Data-driven entropic spatially inhomogeneous evolutionary games

TL;DR

This paper introduces a new class of multi-agent evolutionary game models with spatial inhomogeneity and entropic effects, focusing on their well-posedness, payoff learning from data, and numerical implementation, with applications including pedestrian movement.

Contribution

It develops a comprehensive framework for entropic spatially inhomogeneous evolutionary games, including payoff learning from observational data and convergence analysis to mean field limits.

Findings

Convergence of payoff learning solutions to mean field limits.

Numerical methods successfully reconstruct payoff functions.

Applications demonstrated on pedestrian movement models.

Abstract

We introduce novel multi-agent interaction models of entropic spatially inhomogeneous evolutionary undisclosed games and their quasi-static limits. These evolutions vastly generalize first and second order dynamics. Besides the well-posedness of these novel forms of multi-agent interactions, we are concerned with the learnability of individual payoff functions from observation data. We formulate the payoff learning as a variational problem, minimizing the discrepancy between the observations and the predictions by the payoff function. The inferred payoff function can then be used to simulate further evolutions, which are fully data-driven. We prove convergence of minimizing solutions obtained from a finite number of observations to a mean field limit and the minimal value provides a quantitative error bound on the data-driven evolutions. The abstract framework is fully constructive and numerically implementable. We illustrate this on computational examples where a ground truth payoff function is known and on examples where this is not the case, including a model for pedestrian movement.