QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

Price and Quantity Competition in a Differentiated Duopoly With Network Compatibility Effects

We consider the efficiency of price and quantity competition in a network products market, where we observe product compatibility with network externalities (hereafter, network compatibility effects). In particular, if network compatibility effects between firms are sufficiently asymmetric, the Cournot equilibrium is more efficient than the Bertrand equilibrium in terms of larger consumer, producer and total surpluses. Then, we consider an endogenous choice of the strategic variables, price and quantity. If the degree of network compatibility effects of the rival firm is larger (smaller) than the degree of product substitutability, then choosing prices (quantities) is a dominant strategy for the firm. Thus, if the network compatibility effects of both firms are larger (smaller), the Bertrand (Cournot) equilibrium arises. Furthermore, if the network compatibility effects between the firms are sufficiently asymmetric, the firm with a larger (smaller) network compatibility effect than a certain level of product substitutability chooses quantities (prices). In this case, the Cournot–Bertrand equilibrium arises, which is less (more) efficient than the Cournot equilibrium in terms of consumer (producer) surplus.     

Codetermination,Price Competition and the Network Industry

This research develops a tractable two‐stage non‐cooperative game with complete information describing the behaviour of price‐setting firms that must choose to be profit maximisers or bargainers under codetermination in a network industry with horizontal product differentiation. The existing theoretical literature has already shown that codetermination might arise as the endogenous market outcome in a strategic competitive quantity‐setting duopoly. In sharp contrast with this result, the present article shows that codetermination does never emerge as a Nash equilibrium in a price‐setting non‐network duopoly. Then, it aims at highlighting the role of network externalities in determining changes of paradigm of the game and letting codetermination become a sub‐game perfect Nash equilibrium when prices are strategic substitutes or strategic complements. This equilibrium may be Pareto efficient. Results allow distinguishing between mandatory codetermination and voluntary codetermination. The article also proposes a model of endogenous codetermination according to which every firm may choose to bargain with its own corresponding union bargaining unit only whether the firm's bargaining strength is exactly the profit‐maximising one. The equilibrium outcomes emerging in this case range from a uniform Nash equilibrium, in which both firms are codetermined, to mixed Nash equilibria, in which only one of them chooses to be codetermined. These results are ‘network depending’ and do not hold in a non‐network duopoly.     

ENDOGENOUS TIMING IN QUALITY CHOICES AND PRICE COMPETITION

We modify the price‐setting version of the vertically differentiated duopoly model by Aoki (2003) by introducing an extended game in which firms noncooperatively choose the timing of moves at the quality stage. Our results show that there are multiple equilibria in pure strategies, whereby firms always select sequential play at the quality stage. We also investigate the mixed‐strategy equilibrium, revealing that the probability of generating outcomes out of equilibrium is higher than the probability of playing one Nash equilibria in pure strategies. In the alternative case with full market coverage, we show that the quality stage is solved in dominant strategies and therefore the choice of roles becomes irrelevant as the Nash and Stackelberg solutions coincide. With full market coverage and corner solution, the results show that the game has a unique subgame perfect equilibrium in pure strategies, where the high‐quality firm takes the lead in the quality stage.     

Horizontal mergers and product quality

We study the effects of a horizontal merger when firms compete on price and quality. In a Salop framework with three symmetric firms, several striking results appear. First, the merging firms reduce quality but possibly also price, whereas the outside firm increases both price and quality. As a result, the average price in the market increases, but also the average quality. Second, the outside firm benefits more than the merging firms from the merger, and the merger can be unprofitable for the merger partners, i.e., the “merger paradox” may appear. Third, the merger always reduces total consumer utility (though some consumers may benefit), but total welfare can increase due to endogenous quality cost savings. In a generalized framework with n firms, we identify two key factors for the merger effects: (i) the magnitude of marginal variable quality costs, which determines the nature of strategic interaction and (ii) the cross‐quality and cross‐price demand effects, which determines the intensity of price relative to quality competition. These findings have implications for antitrust policy in industries where quality is a key strategic variable for the firms.     

Stakeholders’ relationships and product market competition

In this article, we study the relationships between main stakeholders (shareholders, consumers and employees) when firms are consumer oriented (CO) in the sense of caring about consumers’ interests in the objective function. We let these firms first bargain with labour union over their employees’ wages and then compete either in the quantity space (Cournot competition) or in the price space (Bertrand competition). Our model shows that taking care of the consumers’ interests when determining product market strategies may reverse the traditional ranking between Cournot and Bertrand equilibria. This implies that if shareholders in a CO firm can choose either a quantity or a price strategy, they will surprisingly choose the latter. Moreover, we show that the conflicting interests between main stakeholders are attenuated under Bertrand competition compared to Cournot competition.     

