A Label-State Formulation of Stochastic Graphon Games and Approximate Equilibria on Large Networks

Daniel Lacker () and Agathe Soret ()
Additional contact information
Daniel Lacker: Industrial Engineering & Operations Research, Columbia University, New York, New York 10027
Agathe Soret: Industrial Engineering & Operations Research, Columbia University, New York, New York 10027

Mathematics of Operations Research, 2023, vol. 48, issue 4, 1987-2018

Abstract: This paper studies stochastic games on large graphs and their graphon limits. We propose a new formulation of graphon games based on a single typical player’s label-state distribution. In contrast, other recently proposed models of graphon games work directly with a continuum of players, which involves serious measure-theoretic technicalities. In fact, by viewing the label as a component of the state process, we show in our formulation that graphon games are a special case of mean field games, albeit with certain inevitable degeneracies and discontinuities that make most existing results on mean field games inapplicable. Nonetheless, we prove the existence of Markovian graphon equilibria under fairly general assumptions as well as uniqueness under a monotonicity condition. Most importantly, we show how our notion of graphon equilibrium can be used to construct approximate equilibria for large finite games set on any (weighted, directed) graph that converges in cut norm. The lack of players’ exchangeability necessitates a careful definition of approximate equilibrium, allowing heterogeneity among the players’ approximation errors, and we show how various regularity properties of the model inputs and underlying graphon lead naturally to different strengths of approximation.

Keywords: Primary: 91A16; secondary: 91A43; 93E03; graphon games; mean field games; approximate Nash equilibrium (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2022.1329 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:4:p:1987-2018

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().