International Game Theory Review, Vol. 13, No. 2 (2011) 181–194 c  World Scientific Publishing Company DOI: 10.1142/S0219198911002939 NASH NETWORKS WITH IMPERFECT RELIABILITY AND HETEROGEOUS PLAYERS PASCAL BILLAND ∗ and CHRISTOPHE BRAVARD † GATE-LSE, Jean Monnet University Saint-Etienne, France ∗ pascal.billand@univ-st-etienne.fr † christophe.bravard@univ-st-etienne.fr SUDIPTA SARANGI DIW Berlin and Louisiana State University sarangi@lsu.edu This paper combines the imperfect reliability model of Bala and Goyal [2000b] with the heterogeneous player model of Galeotti et al. [2006]. We compare existence, char- acterization and efficiency results in the resulting framework with the results in other frameworks allowing for imperfect reliability or heterogeneity. Specifically, we compare our work with the framework of Haller and Sarangi [2005] which allows for heterogeneity in link reliability but assumes that players are homogeneous. We find, by contrast with their paper, that non existence of Nash networks is possible in our framework even if the population is very small. Moreover, although the incentives of players to maintain (or delete) links are different, in both frameworks there exist parameters such that every essential network is strict Nash and efficient. Keywords : Strategic reliability; two-way flow models; heterogeneous players. Subject Classification: C72, D85 1. Introduction In this paper, we introduce both imperfect link reliability and player heterogeneity in the two-way flow version of the connections model explored in Bala and Goyal [2000a]. In the two-way flow version of the model, if player i forms a link with player j , then both players can access each other’s information, while the player forming the link incurs the costs. Imperfect link reliability in this context means that links fail to transmit information with some probability. Such a link imperfection describes situations like a phone call where the caller has a positive probability of not reaching the other person and was first proposed by Bala and Goyal [2000b]. Moreover, as in Galeotti et al. [2006], in our model players are heterogeneous in the sense that the information (or the benefits) that each player i obtains from player j is specific to the identity of both i and j . Player heterogeneity arises naturally 181