ENDOGENOUS TIMING IN A MIXED DUOPOLY AND PRIVATE DUOPOLY –‘CAPACITY‐THEN‐QUANTITY’ GAME: THE LINEAR DEMAND CASE*

We consider a game of endogenous timing of sequential choice of capacity and quantity with observable delay in a mixed duopoly and a private duopoly. In mixed duopoly, we find that a simultaneous play at the capacity stage or at the quantity stage can never be supported as subgame perfect Nash equilibrium (SPNE); whereas a simultaneous play at each stage turns out to be the unique SPNE in a private duopoly. In mixed duopoly there is multiplicity of equilibria and all SPNEs require sequentiality at the capacity as well as quantity stage.     

Endogenous Timing in Mixed Duopolies With Externality

We investigate endogenous timing in a mixed duopoly with a negative externality. We find that quantity (price) competition yields a simultaneous‐move (sequential‐move) outcome under a significant negative externality. These results indicate that mixed duopolies yield the same results as private duopolies under a significant negative externality, which is in sharp contrast to the results in mixed duopolies without a negative externality. Unless the negative externality is insignificant, public leadership yields greater welfare than private leadership, and public leadership is more robust than the private leadership as equilibrium. If optimal environmental tax policy is introduced, however, private leadership yields the greatest welfare and this an equilibrium outcome in the endogenous timing game under quantity competition.     

On Stackelberg games in a homogeneous product market

In a homogeneous product duopoly with concave demand and strictly convex costs we bring together all the standard results of quantity Stackelberg games, provide some new results with price Stackelberg games and compare the equilibrium configuration of the quantity games with the price games. In the price Stackelberg game we show there is a unique SPNE where the leader chooses a lower price than the follower, but both get equal payoffs. We prove that generally quantity Stackelberg games are less competitive than price Stackelberg games. However, we also demonstrate the possibility of a reversal of this result.     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

Optimal manipulation rules in a mixed oligopoly

We study the optimal manipulation rules of a public firm’s objective function in a mixed oligopoly with imperfect product substitutability. We start with a baseline duopoly model and compare the solutions under quantity and price competition, and the way they are affected by product substitutability. This allows us to show that partial privatization, strategic delegation and other specific government’s commitments on the objective function of the public management can be looked at as special cases of these optimal rules, and to evaluate the viability of these policies under the two modes of competition. In this framework, we also discuss the equivalence between manipulation of the objective function and Stackelberg leadership. Since optimal manipulation rules change as new dimensions are added, we also derive the optimal rules under oligopoly, quadratic costs, and competition of international firms. This fairly general unified framework allows to discuss the impact of these factors on the government’s implementation policies of the optimal manipulation rules.     

Quantity competition vs. price competition under optimal subsidy in a mixed oligopoly

This paper reconsiders the literature on the irrelevance of privatization in mixed markets within which both quantity and price competition are investigated under product differentiation. By allowing for partially privatization of a state-controlled firm, we explore competition under different timings of firms' moves and derive the conditions under which an optimal subsidy allows to achieve maximum efficiency. We show that, irrespective of the mode of competition, while the ownership of the controlled firm is irrelevant when firms play simultaneously, it matters when firms compete sequentially, requiring the leader to be publicly-owned for an optimal subsidy to restore the first-best. The paper also focuses on the extent to which a subsidy is needed to attain the social optimum in the considered scenarios, providing an ordering which highlights the subsidy equivalence between Cournot (Bertrand) private leadership and simultaneous Bertrand (Cournot) under duopoly, and the dominance of the former in oligopoly.     

Endogenous Timing in a Mixed Duopoly: Price Competition

The endogenous order of moves is analyzed in a mixed duopoly for differentiated goods, where firms choose whether to set prices sequentially or simultaneously. It is shown that, in contrast to the private duopoly where firms set prices sequentially, in the mixed duopoly firms choose prices simultaneously. Moreover, the result obtained in the mixed duopoly under price competition differs from the one under quantity competition, since in the latter case decisions are taken sequentially.      

Can a decline in search cost increase prices?

This paper provides a new explanation of why a decline in consumers’ price search cost may not lead to lower prices. In a duopoly with price competition, I show that when some consumers are captive to one firm, there may be a non‐monotonic relationship between search cost and market power; firms may charge high prices with higher probability and the average price charged may be higher when consumers’ price search cost falls below a critical level. Furthermore, when firms have asymmetric captive segments, expected prices charged by each firm may move in opposite directions as search cost declines.     

Choosing price or quantity? The role of delegation and network externalities

We consider a differentiated duopoly and endogenise the firm choice of the strategy variable (price or quantity) to play on the product market in the presence of network externalities. We model this choice by assuming both competition between entrepreneurial (owner-managed) firms and competition between managerial firms in which market decisions are delegated from owners to revenue-concerned managers. While network externalities are shown not to alter the symmetric equilibrium quantity choice arising in the no-delegation case, sufficiently strong network effects allow us to eliminate the multiplicity of equilibria under delegation and lead to a unique equilibrium in which both firms choose price.     

Strategic competition and optimal parallel import policy

Abstract In a two‐country Hotelling type duopoly model of price competition, we show that parallel import (PI) policy can act as an instrument of strategic trade policy. The home firm’s profit is higher when it cannot price discriminate internationally if and only if the foreign market is sufficiently bigger than the domestic one. The key mechanism in the model is that the home firm’s incentive to keep its domestic price close to the optimal monopoly price affects its behavior during price competition abroad. We also analyze the welfare implications of PI policies and show that our key insights extend to quantity competition.     

