Socially Optimal Non-discriminatory Restrictions for Continuous-Action Games

We address the following mechanism design problem: Given a multi-player Normal-Form Game (NFG) with a continuous action space, find a non-discriminatory (i.e., identical for all players) restriction of the action space which maximizes the resulting Nash Equilibrium with respect to a fixed social utility function. First, we propose a formal model of a Restricted Game and the corresponding restriction optimization problem. We then present an algorithm to find optimal non-discriminatory restrictions under some assumptions. Our experimental results with Braess’ Paradox and the Cournot Game show that this method leads to an optimized social utility of the Nash Equilibria, even when the assumptions are not guaranteed to hold. Finally, we outline a generalization of our approach to the much wider scope of Stochastic Games.