Optimal Payoff 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 payoff utility function. For such cases the central design issue is how to initialize/update those payoff utility functions of the individual processes so as to induce behavior of the entire collective having good values of the world utility. Traditional “team game” approaches to this problem simply assign to each process the world utility as its payoff utility function. In previous work we used the “Collective Intelligence” (COIN) framework to derive a better choice of payoff 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 payoff 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 significantly improved performance over that of previously investigated COIN payoff utilities, over and above those previous utilities’ superiority to the conventional team game utility. These results also illustrate the substantial superiority of these payoff functions to the perhaps the most natural version of the economics technique of “endogenizing externalities”.