Quantity Competition Research Articles

Competition or coopetition? Equilibrium analysis in the presence of process improvement

Coopetition is a business phenomenon that dominates many supply chains. We aim to understand why and how coopetition occurs in supply chains with the presence of process improvement in upstream component production. An original equipment manufacturer (OEM) can purchase the component from either a non-competing supplier (NS) or a competing supplier (CS) that also sells substitutable products in the end consumer market. We demonstrate that without process improvement, coopetition does not exist, because the OEM prefers sourcing from the NS, even though the CS is willing to sell the component to the OEM. Two cases are considered in which process improvement is present: supplier-initiated investment, where the suppliers conduct self-investment, and OEM-initiated investment, where the OEM invests in the supplier's process. We find that with supplier-initiated investment, the CS always prefers coopetition, but the OEM may not. When the investment is efficient, coopetition occurs as an equilibrium outcome; otherwise, competition occurs. The cause of coopetition equilibrium comes from variable process improvement incentives of the CS that derive from two driving forces: the vertical wholesale price effect and the horizontal quantity competition effect. When the degree of product substitution is low, the CS increases its investment and lowers its wholesale price, benefiting the OEM. When the degree of product substitution is high, the CS reduces its investment as well as production quantity, which also benefits the OEM. Interestingly, with OEM-initiated investment, the CS might not always choose to sell the component to the OEM, and as a result, coopetition never occurs.

On pure-strategy Nash equilibria in price–quantity games

This paper examines the existence and characteristics of pure-strategy Nash equilibria in oligopoly models in which firms simultaneously set prices and quantities. Existence of a pure-strategy equilibrium is proved for a class of price–quantity games. If the demand function is continuous, then the equilibrium outcome is similar to that of a price-only model. With discontinuous demand and limited spillover, there are rationing equilibria in which combined production falls short of market demand. Moreover, there might again be an equilibrium reflecting the outcome of a price game. Competition in price and quantity thus yields Bertrand outcomes under a variety of market conditions.

Sharing managerial contract information in a vertically related market

Recent research shows that in duopolies with strategic delegation, firm owners have an incentive to always share information about managerial compensation contracts. We study how sharing of contract information is affected by the presence of a supplier. We find that under quantity competition, a partial information‐sharing equilibrium may occur. Firms that share contract information punish their managers for sales to soften supplier pricing. Mandating information sharing increases total welfare but decreases consumer surplus. Under price competition, firms always want to share managerial contract information. Finally, firm profits can be higher under price competition than under quantity competition.

Information sharing motivated by production cost reduction in a supply chain with downstream competition

AbstractThis paper studies demand information sharing in a two‐echelon supply chain consisting of one manufacturer and two retailers, an informed retailer and an uninformed retailer. The retailers engage in Cournot competition or Bertrand competition. The manufacturer can conduct cost reduction, while the informed retailer has the decision power to opt for a sharing format, among no sharing, partial sharing (only with the manufacturer), and full sharing. Under partial sharing, the uninformed retailer infers the demand information from the manufacturer's wholesale price. We find that the inference effect, that is, the presence of the manufacturer's pricing distortion, depends on the manufacturer's cost‐reduction efficiency and the retailers' competition mode. Under low cost‐reduction efficiency, the inference effect makes the retailers worse off in quantity competition, whereas it is beneficial to them in price competition. On the contrary, under high efficiency, the retailers benefit from the inference effect in quantity competition, whereas they become worse off in price competition. By contrast, the inference effect only makes the manufacturer worse off. The uninformed retailer may prefer partial sharing to full sharing, while the informed retailer may be indifferent between full sharing and partial sharing.

