Network Cournot Competition

Cournot competition is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility---a function of the production cost as well as market price of the product---by deciding on the amount of production. In today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game \emph{Network Cournot Competition} (NCC). In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. However, for nonlinear price functions, this approach is not feasible. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical \emph{Cournot Oligopoly} problems. We give the first combinatorial algorithm for this widely studied problem

On Welfare under Cournot and Bertrand Competition in Differentiated Oligopolies

Häckner (2000, Journal of Economic Theory 93, 233–239) shows that in a differentiated oligopoly with more than two firms, prices may be higher under Bertrand competition than under Cournot competition, implying that the classical result of Singh and Vives (1984, Rand Journal of Economics, 15, 546–554) that Bertrand prices are always lower than Cournot prices is sensitive to the duopoly assumption. Häckner (2000, Journal of Economic Theory, 93, 233–239), however, leaves unanswered the important question of whether welfare may be lower under price competition. This note shows that in Häckner’s model both consumer surplus and total surplus are higher under price competition than under quantity competition, regardless of whether goods are substitutes or complements. Copyright Springer 2005Bertrand, Cournot, differentiated oligopoly, welfare,

Optimal punishments in linear duopoly supergames with product differentiation

penal codes, security level, product differentiation, positivity constraints, C72, D43, L13,