CHOOSING ROLES IN A DUOPOLY FOR ENDOGENOUSLY DIFFERENTIATED PRODUCTS*

The choice of the roles by firms in a vertically differenitated duopoly is analysed introducing a preplay stage where firms set the timing of moves, under the alternative assumptions of full or non full market coverage. Under the first, it turns out that the unique subgame perfect equilibrium entails simultaneous play in the quality stage, followed by sequential play in the price stage, where both firms would prefer to be price leader, contrarily to the results obtained by previous literature. Under partial market coverage, it is possible to analyse both price and quantity competition. In such a case, simultaneous play in both stages emerges as the optimal behaviour. Overall, contrarily to the conclusions reached by the previous literature, it is not possible to claim that the choice of the strategy space dominates the distribution of roles.     

Endogenous rationing,price dispersion and collusion in capacity constrained supergames

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price–quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell at this price. Under price–quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with optimal collusion, it may be a requirement of optimal collusion.     

Cartel sustainability with vertical product differentiation: Price versus quantity competition

In the context of a vertically differentiated duopoly, we analyse the influence of the degree of differentiation on cartel sustainability, under both price and quantity competition. We find that, under both Bertrand and Cournot competition, the effect of vertical product differentiation on sustainability of the collusive equilibrium is unclear. It is shown that, given a degree of differentiation, price collusion is more sustainable than quantity collusion.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

Choosing Price or Quantity? The Role of Delegation and Network Externalities in a Mixed Duopoly

This paper considers a differentiated goods managerial mixed duopoly composed of one social welfare‐maximising public firm and one profit‐maximising private firm. We model the firm choice of the strategic contract. We find that when the strength of network effects is sufficiently strong, the price competition can become the unique equilibrium market structure. Furthermore, we show that there exists an area of the degree of product differentiation and the strength of network effects such that the situation wherein the public firm chooses its price contract whereas the private firm chooses its quantity contract can become the unique equilibrium structure.     

Market Instability in a Stackelberg Duopoly

m -period duopoly model with inventory costs, where each firm chooses when to produce. We find that, in contrast to most existing works concerning endogenous roles of the firms, no pure strategy equilibrium exists when m is strictly larger than two. This result indicates that no stable pattern of allocation of roles exists except for a two-period model; thus the leader-follower relationship inevitably becomes instable. Received August 1, 2000; revised version received July 20, 2001     

Spatial Cournot competition in a circular city with more than two dispatches

This paper investigates spatial Cournot competition in a circular city, where the maximal service range of a vehicle is less than half of the perimeter, and a firm needs to initiate more than two dispatches to serve the whole market. We examine a multi‐stage game of location and transportation mode choices, and the subsequent quantity competition between duopoly firms. The findings reveal that non‐maximum dispersion is the unique location equilibrium when duopoly firms deliver products in different transportation modes or when the transportation mode decisions are made endogenously and the fixed cost of a transportation instrument is relatively high.     

Biased managers as strategic commitment: The relative profit approach

This paper analyzes a duopolistic model wherein each firm׳s owner can hire a biased manager for strategic reasons. We focus on the situation wherein each firm׳s owner evaluates the performance of her/his manager on the basis of her/his relative profit, which is equal to the weighted sum of her/his absolute profit and the absolute profit of her/his opponent firm. We show that in both price-setting and quantity-setting competitions, the owners of the two private firms employ aggressive managers rather than absolute profit maximizing managers regardless of the degree of importance of each firm׳s relative performance. Furthermore, in both the price competition and the quantity competition, as the degree of importance of each firm׳s relative performance increases, we show that the firms׳ owners tend to hire more aggressive managers when the degree of importance of each firm׳s relative performance is sufficiently low, whereas in both the price competition and the quantity competition, the firms׳ owners tend to hire less aggressive managers otherwise. Thus, in both the price competition and the quantity competition, the type of each firm׳s manager is not monotone with respect to the degree of each firm׳s relative performance. Thus, in both the price competition and the quantity competition, we find that the change in the optimal type of manager hired by each firm is non-monotone against the change of competitiveness in the market with the increase in the degree of importance of each firm׳s relative performance.     

Partial privatization in mixed duopoly with price and quality competition

We analyze price and quality competition in a mixed duopoly in which a profit-maximizing private firm competes against a state-owned public firm. We first show that the welfare-maximizing public firm provides a lower quality product than the private firm when they are equally efficient. In order to maximize social welfare, government manipulates the objective of the public firm that is given by a convex combination of profits and social welfare. It is demonstrated that an optimal incentive of the public firm is welfare maximization under the absence of quality competition, but it is neither welfare maximization nor profit maximization under the presence of quality competition. The result supports a completely mixed objective between welfare and profit maximizations or partial privatization of the public firm.      

A note on merger in mixed duopoly: Bertrand versus Cournot

In this note we analyze the incentives to merge in a mixed duopoly if firms compete in prices or quantities. Our model framework mainly follows Barcena-Ruiz and Garzon (J Econ 80:27–42, 2003) who set up the model with quantity competition. We extend their analysis by analyzing the case of competition in prices. Further we compare the incentives to merge with Bertrand and Cournot competition. Comparing quantity with price competition we can show that a merger is more likely with Cournot competition than with Bertrand competition.