Non-cooperative networks in oligopolies

Abstract

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.

Complexity and Geographical Economics

“…Cournot or Bertrand), see in particular the analysis in Billand and Bravard (2004); the cost of forming a link (Billand and Bravard 2004;Goyal and Joshi 2003;König et al 2012); the architecture of the network (Cowan and Jonard 2004;Goyal and Moraga-Gonzales 2001;König et al 2012;Meagher and Rogers 2004;Bischi and Lamantia 2012a,b); the efficiency and the stability of the networks (König et al 2012;Westbrock 2010;Goyal and Moraga-Gonzales 2001;Jackson and Wolinsky 1996;Bloch and Jackson 2006); the direction of the information flow, which can be one-sided (see Billand and Bravard 2004) or two-sided (Goyal and Moraga-Gonzales 2001;Goyal and Joshi 2003;Bischi and Lamantia 2012a,b); the decisions to establish a link, which can depend on a single firm Billand and Bravard 2004) or on couples of firms (Goyal and Moraga-Gonzales 2001;Goyal and Joshi 2003;Westbrock 2010;Bischi and Lamantia 2012a,b).…”

“…In most cases, the graph representing the R&D network is undirected, so that if .i; j / 2 E then also .j; i / 2 E. This property clearly models situations where firms' R&D agreement are bilateral, with a two-way (symmetric) flow of information. In some papers (see Billand and Bravard 2004;, the previous property does not necessarily hold and the underlying network is directed, in order to model cases where firm i can access to j 's information but not vice versa, so that the flow of information is one-way (asymmetric). Another property often employed to simplify the analysis is that of symmetry (see Goyal and Moraga-Gonzales 2001;Bischi and Lamantia 2012a,b), i.e.…”

“…In these models, the flow of information can be one-way, as in Billand and Bravard (2004), or two-ways, as in that consider both cases. In other words, the (R&D) network can be directed or undirected.…”

What factors determine the number of trading partners?

“…Belleflamme and Bloch (2004), Billand and Bravard (2004), Goyal and Joshi (2006), and Furusawa and Konishi (2007) applied the theory to the models of oligopoly.…”

Industrial marketing firms and knowledge transfer: Toward a basic typology of community structures

“…For example, Séance has been described as a non-hierarchical enterprise network (Jagdev & Thoben, 2001). What we call the Guru has also been called a hub (Goyal & Joshi, 2003;Anderson & Jack, 2002, Bangens & Araujo, 2002Kranton & Minehart, 2001) and a star (Billand & Bravard, 2004).…”