Maximizing Social Welfare in Fractional Hedonic Games using Shapley Value

Abstract

Fractional hedonic games (FHGs) are extensively studied in game theory and explain the formation of coalitions among individuals in a group. This paper investigates the coalition generation problem, namely, finding a coalition structure whose social welfare, i.e., the sum of the players’ payoffs, is maximized. We focus on agent-based methods which set the decision rules for each player in the game. Through repeated interactions the players arrive at a coalition structure. In particular, we propose CFSV, namely, coalition formation with Shapley value-based welfare distribution scheme. To evaluate CFSV, we theoretically demonstrate that this algorithm achieves optimal coalition structure over certain standard graph classes and empirically compare the algorithm against other existing benchmarks on real-world and synthetic graphs. The results show that CFSV is able to achieve superior performance.