Club Networks with Multiple Memberships and Noncooperative Stability
Frank H. Page Jr.
Indiana University, Bloomington - Department of Economics; London School of Economics & Political Science (LSE) - Systemic Risk Centre
Myrna H. Wooders
Vanderbilt University - College of Arts and Science - Department of Economics
February 24, 2009
CAEPR Working Paper No. 005-2009
Modeling club structures as bipartite directed networks, we 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. Our 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). We refer to our conditions on rules as noncooperative free mobility. We also require that players' payoffs be additively separable in player-specific payoffs and externalities (additive separability) and that payoff externalities - a function of club membership, club activities, and crowding - be identical across players (externality homogeneity). We then show that under these conditions, the noncooperative game of club network formation is a potential game over directed club networks and we discuss the implications of this result.
Number of Pages in PDF File: 16
Keywords: clubs, network formation games, potential games, path dominance core, Nash club equilibria, admissible set
JEL Classification: A14, D20, J00
Date posted: February 26, 2009