Stochastic Graphon Games: I. The Static Case: I. The Static Case

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

doi:10.1287/moor.2021.1148

Stochastic Graphon Games: I. The Static Case: I. The Static Case

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

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	750-778
Number of pages	29
Journal	Mathematics of Operations Research
Volume	47
Issue number	1
DOIs	https://doi.org/10.1287/moor.2021.1148
State	Published - Feb 2022
Externally published	Yes

Keywords

Graphon games
Mean field games
Networks

ASJC Scopus subject areas

General Mathematics
Computer Science Applications
Management Science and Operations Research

Online availability

10.1287/moor.2021.1148

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title = "Stochastic Graphon Games: I. The Static Case: I. The Static Case",

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.",

keywords = "Graphon games, Mean field games, Networks",

author = "Ren'e Carmona and Cooney, {Daniel B.} and Graves, {Christy V.} and Mathieu Lauri{\'e}re",

note = "Funding Information: Funding: This work was supported by National Science Foundation (NSF) Mathematical Sciences [DMS 1514606], Army Research Office [W911NF-18-1-0325 and W911NF1710578], and NSF [DMS 1716673]. R. Carmona and M. Lauriere were partially supported by ARO [Grant AWD1005491] and AFOSR [Award A9550-19-1-0291]. C. Graves was partially supported by NSF [Award AWD1005433]. Publisher Copyright: {\textcopyright} 2021 INFORMS.",

year = "2022",

month = feb,

doi = "10.1287/moor.2021.1148",

language = "English (US)",

volume = "47",

pages = "750--778",

journal = "Mathematics of Operations Research",

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publisher = "INFORMS Institute for Operations Research and the Management Sciences",

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T2 - I. The Static Case

AU - Carmona, Ren'e

AU - Cooney, Daniel B.

AU - Graves, Christy V.

AU - Lauriére, Mathieu

N1 - Funding Information: Funding: This work was supported by National Science Foundation (NSF) Mathematical Sciences [DMS 1514606], Army Research Office [W911NF-18-1-0325 and W911NF1710578], and NSF [DMS 1716673]. R. Carmona and M. Lauriere were partially supported by ARO [Grant AWD1005491] and AFOSR [Award A9550-19-1-0291]. C. Graves was partially supported by NSF [Award AWD1005433]. Publisher Copyright: © 2021 INFORMS.

PY - 2022/2

Y1 - 2022/2

N2 - 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.

AB - 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.

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KW - Mean field games

KW - Networks

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IS - 1

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Stochastic Graphon Games: I. The Static Case: I. The Static Case

Abstract

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