Cournot competition in networked markets

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 compete a 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. © 2014 Authors

Quantity Competition in Networked Markets Outflow and Inflow Competition

This paper investigates how quantity competition operates in economies in which a network describes the set of feasible trades. A general equilibrium model is presented in which prices and .ows of goods are endogenously determined. In such economies equilibrium dictates whether an individual buys, sells or does both (which is possible). The first part of the analysis provides sufficient conditions for pure strategy equilibrium existence; characterizes equilibrium prices, flows and markups; and details negative effects on welfare of changes in the network structure. The main contributions show that goods do not cycle, since prices strictly increase along the supply chains; that not all connected players with different marginal rates of substitution trade; and that adding trading relationships may decrease individual and social welfare. The second part of the analysis provides necessary and sufficient conditions for a networked economy to become competitive as the number of players grows large. In this context it shown that no economy in which goods are resold can ever be competitive; and that large well connected economies are competitive.

Transparency and Control in Platforms for Networked Markets

In this work, we analyze the worst case efficiency loss of online platform designs under a networked Cournot competition model. Inspired by some of the largest platforms today, the platform designs considered tradeoffs between transparency and control, namely, (i) open access, (ii) controlled allocation and (iii) discriminatory access. Our results show that open access designs incentivize increased production towards perfectly competitive levels and limit efficiency loss, while controlled allocation designs lead to producer-platform incentive misalignment, resulting in low participation and unbounded efficiency loss. We also show that discriminatory access designs seek a balance between transparency and control, and achieve the best of both worlds, maintaining high participation rates while limiting efficiency loss. We also study a model of consumer search cost which further distinguishes between the three designs

Networked Cournot Competition in Platform Markets: Access Control and Efficiency Loss

This paper studies network design and efficiency loss in open and discriminatory access platforms under networked Cournot competition. In open platforms, every firm connects to every market, while discriminatory platforms limit connections between firms and markets to improve social welfare. We provide tight bounds on the efficiency loss of both platforms; (i) that the efficiency loss at a Nash equilibrium under open access is bounded by 3/2, and (ii) for discriminatory access platforms, we provide a greedy algorithm for optimizing network connections that guarantees efficiency loss at a Nash equilibrium is bounded by 4/3, under an assumption on the linearity of cost functions

Temporally Networked Cournot Platform Markets

In networked markets, information can help firms make better decisions on which market (platform), and how much, to participate. However, these markets may be temporally separated, e.g., independent system operators in different geographical locations. We model these via networked Cournot markets, but instead consider the participation of one firm to either be with the realization (or full information) of a random market, or only with the statistics of the random market, modeled by an additive zero-mean random variable on the maximal price. We show that firms not knowing the realization of the random variable would participate in both markets in the same way as if the mean was realized. We then present global effects: we prove that profit is improved for every firm when one\u27s information improves but social welfare may get better or worst with more information

Distributed Learning for Stochastic Generalized Nash Equilibrium Problems

This work examines a stochastic formulation of the generalized Nash equilibrium problem (GNEP) where agents are subject to randomness in the environment of unknown statistical distribution. We focus on fully-distributed online learning by agents and employ penalized individual cost functions to deal with coupled constraints. Three stochastic gradient strategies are developed with constant step-sizes. We allow the agents to use heterogeneous step-sizes and show that the penalty solution is able to approach the Nash equilibrium in a stable manner within $O(\mu_\text{max})$, for small step-size value $\mu_\text{max}$ and sufficiently large penalty parameters. The operation of the algorithm is illustrated by considering the network Cournot competition problem