Optimal Payo Functions for Members of Collectives

We consider the problem of designing perhaps massively distributed collectives of computational processes to maximize a provided world utility function We consider this problem when the behavior of each process in the collective can be cast as striving to maximize its own payo utility function For such cases the central design issue is how to initialize update those payo utility functions of the individual processes so as to induce behavior of the entire collective having good values of the world utility Tradi tional team game approaches to this problem simply assign to each process the world utility as its payo utility function In previous work we used the Collective Intelli gence COIN framework to derive a better choice of payo utility functions one that results in world utility performance up to orders of magnitude superior to that ensuing from use of the team game utility In this paper we extend these results using a novel mathematical framework We review the derivation under that new framework of the general class of payo utility functions that both i are easy for the individual processes to try to maximize and ii have the property that if good values of them are achieved then we are assured of a high value of world utility These are the Aristocrat Utility and a new variant of the Wonderful Life Utility that was introduced in the previous COIN work We demonstrate experimentally that using these new utility functions can result in signi cantly improved performance over that of previously investigated COIN payo utilities over and above those previous utilities superiority to the conventional team game utility These results also illustrate the substantial superiority of these payo functions to the perhaps the most natural version of the economics technique of endo genizing externalities