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Club Networks with Multiple Memberships and Noncooperative Stability

16 Pages Posted: 26 Feb 2009  

Frank H. Page Jr.

Indiana University, Bloomington - Department of Economics; Systemic Risk Centre, LSE

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics

Date Written: February 24, 2009

Abstract

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.

Keywords: clubs, network formation games, potential games, path dominance core, Nash club equilibria, admissible set

JEL Classification: A14, D20, J00

Suggested Citation

Page, Frank H. and Wooders, Myrna H., Club Networks with Multiple Memberships and Noncooperative Stability (February 24, 2009). CAEPR Working Paper No. 005-2009. Available at SSRN: https://ssrn.com/abstract=1348634 or http://dx.doi.org/10.2139/ssrn.1348634

Frank H. Page Jr. (Contact Author)

Indiana University, Bloomington - Department of Economics ( email )

Wylie Hall
Bloomington, IN 47405-6620
United States

Systemic Risk Centre, LSE ( email )

Houghton St
London, WC2A 2AE
United Kingdom

HOME PAGE: http://www.systemicrisk.ac.uk/

Myrna H. Wooders

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

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