A Note on Networks of Collaboration in Multimarket Oligopolies

In this note, we extend the Goyal and Joshi’s model of collaboration networks in oligopoly to multi-market situations. We examine the incentive of firms to form links and the architectures of the resulting equilibrium networks in this setting. We then present some results on efficient networks.

Business Intelligence and Multi-market Competition

We consider a multi-market 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 links gathering business intelligence about 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 multi-market 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.

Partial Cooperation in Strategic Decision Situations

We consider a normal form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. These collective actions typically represent a certain number of dimensions in the players’ strategy space. The actions represented by the other dimensions of the strategy space remain under the complete, individual control of the players.
We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are developed for these new equilibrium concepts. We identify conditions on these partial cooperative games under which the various equilibrium concepts are equivalent.
We apply this game theoretic framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly typically a merger paradox emerges in the partial cooperative equilibrium, which vanishes if the cartel of collaborators exploits its leadership position. Our application to international pollution abatement treaties shows that cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.