Cournot Competition in Networked Markets

Abstract

The paper considers a model of competition among firms that produce a homogeneous good in a networked environment. A bipartite graph determines which subset of markets a firm can supply to. Firms competeà la Cournot and decide how to allocate their production output to the markets they are directly connected to. We assume that markets have inverse linear demand and firms have quadratic production costs. First, we show that the resulting Cournot game has a unique equilibrium for any given network and provide a characterization of the production quantities at equilibrium. Our results identify a close connection between the equilibrium outcome and supply paths in the underlying network structure. In particular, we show that whether two firms see their output in different markets as strategic substitutes or complements depends critically on the paths between those markets in the line graph induced by the original bipartite network.Armed with a characterization of the equilibrium supply decisions, we explore the effect of changes in the network structure on firms' profits and consumer welfare. First, we study the question of a firm entering a new market. We show that entry may not be beneficial for either the firm or the consumers as such a move affects the entire vector of production quantities. The firm might face a more aggressive competition in its original markets due to its entry to a new market. Moreover, the effect on other firms and consumers also depends on their location in the network. This is in stark contrast with standard results in Cournot oligopoly where entry implies more competition in the market and thus higher consumer welfare.Similarly, the effect of a merger between two firms on profits and overall welfare largely depends on the structure of competition in the original Cournot market. In particular, we show that insights from analyzing mergers in a single market do not carry over in a networked environment. Market concentration indices are insufficient to correctly account for the network effect of a merger and one should not restrict attention to the set of markets that the firms participating in the merger supply to.Finally, we study the operations of a cartel including the entire set of firms. We show that the cartel maximizes its profits by appropriately segmenting the markets among its members so that a firm supplies solely to the ones allocated to it, and we provide an algorithm that computes the optimal production quantities for each firm in the cartel.

Fully Distributed Nash Equilibrium Seeking Over Time-Varying Communication Networks With Linear Convergence Rate

“…the decisions of all the competitors [5], [6], [7]. This fulldecision information hypothesis requires the presence of a coordinator, that broadcast the data to the network, and it is impractical for some applications [8], [9]. One example is the Nash-Cournot competition model described in [10], where the profit of each of a group of firms depends not only on its own production, but also on the whole amount of sales, a quantity not directly accessible by any of the firms.…”

Competitive pricing strategies in social networks

“…See also Shi (), Deroïan and Gannon (), Billand, Chakrabarti, and Sarangi (), Bloch (), Carroni and Righi (), Currarini and Feri (), Belhaj and Deroïan (), Bimpikis, Ehsani, and Ilkilic (), Ushchev and Zenou (), Zhang and Chen (), and Zhou and Chen (). These papers also study network effects in an imperfect competition setting.…”

Farmers' Information Management in Developing Countries—A Highly Asymmetric Information Structure

“…This observation can also be explained in terms of strategic complementarity/substitutability as that in Bimpikis et al. (). In this example, farmer 1's response to signal 1 and her response to signal 2 are strategic substitutes.…”

“…For example, in Bimpikis et al. (), firms engage in Cournot competitions in multiple markets and a bipartite graph describes which subset of markets a firm can supply its products to. The authors show that this network between farmers and markets can lead to various novel results.…”