Oxford student speaker: Martin Geller "Calculus in Rough Path Space"
Imperial student speaker: Martin Peev
Invited speaker: Prof Eyai Neuman
Title: Stochastic Graphon Games with Memory
Abstract: We analyze finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals, deriving explicit Nash equilibria in terms of operator resolvents. When interactions are represented by a weighted graph, we extend the framework to a continuum-player game with interactions modeled by a graphon. We then derive the explicit Nash equilibrium for the graphon game by reducing the first-order conditions to an infinite-dimensional coupled system of stochastic Fredholm equations. To solve this system, we introduce a novel approach based on the spectral decomposition of the graphon operator. Additionally, we demonstrate the convergence of Nash equilibria from finite-player games to the equilibrium of the graphon game as the number of agents grows, providing explicit convergence rates. Finally, we apply these results to various stochastic games, including systemic risk models with delay and stochastic differential network games, thereby showcasing the broad applicability of our framework.
This is a joint work with Sturmius Tuschmann
