Data-driven entropic spatially inhomogeneous evolutionary games

We introduce novel multi-agent interaction models of entropic spatially inhomogeneous evolutionary undisclosed games and their quasi-static limits. These evolutions vastly generalise 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, minimising 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 minimising 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.