Stochastic Graphon Games with Memory
Eyal Neuman, Sturmius Tuschmann

TL;DR
This paper develops explicit solutions for stochastic graphon games with memory, analyzing how finite-player games converge to continuum models and applying the results to systemic risk and network games.
Contribution
It introduces a method to explicitly solve non-Markovian stochastic graphon games and proves convergence of finite-player equilibria to the continuum limit.
Findings
Explicit Nash equilibrium solutions for stochastic graphon games.
Finite-player game equilibria converge to graphon game equilibria as number of agents increases.
Convergence rates depend on graph sequence properties and sampling methods.
Abstract
We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When the agents' interactions are modeled by a weighted graph, we formulate the corresponding non-Markovian continuum-agent game, where interactions are modeled by a graphon. We also derive the Nash equilibrium of the graphon game explicitly by first reducing the first-order conditions to an infinite-dimensional coupled system of stochastic Fredholm equations, then decoupling it using the spectral decomposition of the graphon operator, and finally solving it in terms of operator resolvents. Moreover, we show that the Nash equilibria of finite-player games on graphs…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Computability, Logic, AI Algorithms · Advanced Graph Theory Research