Organizational Structure and the Choice of Price versus Quantity in a Mixed Duopoly

We consider the choice of price/quantity of a public and a private firm in a mixed differentiated duopoly. First, we study the way in which the strategic choice of the market variable is affected by different given organizational structures (managerial or entrepreneurial) of the public and the private firm. Second, we investigate how the price/quantity choice interacts with the endogenous choice of the organizational structure, thus determining a subgame perfect equilibrium at which firms choose to behave as price‐setters and to adopt a managerial structure.     

战略性经营者激励选择与国际市场份额竞争

本文首先用具有线性需求和规模收益不变生产技术的Cournot双头模型来刻画国际市场份额竞争。指出 ,如果参与国际竞争的本国企业是所有权与经营权分离的企业 ,那么 ,无论竞争对手是否是所有权与经营权分离的企业 ,本国企业所有者总是有积极性操纵经营者的激励 ,特别的 ,在只有本国企业作出单边激励选择的情况下 ,这种操纵可以使本国企业生产Stackelberg领先者产量成为可以置信的承诺。它在这里所起到的作用是与出口补贴在战略性贸易政策分析中所起到的作用相一致的。如果考虑到从过去的GATT到现在的WTO都规定政府不得以任何形式参与国际竞争 ,这个结论就更有趣了。因为无须政府帮助 ,本国企业所有者凭借自身的力量就能实现有利于本国企业的竞争结果。这种民间对政府的替代是有意义的。在双边激励选择的情况下 ,两国企业陷入了“囚徒困境”。本国企业只有诉诸于本国政府对国际市场的干预 ,才能重新获得Stackelberg领先者的地位 ;但与对它的传统理解相比 ,这种地位已然弱化。最后 ,我们还证明 ,根据相当一般的条件 ,所有者决定的最优经营者激励只与竞争类型 (数量竞争还是价格竞争 )有关 ,而与企业的产品类型 (替代品还是互补品 )无关。     

Trade policy in the face of price and non-price strategies

When selling their products domestically or internationally, firms rely on more than just price as a strategic variable. They also rely on non-price instruments such as advertising and/or R&D investments. Any trade policy that affects or limits the use of one variable will likely have strategic consequences for the use of all the others. Using a Hotelling model with vertical differentiation we focus on how trade policy barriers alter price and non-price competition on the goods market. The main results are as follows: first, no matter whether the trade restriction (tariff) is placed on the non-price instrument or on the good itself, the foreign (domestic) firm prefers to increase (decrease) its use of its pricing tool and give up some of (increase) its use of the non-price instrument. Second, in the presence of a non-price instrument, tariffs do not always lead both firms to increase their price: it can lead the foreign firm to decrease its (final) price.     

Price Competition and Product Differentiation When Consumers Care for the Environment

Increasing environmental awareness may affect the pleasure of consuming a good for which an environment friendly substitute is available. In this paper, we investigate the market implication of product differentiation when customers are concerned about environmental aspects of the good. We use the spatial duopoly model to determine how environmental concern affects prices, product characteristics and market shares of the competing firms. Our analysis is based on a two-stage game, where at the first stage each firm chooses the characteristic of its product. At the second stage, each firm chooses its price. Equilibrium prices and market shares are affected by consumer awareness of the environment and by the higher costs for producing those goods. As for the Nash equilibria in the characteristics, we find three equilibria depending on the parameter constellation. In order to find out whether the market functions in an optimal way, we determine the choice of environmental characteristics by a welfare maximizing authority. The objective of the paper is to understand the environmental quality choices facing firms and to provide policies that would align private choices with the social optimum.JEL classifications: L11, Q38, H23     

PRIVATISATION AND TIMING IN A MIXED OLIGOPOLY WITH BOTH FOREIGN AND DOMESTIC FIRMS*

This paper models a mixed oligopoly with both a domestic and a foreign private firm and examines the resulting timing in the quantity setting game. We demonstrate that with a single simultaneous pre‐game delay stage, the resulting endogenous timing has either the public firm leading or the two private firms leading. An alternative characterisation of the pre‐game stage results in the single timing in which the two private firms lead and the public firm follows. For all timings that emerge endogenously, we show that privatisation will always lower domestic welfare but its influence on global welfare is ambiguous.     

