Cournot Firms Research Articles

Network facility-location models in Stackelberg-Nash-Cournot spatial competition

A hierarchical mathematical programming approach is combined with sensitivity analysis (of variational inequalities) to formulate a facility-location model for a firm competing on a discrete network. It is assumed that the locating firm will act as the leader firm in an industry characterized by Stackelberg leader-follower(s) oligopolistic competition. The othern competitors in this industry are assumed to act as Cournot firms that each operate under the Cournot assumption of zero conjectural variation with respect to theirn — 1 Cournot competitors. It is further assumed that then Cournot firms will react to the location/production/shipping activities of the Stackelberg firm. Therefore, when the Stackelberg firm makes its location, production, and shipping decisions it takes into account the reaction of then Cournot firms to its (the Stackelberg firm's) integrated location and distribution decisions. Specifically, a Cournot reaction function is developed and imbedded in the Stackelberg firm's profit-maximizing objective function to project the anticipated reaction of the Cournot firms to the Stackelberg firm's location decision.

NETWORK FACILITY‐LOCATION MODELS IN STACKELBERG‐NASH‐COURNOT SPATIAL COMPETITION

ABSTRACT A hierarchical mathematical programming approach is combined with sensitivity analysis (of variational inequalities) to formulate a facility‐location model for a firm competing on a discrete network. It is assumed that the locating firm will act as the leader firm in an industry characterized by Stackelberg leader‐follower(s) oligopolistic competition. The other n competitors in this industry are assumed to act as Cournot firms that each operate under the Coumoi assumption of zero conjectural variation with respect to their n–1 Cournot competitors. It is further assumed that the n Cournot firms will react to the location/production/shipping activities of the Stackelberg firm. Therefore, when the Stackelberg firm makes its location, production, and shipping decisions it takes into account the reaction of the n Cournot firms to its (the Stackelberg firm's) integrated location and distribution decisions. Specifically, a Cournot reaction function is developed and imbedded in the Stackelberg firm's profit‐maximizing objective function to project the anticipated reaction of the Cournot firms to the Stackelberg firm's location decision.

On the theory of monopolistic competition under demand uncertainty

Establishing a model of a monopolistically competitive industry in which risk-averse Cournot firms act under demand uncertainty and in which the output of individual firms and the number of firms in the industry are both endogenously determined by free entry and exit, this paper attempts to investigate the effects of demand uncertainty on the market equilibrium of a monopolistically competitive industry. It is assumed, for calculus simplification, that the firms are identical in the sense that they have the same monopolistic power and the same production technology. The paper presents some interesting and useful comparative statics results which are contrary to those proposed in the existing papers.

Competitive Approximation of a Cournot Market

It is a longstanding intuitive notion that a market with small Cournot firms and free entry is well approximated as a perfectly competitive market. Not until Novshek's recent paper (1980), however, was this folk theorem turned into a real theorem. The basic ingredients of Novshek's model are a downward sloping demand curve for the market and a U-shaped average cost curve common to all firms. Let y * denote the smallest firm output which achieves minimum average cost; and let Y* denote the market output which would prevail under a perfectly competitive approximation (the market demand when price equals minimum average cost). A small value for the ratio y */ Y* indicates that the market can accommodate a sizeable number of firms. Roughly speaking, Novshek's main result is this. If y*/Y* is sufficiently close to zero, then there exists one or more Cournot equilibria (with free entry), each of which has market output Y in the interval Y* - ' Y_ Y*. Given a small y */ Y*, this interval is tight; hence Novshek's result supports the use of the competitive approximation Y = Y*. This paper presents an alternative model of the same issue, based on the same demand and cost curve ingredients. Novshek's model is static and (to me at least) technically demanding. The model below, in contrast, is dynamic and simple. The train of thought which led me to the alternative model may be of interest.

Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations

The supply side of an oligopolistic market supplying a homogeneous product noncooperatively is modeled. In this market, there is one leader and N followers. The followers operate under the Cournot assumption of zero conjectural variation and are accordingly called Cournot firms. The leader, called a Stackelberg firm, specifically takes into account the reaction of the Cournot firms to its output. For this situation, we study the behavior and implications of the joint Cournot reaction curve as generated by plausible economic market assumptions. In particular, we study the existence and uniqueness of a Stackelberg-Nash-Cournot equilibrium. In addition, we prescribe an efficient algorithm to determine a set of equilibrating output quantities for the firms.