  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.
