Solving Infinite-Player Games with Player-to-Strategy Networks

TL;DR

This paper introduces Player-to-Strategy Networks (P2SN) and the Shared-Parameter Simultaneous Gradient (SPSG) algorithm to solve infinite-player games, enabling approximation of Nash equilibria in complex, large-scale multiagent systems.

Contribution

The paper proposes a novel neural network-based representation for infinite-player games and an algorithm to find approximate Nash equilibria, extending multiagent learning methods to infinite settings.

Findings

The approach converges to approximate Nash equilibria in infinite-player games.

The method handles infinite states, actions, and discontinuous utilities.

It generalizes classical gradient ascent for equilibrium seeking.

Abstract

We present a new approach to solving games with a countably or uncountably infinite number of players. Such games are often used to model multiagent systems with a large number of agents. The latter are frequently encountered in economics, financial markets, crowd dynamics, congestion analysis, epidemiology, and population ecology, among other fields. Our two primary contributions are as follows. First, we present a way to represent strategy profiles for an infinite number of players, which we name a Player-to-Strategy Network (P2SN). Such a network maps players to strategies, and exploits the generalization capabilities of neural networks to learn across an infinite number of inputs (players) simultaneously. Second, we present an algorithm, which we name Shared-Parameter Simultaneous Gradient (SPSG), for training such a network, with the goal of finding an approximate Nash equilibrium. This algorithm generalizes simultaneous gradient ascent and its variants, which are classical equilibrium-seeking dynamics used for multiagent reinforcement learning. We test our approach on infinite-player games and observe its convergence to approximate Nash equilibria. Our method can handle games with infinitely many states, infinitely many players, infinitely many actions (and mixed strategies on them), and discontinuous utility functions.