Club Networks With Multiple Club Memberships And Noncooperative Stability

Modeling club structures as bipartite directed networks, the authors formulate the problem of club formation as a noncooperative game of network formation and identify conditions on network formation rules and players' network payoffs sufficient to guarantee that the game has a potential function. This sufficient conditions on network formation rules require that each player be choose freely and unilaterally those clubs he joins and also his activities within these clubs (subject to his set of feasible actions). They refer to the conditions on rules as noncooperative free mobility. They then show that under these conditions, the noncooperative game of club network formation is a potential game over directed club networks and they discuss the implications of this result.