Spatially Inhomogeneous (Entropic) Evolutionary Games and their Inferences

Abstract: Newtonian models of multiagent systems are not well-accepted by economists or sociologists because they do not take into consideration the mechanism of optimization of an individual payoff. Mean-field games offer an alternative approach, but they are formulated as an optimal control problem whose optimization needs to take into consideration the future realization. We propose an alternative and simpler model of spatially inhomogenous evolutionary game where players draw at random their moves according to time dependent mixed strategies evolving according to a replicator dynamics that strives to optimize a game payoff. We shall show the well-posedness of such a model and its population description. Additionally we further modify the model with an entropic term, which allows to obtain more realistic time evolving changes of behavior. We conclude with results of inference of the playoff from the observation of the realization of the game.