Credence Goods,Misleading Labels,and Quality Differentiation

Due to differences in information disclosure mechanisms, consumer misinformation about the quality of many credence goods is more endemic at intermediate levels of the quality spectrum rather than at the extremes. Using an oligopoly model of vertical product differentiation, we examine how consumers’ overestimation of the quality of intermediate-quality products affects firms’ incentives to improve product quality. The firms non-cooperatively choose the quality of their product before choosing its price or quantity. Irrespective of the nature of second stage competition, Bertrand or Cournot, we find that quality overestimation by consumers increases profit of the intermediate-quality firm, and motivates it to raise its product’s quality. In response, the high-quality firm improves its product quality even further but ends up with lower profit. Overall, average quality of the vertically differentiated product improves, which raises consumer surplus. Social welfare increases when the firms compete in prices but falls when they compete in quantities.     

Corporate social responsibility and strategic relationships

We analyze a delegation game relevant to the conduct of corporate social responsibility (CSR) in which the firm’s owner offers the manager a contract consisting of firm profit and social welfare. We derive three results that distinctly differ from existing findings. First, CSR decisions are strategic complements for firms. Second, with simultaneous CSR decisions, the equilibrium price is equal to marginal cost, despite the fact that firms compete in a Cournot duopoly. Finally, with sequential CSR decisions, unlike the follower firm, the leader firm never exhibits CSR. However, the follower firm can enjoy a profit equal to that derived by the leader in a Cournot–Stackelberg game.     

ENDOGENOUS TIMING IN MULTI-STAGE DUOPOLY GAMES*

This paper presents an investigation of the endogenous timing in multi-stage duopoly games in which duopolists choose two variables over two periods. The paper elaborates the two-stage strategic commitment game discussed by Brander and Spencer (1983). Duopolists decide their outputs and cost-reducing investments and they are allowed to choose which action to take first. The paper discusses two types of games; one is a three-stage game in which each duopolist can commit to the order of choices before it chooses its output or cost-reducing investments, and the other is a two-stage game in which it cannot. The paper finds that at least one firm chooses its output first. Furthermore, the three-stage game has the unique equilibrium outcome in which both firms choose their outputs first.     

A generalized framework for endogenous timing in duopoly games and an application to price-quantity competition

This paper extends the analysis of duopoly market by distinguishing two types of competition: (i) the basic form of competition where each firm is unrestricted in its choice of price and quantity and (ii) the non-basic form of competition where firms’ strategic choices over price and quantity are limited a priori. Our analysis focuses on the former rather than the latter. Under a very general setting of concave industrial revenue and asymmetric convex costs, we show that each firm typically makes more profit in the subgame perfect Nash equilibrium (SPNE) of the leader-follower price-quantity competition, one of the basic competition forms, than in the SPNE of the leader-follower price competition and that each firm always makes more profit under simultaneous move price-quantity competition than under simultaneous move price competition. We establish a generalized framework for endogenous timing in duopoly games which is capable of embodying and overcoming the inconsistency across the existing three frameworks in the field. We highlight the advantages of a 3-period general framework.     

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.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Quality competition,welfare, and regulation

In this paper, we study the supply of quality in imperfectly competitive markets, and explore the role of regulation in markets where firms may use both quality and price to compete for customers. In a model where firms first choose qualities and then prices, we find that quality decisions have strategic effects: firms react to quality disadvantages by price reductions. Because of this strategic effect, firms do not have the correct incentive to set socially efficient quality levels. Price and quality competition results in a socially suboptimal quality level. Efficiency can be restored by lump-sum transfers and price regulatory policies. Simple price regulation may result in lower price and higher quality.We thank Nicholas Economides, Randall Ellis, Thomas McGuire, Michael Riordan, and Monika Schnitzer for discussing various issues in this research with us. We are also grateful to a referee for helpful comments and suggestions. The first author acknowledges support from the Management Science Group, Department of Veterans Affairs at Bedford, Massachusetts. The ideas here do not represent those of the Department of Veterans Affairs.     

Asynchronized multiperiod commitments and cycles

We consider a game where agents can synchronize or stagger their decisions. We compare the outcomes of both timing patterns, and show that spillovers and strategic interactions are crucial for such a comparison. A typology used in industrial organization, distinguishing four cases (‘Fat-Cat’, ‘Top Dog’, Lean and Hungry’, ‘Puppy Dog’), allows us to compare the actions taken in the staggered variant and in the synchronized one. The staggered variant exhibits cycles and players are both better-off when there are strategic complementarities between them. A timing game is then set-up so as to endogenize the choice between the two variants we study.Two examples are developed: (i) Bertrand competition and (ii) a wage setting game when there are two monopoly unions in two interrelated firms. We show that the staggering of price decisions generates counter-cyclical mark-ups in the first example, and the staggering of wage decisions generates cycling output in the industry in the second example.     

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.