Quantity Competition Research Articles

Privatization in mixed duopoly with vertical differentiation: Price versus quantity competition

AbstractIn this paper, we investigate the issue of privatization in a mixed duopoly with vertical differentiation under Cournot and Bertrand competition. The public firm is assumed to produce a lower‐quality product with lower production costs. We find that under both Bertrand and Cournot competition, privatization is socially desirable (undesirable) if the quality level of the private firm is sufficiently high (low). However, if the quality of the private firm is intermediate, Bertrand and Cournot competition yields opposite policy implications: privatization is desirable under Bertrand competition while undesirable under Cournot competition. Therefore, under Bertrand competition, privatization is more likely to be welfare‐improving than under Cournot competition.

On Cournot and Bertrand competition in collusive mixed oligopolies

AbstractWe consider a mixed oligopoly of one public and N private firms where goods are horizontally differentiated. In our setting, an interdependent payoff structure characterizes the degree of collusion among private firms. We show that, whereas in the Bertrand model, private firms are willing to collude as much as possible, in the Cournot model, the existence of a public firm reduces the scope of collusion. We also prove that the classic discussion comparing price and quantity competition crucially depends on market collusion. More precisely, price competition unambiguously yields larger profits for private firms only if collusion is high enough. In an infinitely repeated game, we prove that collusion is easier to sustain in a larger oligopoly because, in this case, a larger N helps mitigate the effect of the public firm on private firms’ collusion sustainability. Finally, we also find that collusion is always more easily sustained in the Bertrand case than in the Cournot case.

Stable cartel configurations and product differentiation: The case of multiple cartels

We develop a framework to analyse stable cartelisation when firms can form multiple cartels. This contrasts with the existing literature which generally assumes, without further justification, that at most one cartel may form. We define cartelisation to be stable in the multiple cartels framework if: (i) a firm in a cartel does not find it more profitable to leave the cartel and operate independently, (ii) a firm that operates independently does not find it more profitable to join an existing cartel, (iii) a firm in a cartel does not find it more profitable to join another existing cartel or form a new cartel with an independent firm, and (iv) two independent firms do not find it more profitable to form a new cartel. In the context of quantity competition in differentiated markets, we show that a single cartel is never stable whenever multiple cartels may be formed. We completely characterise the stable cartelisation structure — there is at most one firm that is not a part of any cartel while each of the remaining firms is part of a two-firm cartel. The implication for competition policy is that efforts towards the detection of cartels should also be directed at smaller cartels that may operate in less concentrated markets rather than only on large dominant cartels in concentrated markets.

Service provision decisions of competitive manufacturers: From service spillover perspective

This paper investigates competing manufacturers’ strategic choice of service provision in a two-level supply chain composed two manufacturers and one common retailer. Our results indicate that the strategy that two competing manufacturers provide services is always the dominant choice, and two competing manufacturers could have the highest profit in that case. But when only one of them provides services, the result is related to the potential market size, the unit service cost coefficient and the service spillover intensity. Finally, through the cost sharing and quantity competition extensions, we find the Pareto regions of cost sharing under the equilibrium strategy, and there will be multiple Nash equilibrium regions under the quantity competition.

Sourcing Channel Decision in the Presence of Platform Encroachment with Quantity Competition

The decision of sourcing channels is a critical strategy for online retail platforms (ORs) when they encroach into the product market of the third-party retailers (3PRs). Whether the products of the OR are provided by the common supplier or the one different from that of the 3PR leads to different supply chain structures. This paper focuses on the sourcing channel decision of an encroaching OR given the sourcing channel of a 3PR. The OR may source either from the common supplier, i.e., the same supplier as that of the 3PR, or from a different supplier, i.e., one different from that of the 3PR. This paper develops two game-theoretical models to examine the sourcing channel decision of an OR in quantity competition with a 3PR on the platform. The results show that the OR’s preference for the sourcing channel is significantly affected by the production cost, product substitutability and commission rate. By comparing the performances of the OR under these two sourcing channels, we find that when the production cost of the different supplier is very low, or when the product substitutability of the different supplier is low, or when the commission rate is either very low or very high, the OR prefers to source from the different supplier. Otherwise, the OR tends to source from the common supplier. We also find that the OR’s encroachment into the sales market of a 3PR by sourcing from the common supplier will always hurt the 3PR, but the platform encroachment by sourcing from the different supplier will not necessarily hurt, especially when the supplier selected by the OR has a significant disadvantage in production cost compared to those of the 3PR. Furthermore, when the OR encroaches by sourcing from the common supplier, it becomes the largest retailer in the market; otherwise, the 3PR is the largest retailer in that market. Our results also indicate that platform encroachment by different sourcing can not only expand the sales market, but also weaken the negative effects of platform encroachment on the profit of the 3PR.

