Stochastic Graphon Games with Jumps and Approximate Nash Equilibria

37 Pages Posted: 18 Apr 2023 Last revised: 3 Aug 2023

See all articles by Hamed Amini

Hamed Amini

University of Florida

Zhongyuan Cao

INRIA Paris

Agnes Sulem

INRIA Paris

Date Written: April 7, 2023

Abstract

We study continuous stochastic games with inhomogeneous mean field interactions on large networks and explore their graphon limits. We consider a model with a continuum of players, where each player's dynamics involve not only mean field interactions but also individual jumps induced by a Poisson random measure. We examine the case of controlled dynamics, with control terms present in the drift, diffusion, and jump components. We introduce the graphon game model based on a graphon controlled stochastic differential equation (SDE) system with jumps, which can be regarded as the limiting case of a finite game's dynamic system as the number of players goes to infinity. Under some general assumptions, we establish the existence and uniqueness of Markovian graphon equilibria. We then provide convergence results on the state trajectories and their laws, transitioning from finite game systems to graphon systems. We also study approximate equilibria for finite games on large networks, using the graphon equilibrium as a benchmark. The rates of convergence are analyzed under various underlying graphon models and regularity assumptions.

Keywords: Graphons, mean field games, jump measures, heterogenous interactions, controlled dynamics, approximate Nash equilbria

JEL Classification: C02

Suggested Citation

Amini, Hamed and Cao, Zhongyuan and Sulem, Agnes, Stochastic Graphon Games with Jumps and Approximate Nash Equilibria (April 7, 2023). Available at SSRN: https://ssrn.com/abstract=4412999 or http://dx.doi.org/10.2139/ssrn.4412999

Hamed Amini (Contact Author)

University of Florida ( email )

University of Florida
Gainesville, FL 32611
United States

Zhongyuan Cao

INRIA Paris ( email )

2 rue
Simone Iff
Paris, 75589
France

Agnes Sulem

INRIA Paris ( email )

2 rue Simone Iff, CS 42112
Paris, 75589
France

HOME PAGE: http://https://www.rocq.inria.fr/mathfi/Sulem.html

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