Simple Utility Design for Welfare Games under Global Information

Welfare game is a game-theoretic model for resource allocation problem which is to find an allocation to maximize the welfare function. In order to determine it in a distributed way, each agent is assigned to an admissible utility function such that the resulting game possesses desirable properties, for example, scalability, existence and efficiency of pure Nash equilibria, and budget balance. In this paper, supposing that each agent can access the global information, marginal contribution based utility design is proposed. It is shown that utility functions based on the above design have scalability and existence of pure Nash equilibria. Furthermore, efficiency is the same as that of the conventional utility design via Shapley value.