The formation of cooperatives with the implications of information sharing and contract farming

ABSTRACT Although some cooperatives can provide an exclusive selling channel and impel information sharing among farmers, research on the formation of such cooperatives is limited. In this paper, we design a supply chain structure that includes a spot market operating with a quantity-dependent price setting accessible to all farmers, and a forward market accessible only to cooperative farmers. This enables us to analyse the conditions under which two pools of farmers are willing to form a cooperative, considering information sharing under competition. Compared to non-cooperative farmers, farmers in the cooperative can use the shared demand information to produce and sell products in the forward market. Interestingly, we find that information sharing would strengthen the intensity of quantity competition since the cooperative farmers overreact to the same signal. In addition, information sharing has a crowding effect: the expected value of information increases with the number of cooperative farmers. Thus, information sharing is a double-edged sword, which results in profit growth enabled by the crowding effect and profit loss due to quantity competition. We further show how the trade-off between the crowding effect and the quantity competition impacts farmers' decisions on whether to form a cooperative or not.

Consumers' environmental awareness and endogenous managerial delegation choice between sales and environmental incentives

This study considers consumers' environmental awareness (CEA) and examines firms' managerial delegation contracts between sales and environmental performance incentives under different competition modes. Under sales delegation contracts, quantity competition yields higher sales incentives and better environmental performance, whereas welfare depends on marginal environmental damage. Under environmental delegation contracts, however, price competition yields higher environmental incentives and welfare, whereas environmental performance depends on CEA. Then, we discover that environmental delegation contracts result in higher abatement levels and better environmental and social performances than sales delegation contracts, regardless of competition modes; bilateral environmental (sales) delegation contracts can be an equilibrium in an endogenous delegation choice game when CEA is high (low). Finally, we examine a successive endogenous competition mode choice game and determine that unless CEA is sufficiently high, firms choose a quantity contract followed by either sales or environmental delegation contracts, leading to socially undesirable outcomes.

Quantity Conjectural Variations in Oligopoly Games under Different Demand and Cost Functions and Multilevel Leadership

This paper considers a noncooperative game of quantity competition among firms in an oligopoly market under general demand and cost functions. Each firm’s optimal response to the strategies of other firms is assessed by the magnitude and sign of its conjectural variation, expressing the firm’s expectation regarding the counterparty’s supply quantity change in response to the firm’s unit change in its supply quantity. A game of n firms with the sum of conjectural variations (SCV) regarding all counterparties as the generalized response characteristic is studied. The existence of a bifurcation of the players’ response is revealed; a bifurcation is a strategy profile of the game in which both positive and negative responses are possible with an infinite-magnitude SCV value. Methods are developed for calculating the SCV value under different types of inverse demand functions (linear and power) and cost functions (linear, power, and quadratic), and the impact of these characteristics of firms on the bifurcation state is comparatively analyzed.

Endogenous timing with upstream corporate social responsibility

ABSTRACT In this study, considering a vertical market, we analyze the endogenous timing of two downstream firms providing differentiated goods in response to an upstream firm’s commitment to Corporate Social Responsibility (CSR). We demonstrate that sequential play is realized under quantity competition when the degree of upstream CSR is high and the goods are less substitutable. This is because the upstream firm offers a lower input price under a more competitive environment. Using similar logic, we also illustrate that simultaneous play may be realized under price competition. Additionally, we extend the model in several directions.