Identification of firms’ beliefs in structural models of market competition

AbstractFirms make decisions under uncertainty and differ in their ability to collect and process information. As a result, in changing environments, firms have heterogeneous beliefs on the behaviour of other firms. This heterogeneity in beliefs can have important implications on market outcomes, efficiency and welfare. This paper studies the identification of firms’ beliefs using their observed actions—a revealed preference and beliefs approach. I consider a general structural model of market competition where firms have incomplete information and their beliefs and profits are nonparametric functions of decisions and state variables. Beliefs may be out of equilibrium. The framework applies both to continuous and discrete choice games and includes as particular cases models of competition in prices or quantities, auction models, entry games and dynamic games of investment decisions. I focus on identification results that exploit an exclusion restriction that naturally appears in models of competition: an observable variable that affects a firm's cost (or revenue) but does not have a direct effect on other firms’ profits. I present identification results under three scenarios—common in empirical industrial organization—on the data available to the researcher.

Capacity Reservation Strategies under Quantity Competition with Demand Uncertainty

In this paper, we consider a supplier serving two competing manufacturers who produce and sell their products in the same market faced with the uncertain demand. The manufacturers can either participate in the supplier development programme by reserving their capacities from the supplier before the demand is realized, which is referred to as the advance reservation, or do not by reserving their capacities after the demand is realized, which is referred to as the regular reservation. Given the unit capacity wholesale prices for both the advance reservation and the regular reservation, we study the manufacturers' capacity reservation and selling, and the supplier's capacity building decisions in equilibrium when the advance reservation strategy is adopted by neither, one, or both of manufacturers. We further investigate the equilibrium reservation strategies of manufacturers. We discover that completely symmetric manufacturers may choose different capacity reservation strategies, in which case, a unique mixed strategy equilibrium also arises. We also identify the conditions under which the capacity reservation preferences of all supply chain members can be aligned, thus achieving the efficiency of the supply chain. Our findings underscore the importance of operational characteristics in determining the capacity reservation strategies.

Market share transparency, signaling and welfare: Cournot and Bertrand

When demand is noisy and firms’ costs are private information, the availability of market share data increases the accuracy of each firm’s information, and it creates incentives for signaling. Taking both effects into account, we find that under quantity competition with a homogeneous good, the availability of market share data has a positive impact on total surplus and an ambiguous one on consumer surplus. Under price competition with differentiated substitutes, it has a negative impact on consumer surplus and an ambiguous one on total surplus. If the cost difference is small, the effect of first-period signaling dominates the effect of second-period full information. Accordingly, in this case, the availability of market share data causes total and consumer surplus to increase in the case of quantity competition and to decrease in the case of price competition.JEL classification: C73, D82, L13.

Strategic delegation under rational and fulfilled expectations in quantity competition

ABSTRACT In an asymmetric duopoly with quantity competition such that consumers form expectations about network sizes before and after the owners of both firms choose their incentive parameters (fulfilled and rational expectations, respectively), this paper reconsidered the level of their incentive parameters adopting the approach emplyed in two important existing works in this field. In quantity competition, we demonstrate that in such an asymmetric duopoly, the owners of both firms make their managers more aggressive than their sole profit maximizers, regardless of the strength of network effects.

Managing green innovation investment in a Co-opetitive supply chain under capital constraint

Responding the increasing concerns on environment and green consumerism, many firms found specialized environmental foundations to invest in green technology innovators (GTIs) and achieve green features in their products to attract consumers. However, facing increasing financial pressure during the economic downturn in recent years, they may have limited capital for green investments. In this paper, we investigate, in the presence of limited environmental foundation sizes, whether a pair of co-opetitive supply chain players (consisting of an Original Equipment Manufacturer (OEM) and a Contract Manufacturer (CM) that serves as both a supplier and a competitor in downstream market for the OEM) should co-invest in a joint GTI. We consider two scenarios, Scenario N where the OEM and CM respectively invest in two independent GTIs, and Scenario Y where the two firms co-invest in a joint GTI. We analyze both the exogenous or endogenous reward rates cases for the promoting of green innovation efforts of the GTIs. Under both exogenous and endogenous reward rates, we find that although Scenario Y always yields higher greenness level than Scenario N for both the OEM and CM, the OEM doesn’t always have incentive to do so due to the CM’s strategic use of wholesale price or reward rate decision responses, while the CM is always better off in Scenario Y when the reward rate is exogenous. We also find that the market size and competitive intensity will post significant impacts on the green innovation outcomes, wholesale price and reward rates decisions in the co-opetitive relationship. Intensified downstream quantity competition can motivate upstream innovation investment. However, greener technology may result in worse environmental performance for the whole supply chain because of increased total quantity.

