Existence of Pure Strategy Nash Equilibrium in Bertrand-Edgeworth Oligopolies

This article is searching for necessary and sufficient conditions which are to be imposed on the demand curve to guarantee the existence of pure strategy Nash equilibrium in a Bertrand-Edgeworth game with capacity constraints.

A Bertrand-Edgeworth-oligopóliumok (Bertrand-Edgeworth oligopolies – a survey of the literature)

Az irodalomban az olyan oligopolmodellek, amelyekben mind az ár, mind a mennyiség döntési változó, Bertrand-Edgeworth-oligopóliumok néven ismertek. E tanulmányban a Bertrand-Edgeworth-oligopóliumokkal kapcsolatos érdekesebb eredményeket tekintjük át. Tárgyaljuk a Bertrand-Edgeworth-típusú oligopolmodellek specifikációját, a Nash-egyensúly létezését, a Nash-egyensúly meghatározását és a Bertrand-Edgeworth-oligopóliumok alkalmazásait. / === / Oligopoly models in which both price and quantity are decisive variables are known in the literature as Bertrand-Edgeworth oligopolies, the most interesting results with which are surveyed in this paper. The author assumes the existence of the Nash equilibrium, as the specification of Bertrand-Edgeworth-type oligopoly models, the determination of the Nash equilibrium, and the application of Bertrand-Edgeworth oligopolies.

Exclusive contracts with private information in successive differentiated oligopolies

The purpose of this article is to analyze the incentives of manufacturers to deal exclusively with retailers in bilaterally duopolistic industries with brand differentiation by manufacturers. In contrast with the previous literature, exclusive contracts are shown to generate higher profits for manufacturers and retailers selling highly differentiated products, who thus have an incentive to insist on exclusive contracting. However, if the products are close substitutes no exclusivity will emerge in equilibrium. Furthermore, we show that exclusive contracts decrease both consumer and social welfare.

Does timing of decisions in a mixed duopoly matter?

We determine the endogenous order of moves in a mixed pricesetting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payo equivalence of the games with an exogenously given order of moves if the most plausible equilibrium is realized in the market. Hence, in this case it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand-Edgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists.

Exclusive contracts with vertically differentiated products

In this paper we develop a simple model to analyze the effects of exclusive contracts in vertically integrated markets where both the upstream and the downstream market are characterized as oligopolies and manufacturers produce vertically differentiated products. We find that firms prefer to deal exclusively with retailers. If the extent of consumers' heterogeneity is small, manufacturers offer exclusive contracts unilaterally. On the other hand, if consumers' valuations differ significantly both manufacturers engage in exclusive contracting.

Price discrimination in asymmetric Cournot oligopoly

In this article we examine the eects of third degree price discrimination in asymmetric Cournot oligopolies. We show that the average price is not affected by the extent of price discrimination. We nd that the asymmetry between firms is reflected only by the output produced for the lowest-valuation consumers and firms produce equal quantities to the other consumer groups.

Price discrimination in asymmetric Cournot oligopoly

In this article we examine the eects of third degree price discrimination in asymmetric Cournot oligopolies. We show that the average price is not affected by the extent of price discrimination. We nd that the asymmetry between firms is reflected only by the output produced for the lowest-valuation consumers and firms produce equal quantities to the other consumer groups.

A Kreps-Scheinkman-állítás érvényessége lineáris keresletű vegyes duopóliumok esetén (The Kreps and Scheinkman result remains valid for mixed duopolies with linear demand)

Vegyes oligopóliumoknak nevezzük az olyan piacszerkezeteket, amelyek esetében a magánvállalatok mellett állami vállalatok is tevékenykednek. A vegyes oligopóliumokban az állami vállalatok részben vagy egészében a társadalmi többletet kívánják maximalizálni. Olyan vegyes duopóliumot vizsgálunk, amelyben a vállalatok előbb kiépítik kapacitásaikat, majd meghatározzák termékük kínálati árát. Kreps-Scheinkman [1983] tisztán magánvállalatos duopóliumokra vizsgált ilyen két időszakos modellt, és megállapította, hogy az első időszaki egyensúlyi kapacitások megegyeznek az azonos költségszerkezetű és kínálati viszonyú Cournot-duopólium egyensúlyi kibocsátásaival. Tanulmányunkban Kreps-Scheinkman [1983] eredményét kiterjesztjük a vegyes duopóliumok - lineáris keresleti görbe és konstans egységköltségek melletti - esetére. _____ In mixed oligopolies, private firms compete with a public firm, which at least partially aims to maximize social surplus. The authors investigate mixed duopolies in which the firms first build capacities simultaneously and then set their prices simultaneously as well. For the same two-stage game with purely private firms Kreps and Scheinkman demonstrated in 1983 that the first-stage equilibrium capacities of the two-stage game are identical with the equilibrium outputs of the Cournot duopoly. This paper extends Kreps and Scheinkman's results to mixed duopolies with linear demands and constant unit costs. It is shown that quantity pre-commitment and Bertrand competition also yield to Cournot outcomes when a public firm is involved, not only in the case of private firms.