Arbitrary Profit Sharing in Federated Learning Utility Games

Eirini Georgoulaki
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{\em Arbitrary cost-sharing} is a model in which the players of a resource selection game get to declare the payments that they will make, rather than have the payments be determined by a cost-sharing protocol. Arbitrary cost-sharing has been studied in various contexts, such as congestion games, network design games, and scheduling games. The natural counterpart of arbitrary cost-sharing in the context of a utility game is {\em arbitrary utility-sharing}, meaning that each player will request certain utility as a reward for their efforts in generating welfare for the system. This concept has received much less attention in the literature. In this paper, we initiate the study of arbitrary sharing in utility games, placing emphasis on the special case of {\em federated learning utility games}, in which players form groups that jointly execute a learning task and each player contributes certain types of data to each group. We present results on the price of anarchy and price of stability, showing that the price of anarchy is $2$ and that arbitrary utility sharing is the only known method to achieve price of stability $1$ with budget-balanced payments.