Endogenous timing in a mixed duopoly under the optimal degree of privatization

ABSTRACTThis study revisits the endogenous timing game in a mixed duopoly by considering the situation in which a welfare‐maximizing government sets the optimal degree of privatization for a partially privatized firm. We present the following results. First, in quantity competition, the government sets the degree of privatization for the partially privatized firm to be positive or zero depending on the equilibrium in the subsequent observable delay game. The observable delay game has multiple equilibria and the firms choose either of two Stackelberg equilibria. Second, in price competition, the government chooses to fully nationalize the partially privatized firm, leading to a unique Bertrand equilibrium in the observable delay game.

Poverty mitigation via solar panel adoption: Smart contracts and targeted subsidy design

An emerging application of FinTech in the commodities market pivots on a blockchain-enabled Peer-to-Peer energy exchange platform, wherein solar energy feed-in tariffs are self-executed via “smart contracts”. With subsidy design versus mechanism design models, this paper evaluates the instrumental value of smart contracts towards poverty mitigation in developing economies via securing sustainable revenue for rural households. We investigate how the adoption levels of solar panels interact with adoption barriers and household energy behaviors. Smart contracts can be applied for self-executing the green energy financing and subsidy distribution process. For the government-led subsidy design scheme, we propose Cournot quantity competition models that incorporate spatial heterogeneity (energy-poor and energy-rich regions) and uncertainty in energy generation costs. We find that the government’s aggregate subsidy expenditure decreases in solar uncertainty, and it is optimal to select households from a single region only for high uncertainty. Smart contracts facilitate heterogeneity and uncertainty to soften quantity competition, benefitting households in both regions and the government. For the mechanism design scheme, we demonstrate that both regions can be chosen only under the incomplete information case with inaccurate forecasts about market conditions and a relatively low baseline energy price. The self-executing feature of smart contracts helps mitigate the potential risks of renegotiation between multiple parties. Moreover, a public policy supported by mechanism design is more likely to outperform that based on market competition regarding cost-effectiveness only when the latter chooses a single region. Otherwise, quantity competition would be significantly softened by contingency-dependent smart contracts under heterogeneous market conditions.

What level do disadvantaged firms weight rivals' profits in relative performance evaluations under quantity competition?

In the context of quantity competition in relative performance evaluation, this study explores the weight placed on rivals' profits through two asymmetry cases—the cost difference between firms and the sequential choice of weight placed on their rivals' profits. We identify high‐cost firms in the cost asymmetry, and followers in the sequential case of weight decisions are labeled “disadvantaged” firms. Whereas the classical literature demonstrates that the weight placed on a rival's profit is negative under quantity competition, we provide theoretical evidence that the disadvantaged firm assigns a positive weight to the rival's profit under asymmetric cases.

On the Private and Social Value of Consumer Data in Vertically-Integrated Platform Markets

We characterize and compare the private and social incentives to collect consumer data by a vertically-integrated online intermediary who competes with third-party sellers listed on its platform and is required by regulation to share with rivals all the information it gathers. With linear intermediation fees and price competition, the intermediary over-invests in accuracy compared to the social optimum when the intra-platform competition is sufficiently weak and when demand is not too responsive to quality. By contrast, the intermediary tends to under-invest in accuracy when the intra-platform competition is strong enough, and demand is sufficiently responsive to quality. With quantity competition, the intermediary always over-invests in accuracy. Importantly, when consumers exhibit privacy concerns, the over-investment problem worsens, whereas the under-investment problem mitigates. We also investigate the impact of alternative (non-linear) contractual arrangements.

