The assignment of utility functions is a central component of a game theoretic approach to distributed resource allocation. The goal is to assign each decision making entity a utility function such that the resulting game possesses a host of desirable properties including scalability, tractability, locality, and existence and efficiency of pure Nash equilibria. In this paper we formally study this question of utility design. We introduce a class of games termed distributed welfare games as our platform for utility design. By viewing utility design in a similar fashion to cost sharing, we identify several utility design methodologies that guarantee desirable game properties irrespective of the specific application domain. Lastly, we illustrate the results in this paper on two well studied resource allocation problem: the graph coloring problem and the vehicle target assignment problem. Key words: resource allocation; game theory; distributed control History: A few of the results in this paper appeared in (Marden and Wierman (2008)), which did not include full proofs.
The problem studied in this paper is related to the field of distributed welfare games REF .
Distributed Welfare Games
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