A new family of solutions for graph-restricted cooperative games: rethinking the weight of intermediary power

Abstract

In graph-restricted cooperative games, a group of agents, represented by the nodes of a graph, work together to make a profit. However, two agents can cooperate within a coalition only if they are connected by the graph in the coalition. Several allocation rules have been proposed for these games, but there is something in common in all of them: if a player is an indispensable intermediary to communicate with the players in a coalition, this player will receive, at least, the same share of the profit generated by the coalition as the players who belong to it. In other words, intermediation power is valued, at least, as much as active cooperation. In some situations, this is neither fair nor realistic. In this paper, we introduce a family of values for graphrestricted games that value intermediary power less than active cooperation.