Utility Design for Infinite Distributed Welfare Games

Abstract

A distributed welfare game is a non-cooperative game-theoretic model for a resource allocation problem that maximizes welfare. In this paper, two utility function designs for resource allocation problems with infinite resources are considered. One is called wonderful life utility, which was proposed for the problem. The second one employs a solution concept of the cooperative game, Egalitarian Non-Separable Contribution (ENSC). The main contributions of the paper are two holds. The first contribution is to clarify the existence of a pure strategy Nash equilibrium in the games defined via the above utility functions when the welfare function is monotone, continuously twice differentiable, and diminishing return (DR) submodular. The second is to derive lower bounds of the Price of Anarchy (PoA) for both games. The PoA is the worst-case ratio between the optimal value and values at the pure strategy Nash equilibria.