Nash networks, Two-way flow models, Point contrabasis, C72, D85,

This paper addresses the existence of Nash networks for the one-way flow model of Bala and Goyal (2000) in a number of different settings. We provide conditions for the existence of Nash networks in models where costs and values of links are heterogeneous and players obtain resources from others through the directed path between them. We find that costs of establishing links play a vital role in the existence of Nash networks.Next we examine the existence of Nash networks when there are congestion effects in the model. JEL Classification: C72, D85

In an oligopoly, prior to competing in the market, firms have an opportunity to pick up externalities from other firms by setting links. The links formation defines an industrial network. We study the incentives for firms to form links and the effect of this links formation on the architecture of the resulting networks. Our analysis shows that equilibrium networks differ dramatically depending on the nature of market competition (Cournot or Bertrand). More precisely, in the case of Cournot oligopoly, we should expect to see networks in which each firm obtains access to externalities of either all firms or no firm. In the case of Bertrand oligopoly, we should expect to see networks in which one firm derives benefits from externalities of all other firms while the latter get no externality. We also present some results on the architecture of socially efficient networks. JEL Classification Number: C70, L13, L20.

Networks facilitate the exchange of goods and information and create benefits. We consider a network with n complementary nodes, i.e. nodes that need to be connected to generate a positive payoff. This network may face intelligent attacks on links. To study how the network should be designed and protected, we develop a strategic model inspired by Dziubiński and Goyal (2013) with two players: a Designer and an Adversary. First, the Designer forms costly protected and non-protected links. Then, the Adversary attacks at most k links given that attacks are costly and that protected links cannot be removed by her attacks. The Adversary aims at disconnecting the network shaped by the Designer. The Designer builds a protected network that minimizes her costs given that it has to resist the attacks of the Adversary. We establish that in equilibrium the Designer forms a minimal 1-link-connected network which contains only protected links, or a minimal (k + 1, n)-link-connected network which contains only non-protected links, or a network which contains one protected link and (n − 1)(k + 1)/2 non-protected links. We also examine situations where the Designer can only create a limited number of protected links and situations where protected links are imperfect, that is, protected links can be removed by attacks with some probabilities. We show that if the available number of protected links is limited, then, in equilibrium, there exists a network which contains several protected and non-protected links. In the imperfect defense framework, we provide conditions under which the results of the benchmark model are preserved.JEL Classification: D74, D85.

We consider a multimarket framework where a set of firms compete on two oligopolistic markets. The cost of production of each firm allows for spillovers across markets, ensuring that output decisions for both markets have to be made jointly. Prior to competing in these markets, firms can establish business intelligence gathering links with other firms. A link formed by a firm generates two types of externalities for competitors and consumers. We characterize the business intelligence equilibrium networks and networks that maximize social welfare. By contrast with single-market competition, we show that in multimarket competition there exist situations where intelligence-gathering activities are underdeveloped with regard to social welfare and should be tolerated, if not encouraged, by public authorities.