Pairwise-stability and Nash equilibria in network formation

Suppose that individual payo¤s depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and su¢ cient conditions on the network link marginal payo¤s such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks. Keywords: network formation, pairwise-stability, proper equilibrium. JEL Classi…cation: C62, C72, D85, L14 We thank Jordi Massó for helpful conversations. The …rst author gratefully acknowledges the …nancial support from the Spanish Ministry of Education through grant BEC2002-02130, the Fundación Ramón Areces, and the Barcelona Economics Program of CREA. The second author acknowledges the …nancial support from IGSOC. All errors belong to the authors. yCorresponding author: Universitat Autònoma de Barcelona, Université de Toulouse Sciences Sociales, and CEPR. Address of correspondence: Department of Economics, UAB, Edi…ci B, 08193 Bellaterra (Barcelona), Spain. Email: [email protected]. http://selene.uab.es/acalvo zUniversitat Autònoma de Barcelona. Email: [email protected]