Princeton University, Princeton, New Jersey 08544)

  • Daniel B. Cooney

    (University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Christy V. Graves

    (Princeton University, Princeton, New Jersey 08544)

  • Mathieu Laurière

    (Princeton University, Princeton, New Jersey 08544)

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 show that equilibrium strategy profiles of a graphon game provide approximate Nash equilibria for the finite-player games. Connections with mean field games are discussed. A motivating application of Cournot competition is presented, and explicit computation of its Nash equilibrium is provided.

Suggested Citation

  • René Carmona & Daniel B. Cooney & Christy V. Graves & Mathieu Laurière, 2022. "Stochastic Graphon Games: I. The Static Case," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 750-778, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:750-778
    DOI: 10.1287/moor.2021.1148
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