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and Jackson Wolinsky (1996) introduced the concept of pairwise stability (known from the matching literature) as an equilibrium concept in models of network formation. This gave rise to a completely new strand of the literature focusing on the tension between stability and e ciency. Pairwise stability requires mutual consent of a pair of agents for link formation whereas links can be deleted unilaterally. Dutta and Muttuswami (1997) and Watts (2001) re ne the Jackson-Wolinksy framework further by introducing other stability concepts and derive implementation results for these concepts. Johnson and Gilles (2000) introduce a geographic dimension to the Jackson-Wolinsky model through spatial costs of link formation. For a recent survey of this literature see Jackson (2003). Several dynamic models using pairwise stability have been investigated as well, starting with Jackson and Watts (2002a). Jackson and Watts (2002b) and Goyal and Vega-Rodondo (1999) consider coordination games played on a network. The choice of partners in the game is endogenous and players are periodically allowed to add or sever links. Droste et al. (2000) also analyze coordination games played on a network with spatial costs of link formation. The non-cooperative version of network formation has rst been developed in two papers by Bala and Goyal (2000a, b). In all cases, agents choose to form links on the basis of costs and a (deterministic or stochastic) ow of bene ts that accrue from links. Bala and Goyal assume that a player can create a one-sided link with another player by making the appropriate investment. Their assumption di ers fundamentally from the concept of pairwise stability since mutual consent of both players is no longer required for link formation. They further investigate the reliability issue in networks by allowing links to fail independently of each other with a certain probability. Links are deterministic in Bala and Goyal (2000a). They are random, with identical probabilities of failure for all established links, in Bala and Goyal (2000b). Thus both their models deal with homogeneous agents. The corresponding static equilibrium outcomes are called Nash networks.2 Our model also belongs to the non-cooperative tradition and is a generalization of Bala and Goyal (2000b). We introduce agent heterogeneity by allowing for the probability of link failure (or success) to di er across 2 They also identify strict Nash networks and study the formation of Nash networks in a modi ed version of best-response dynamics. 3 links. This distinctive feature re ects the nature of the transmission technology or the quality of information. The generalization provides a richer model in terms of answering theoretical as well as practical questions: connectivity and super-connectivity, selection of central agents in star networks, e ciency, and Pareto-optimality. Besides imparting greater realism to the model, the introduction of heterogeneous agents allows us to check the robustness of the conclusions obtained in Bala and Goyal (2000b). Whereas their ndings still hold under certain conditions, heterogeneity gives rise to a greater variety of equilibrium outcomes, tends to alter results signi cantly and even generates some of the results of their deterministic model. Bala and Goyal show for both their models that Nash networks must be either connected or empty. With heterogeneous agents, this proves true only when the probabilities of success not are very di erent from each other. Another central nding of Bala and Goyal is that compared to information decay imperfect reliability has very di erent e ects on network formation. With information decay, minimally connected networks (notably the star) are Nash for a wide range of cost and decay parameters, independently of the size of society. In contrast, with imperfect reliability and small link formation costs, minimally connected networks tend to be replaced by superconnected networks (connected networks with redundant links) as the player set increases. However, with agent heterogeneity neither connectedness nor super-connectedness need arise asymptotically. Furthermore, in order for star networks to be Nash, probabilities must lie in a certain range (depending on costs) as in Bala and Goyal s setting. But we nd that as a rule, they have to satisfy additional conditions. In particular, it never pays in the Bala and Goyal framework to connect to the center of the star indirectly. In our context, however, such a connection might be bene cial and further conditions on probabilities are required to prevent these connections. Interestingly enough, heterogeneity helps resolve a particular ambiguity associated with the homogeneous model: Owing to the additional equilibrium conditions, the coordination problem inherent in selecting the central agent of a star is mitigated to a certain degree. We also investigate e ciency issues and nd that Nash networks may be nested and Pareto-ranked. We demonstrate by example that ine cient Nash networks can be Pareto-optimal. A further example shows that Nash networks do not always exist with non-uniform link success probabilities. Criticisms of the non-cooperative approach to network formation are addressed as well. We extend the model to allow for duplication of links 4 and to analyze Nash networks with incomplete information. Regarding the rst extension, it turns out that double links enable the formation of some networks that could not occur in the single links model. In the second extension, we nd that redundant links will be established when the agents beliefs about the probabilities of the indirect links are lower than the actual probabilities. Finally, the implications of mutual consent and endogenous success probabilities for Nash networks are discussed and explored. The network literature almost completely lacks models with heterogeneous agents, with the notable exception of Johnson and Gilles (2000) and Droste et al. (2000) who introduce spatial heterogeneity of agents and obtain results substantially di erent from both static and dynamic versions of homogeneous-agent pairwise stability models. Their model and ours di er in two respects: the kind of agent heterogeneity and the equilibrium concept. They follow Jackson and Wolinsky (1996) and use pairwise stability as the equilibrium concept. We analyze Nash networks. In a recent paper, Galeotti and Goyal (2002) also incorporate heterogeneity in the context of Nash networks. In their model di erent links may have di erent costs, and the bene ts of obtaining information from other players also varies across agents. They nd that equilibrium networks continue to have some of the key features identi ed by Bala and Goyal (2000a), i.e., centrality, centersponsorship and short network diameter occur in equilibrium despite the presence of heterogeneous players.3 These properties depend on the fa

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