Double managerial delegation contracts with relative profit performance and environmental performance incentives under emission taxes

AbstractThis paper examines the strategic relations between emission taxes and firms' managerial delegation contracts, which include incentives based on relative profit performance (RPP) and environmental performance (EP). We demonstrate that under quantity (price) competition, the government imposes higher (lower) emission taxes, while the firm owner sets lower (higher) EP incentives and negative (positive) RPP incentives, which leads to lower (higher) welfare. We also explore an endogenous competition mode game and find that quantity (price) competition emerges when both consumers' green willingness‐to‐pay (WTP) and product differentiation are low (high). Our findings suggest that public education on greenness is crucial for enhancing EP incentives in the design of managerial delegation contracts, while intense product market competition may be detrimental to consumers and society, especially when consumers' green WTP is low.

Profitable environmental corporate social responsibility under managers’ relative profit performance competition

AbstractWhen managers face relative profit performance competition, we formulate a green managerial delegation contract where the owners impose profit‐oriented environmental corporate social responsibility (ECSR) on their managers. We show that the owner adopts ECSR as a commitment device to reduce outputs under quantity competition if the degree of relative profit performance competition is sufficiently high, which can increase not only industry profits but also environmental quality. We also examine an endogenous choice of ECSR and find that the profitable level of ECSR in the asymmetric ECSR case is higher than that in the symmetric ECSR case while both firms undertake ECSR in equilibrium if the severity of competition is sufficiently high.

Complementary inputs, outsourcing and vertical integration: Price versus quantity competition

AbstractWe compare the effects of price and quantity competition in an industry with complementary inputs, outsourcing and a vertically integrated firm where vertical integration occurs between a final goods producer and a subset of input suppliers. The profit of the integrated firm and the industry profit are higher under Bertrand competition, the profit of the non‐integrated firm is higher under Bertrand competition for high product differentiation, and consumer surplus and welfare are higher under Bertrand competition for low product differentiation. Further, no market foreclosure can be the preferred choice of the vertically integrated firm for any degree of product differentiation.

Licensing of a product innovation by an outside innovator to a Stackelberg duopoly

ABSTRACT We examine the optimal strategy of an outside innovator owning a quality-improved product when licensing it to a Stackelberg duopoly. We show that only a single licence is granted, regardless of whether there is quantity or price competition in the marketplace. However, both the licensee and contractual terms in each context differ. Under quantity competition, the licence is granted to the market-leading firm by means of a non-distorting contract, whereas under price competition the licence is granted to the market-following firm by means of a distorting two-part tariff contract with per-unit royalty. From a welfare perspective, exclusive licensing is beneficial in both contexts compared to the pre-licensing scenario, although under price competition, consumers can be harmed if the innovation is small. Finally, licensing leads price competition to yield a less efficient outcome than quantity competition due to greater market collusion. Licensing by means of three-part tariff contracts is also discussed, as well as licensing when potential licensees operate as a mixed duopoly.

Asymmetric Performance Evaluation Under Quantity and Price Competition with Managerial Delegation

Abstract In this paper, we consider asymmetric performance evaluation contracts under different product market configurations with managerial delegation and specify the optimal decision-making by the social and relative performance evaluation firms. We present a reversal result on the owner’s choice of the social performance and relative performance evaluation contract as the product market competition type changes from quantity to price competition. Surprisingly, results indicate that the consumer surplus increases as the degree of product substitution increases under quantity competition in a specific economic environment. A firm that considers social performance evaluation produces less, charges a higher price, and earns a lower profit than a firm that uses relative performance evaluation. We also endogenize the choice of performance evaluation systems. While relative performance emerges as the endogenous choice under both modes of product market competition, it leads to lower consumer surplus and social welfare in comparison to an asymmetric performance evaluation system.

The welfare effect of release timing of relative performance evaluation under quantity competition and asymmetric costs

AbstractWe examine the welfare effects of the endogenous decision and release timing of weight placed on the rival's profits under relative performance evaluation with quantity competition and asymmetric marginal costs. We find that when the advantaged firm decides and releases the weight as the leader, it always chooses a negative weight on relative performance evaluation, whereas the disadvantaged firm may choose a positive or negative weight depending on the degree of product substitution. Furthermore, we demonstrate that while all firms prefer to release weights early, this situation does not improve social welfare in several economic environments.

