Endogenous timing in a mixed duopoly

This paper addresses the issue of endogenizing the equilibrium solution when a private - domestic or foreign - firm competes in the quantities with a public, welfare maximizing firm. Theoretical literature on mixed oligopolies, in fact, provides results and policy implications that crucially rely on the notion of equilibrium assumed, either sequential or simultaneous. In the framework of the endogenous timing model of Hamilton and Slutsky (1990), we show that simultaneous play never emerges as the equilibrium of mixed duopoly games. We provide sufficient conditions for the emergence of public and/or private leadership equilibria. These results are in sharp contrast with those obtained in private duopoly games in which simultaneous play is the general result. We show that the key difference lies in the fact that the objective of a welfare maximizing firm is generally increasing in the rival's output, while the contrary holds for private firms. We develop a comprehensive analysis of a mixed duopoly considering both the cases of domestic and international competition, and the possible strategic complementarity and substitutability. From a methodological viewpoint we make large use of the basic results of the theory of supermodular games in order to avoid extraneous assumptions such as concavity, existence and uniqueness of the equilibria

Endougenous Timing in a Mixed Duopoly

This paper applies the framework of endogenous timing in games to mixed quantity duopoly, wherein a private – domestic or foreign – firm competes with a public, welfare maximizing firm. We show that simultaneous play never emerges as a subgame-perfect equilibrium of the extended game, in sharp contrast to private duopoly games. We provide sufficient conditions for the emergence of public and/or private leadership equilibrium. In all cases, private profits and social welfare are higher than under the corresponding Cournot equilibrium. From a methodological viewpoint we make extensive use of the basic results from the theory of supermodular games in order to avoid common extraneous assumptions such as concavity, existence and uniqueness of the different equilibria, whenever possible. Some policy implications are drawn, in particular those relating to the merits of privatization.Mixed markets, endogenous timing, Cournot equilibrium, Stackelberg equilibrium, privatization.

Privatization in oligopoly : the impact of the shadow cost of public funds

The aim of this paper is to investigate the welfare eect of privatization in oligopoly when the government takes into account the distortionary eect of rising funds by taxation (shadow cost of public funds). We analyze the impact of the change in ownership not only on the objective function of the rms, but also on the timing of competition by endogenizing the determination of simultaneous (Nash-Cournot) versus sequential (Stackelberg) games. We show that, absent effciency gains, privatization never increases welfare. Moreover, even when large effciency gains are realized, an ineffcient public rm may be preferred

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

Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixed-strategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games

Mixed duopolies with advance production

Production to order and production in advance has been compared in many frameworks. In this paper we investigate a mixed production in advance version of the capacity-constrained Bertrand-Edgeworth duopoly game and determine the solution of the respective timing game. We show that a pure-strategy (subgame-perfect) Nash-equilibrium point exists for all possible orderings of moves. It is pointed out that unlike the production-to-order case, the equilibrium of the timing game lies at simultaneous moves. An analysis of the public firm's impact on social welfare is also carried out. All the results are compared to those of the production-to order version of the respective game

Mixed duopoly, privatization and the shadow cost of public funds

The purpose of this paper is to investigate the effect of privatization in a mixed duopoly, where a private firm complete in quantities with a welfare-maximizing public firm. We consider two inefficiencies of the public sector : a possible cost inefficiency and an allocative inefficiency due to the distortionary effect of taxation (shadow cost of public funds). Furthermore, we analyze the effect of privatization on the timing of competition by endogenezing the determiantion of simultaneous (Nash-Cournot) versus sequential (Stackelberg) games using the model developed by Hamilton and Slutsky (1990). The latter is especially relevant for the analysis of privatization, given that results and policy prescription emerged in the literature crucially rely on the type of competition assumed. We show that privatization has generally the effect of shifting from Stackelberg to Cournot equilibrium and that, absent efficiency gains privatization never increases welfare. Moreover, even when large efficiency gains are realized, an inefficient public firm may be preferred.mixed oligopoly, privatization, endogenous timing, distortionary taxes

Endogenous Timing in a Mixed Duopoly with Managerial Delegation: A Quadratic Cost Case

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