Strategic Partial Inattention in Oligopoly

Abstract This article examines firms’ choices on partial (in)attention prior to quantity competition. Being partially (in)attentive, a firm accounts for a part of its market impact. We find that regardless of the number of firms, there is always a unique subgame perfect Nash equilibrium where all firms choose to be partially attentive. The optimal attention level decreases in the number of firms, increases in product differentiation, and converges to zero, i.e. firms tend to be fully inattentive, as either the number of firms goes to infinity or product differentiation goes to zero.

The impact of technology transfer on managerial delegation under vertical product differentiation

AbstractThis paper analyzes the impact of technology transfer on managerial delegation contracts. Under price competition, if technology transfer occurs, it increases the level of managerial delegation of a firm producing low‐quality product. When the degree of technology transfer is relatively high, technology transfer improves the managerial delegation of producing high‐quality products. When the degree of technology transfer is relatively low, technology transfer reduces the managerial delegation of firms producing high‐quality products. Under quantity competition, technology transfer reduces the managerial delegation coefficient of all firms. We further analyze the Stackelberg competition and the royalty situation.

Bilateral Models of Cross-Licensing for Smart Products

Motivated by the new practice of cross-licensing and price competition in smart products, as well as the lack of cross-licensing literature, this article develops a theoretical framework to investigate the incentive for bilateral cross-licensing between two competing firms with asymmetric bargaining power under price competition in smart products. In this article, one firm possesses quality-improving innovation, and another offers cost-reducing innovation for smart products. We find regardless of cost-reducing innovation scale, when the production cost of a holder of quality-improving technology is high enough, the competing firms have the motivation to cross-licensing; compared with a quantity competition, cross-licensing in price competition draws a higher price and producer surplus, but lower consumer surplus and poorer social welfare. This is an interesting finding for the discussion over whether a Bertrand price competition is more efficient than a Cournot quantity competition; and price competition, plus the stability of tacit collusion in cross-licensing, requires that participants have moderate bargaining power. Our article provides a potential explanation for the use of cross-licensing in the smart product industry with price competition, as well as management insights for decision makers by considering different effects elicited by cross-licensing of the smart products.

Comparison of the Optimal Policies on International Product R&D under Price and Quantity Competition

Purpose - The first objective is to analyze and compare Bertrand and Cournot equilibria in a model wherein two governments compete with regard to research and development (R&D) subsidies, and two firms compete in a third-country market through product R&D investment and substitute goods. The second purpose is to compare the results derived in the presence of government intervention in international trade with those obtained in the case of no-trade and non-intervention.
 Design/Methodology/Approach - For this analysis, we extend Symeonidis’s (2003) work and develop an international R&D subsidy game consisting of three stages.
 Findings - First, the equilibrium levels of R&D expenditure, product quality, subsidies, prices, and firm profits are higher under quantity competition compared to price competition in the presence of government intervention in international trade, as in Symeonidis’s (2003) no-trade and non-intervention model. Second, the rankings of output and consumer surplus in the third country under the two competitions differ from those derived by Symeonidis (2003), who finds that they depend on the degree of horizontal differentiation and R&D spillovers. Third, the ranking of social welfare under the two regimes differs from the results of Symeonidis (2003), who establishes that the ranking of social welfare depends on the degree of horizontal differentiation and R&D spillovers.
 Research Implications - If a country is involved in international trade with substitute goods and its government faces R&D subsidy competition in the presence of product R&D spillovers, it is better for the government to provide R&D subsidies to domestic firms under quantity competition rather than those under price competition to ensure greater social welfare.

Comparison between Simultaneous and Sequential Movements in a Duopoly Game

In general, a Stackelberg competition benefits the leader and the consumer due to making the first move in a sequential game. However, in this paper, sequential movement does not offer an advantage over simultaneous movement in a static duopoly under quantity competition with an isoelastic demand function. By introducing dynamics into the duopoly model through numerical simulations of simultaneous and sequential movements towards the Cournot equilibrium, there is evidence of first-mover advantage. However, simultaneous movement is advantageous over sequential movement in terms of better profits for both firms and lower prices for the consumer.