Collusion with Network Externalities in Price vs. Quantity Competition

In the presence of network externalities, we compare the stability of collusion under Bertrand and Cournot duopoly with differentiated products. Contrast to previous studies, we show that (i) firms have stronger incentive to collude under Bertrand competition than under Cournot competition in the sense of wide range of network externalities; (ii) collusion in prices (quantities) is more stable than in quantities (prices) if network externalities is strong (weak).

Price Versus Quantity Competition in a Vertically Related Market with Retailer’s Effort

Abstract Allowing downstream retailers to engage in demand-enhancing investment, this paper demonstrates that the classical conclusions regarding the comparison of Cournot and Bertrand competition in a vertically related market with decentralized bargaining are completely reversed. It shows that Bertrand competition is more efficient than Cournot competition, in the sense that both consumer surplus and social welfare are always higher in the former.

Price and quantity competition in a differentiated duopoly with heterogeneous beliefs

AbstractThe purpose of this paper is to investigate the impact of heterogeneous beliefs about market demand on the profitability of firms under different competitive settings. To this end I consider a differentiated duopoly model where two firms with different beliefs about the market demand can compete in quantity (Cournot competition) or in price (Bertrand competition). The results show that the optimistic firm can outperform the pessimistic firm in profits under Cournot competition even in the state of Low demand as long as the ratio of High demand over Low demand is sufficiently low. Under Bertrand competition, however, if the ratio of High demand over Low demand is sufficiently low or the overall optimism of the two firms is sufficiently high, the pessimistic firm can gain higher profit than the optimistic one even when demand is high.

Price and quantity competition with network externalities: Endogenous choice of strategic variables

AbstractWe consider the endogenous choice of strategic variable (price or quantity) in a duopoly market for differentiated goods in the presence of network externalities. We show that if the rival goods are substitutes in demand, but the degree of network compatibility is large enough to outweigh the substitution effects, each firm chooses price as its strategic variable. This finding is a rare exception to the usual result that if the goods are substitutes, each firm would choose quantity as its strategic variable. Moreover, we show that two non‐standard results hold when the above condition is satisfied and the efficiency difference between the two firms is large. First, the price of the less efficient firm is higher under price competition than under quantity competition. Second, in a situation where one firm sets quantity and the other firm sets price, the profit of the more efficient firm is higher when it is the quantity‐setter than when it is the price‐setter, and the opposite is true for the less efficient firm.

An Algorithm Approach to FRAND Contracts

In the context of standards development, the current mechanism of negotiation of FRAND royalties frequently brings to undesirable litigation. This is mainly due to the fact that a relevant part of the information concerning the standard, required to stipulate complete license contracts, is revealed only after the standard itself has spread in the market. In this respect, we propose a litigation-reducing algorithm to determine the FRAND level of the licensing royalty. Unlike the current negotiation mechanism, this algorithm can be defined ex-ante, so to increase contract completeness, because it includes a Bayesian-updating rule, able to address the presence of ex-ante uncertainty. We derive the algorithm from a generic oligopolistic-competition model, so to deliver characteristics of applicability to both price and quantity competition. Simulations in a linear-Cournot framework suggest the algorithm calculates FRAND royalties and may be usefully applied to real-life cases.

Two-Player Location Game in a Closed-Loop Market with Quantity Competition

This paper considers the two-player location game in a closed-loop market with quantity competition. Based on the Cournot and Hotelling models, a circle model is established for a closed-loop market in which two players (firms) play a location game under quantity competition. Using a two-stage (location-then-quantity) pattern and backward induction method, the existence of subgame-perfect Nash equilibria is proved for the location game in the circle model with a minimum distance transportation cost function. In addition, sales strategies are proposed for the two players for every local market on the circle when the players are in the equilibrium positions. Finally, an algorithm for simulating the competitive dynamics of the closed-loop market is designed, and two numerical simulations are provided to substantiate the effectiveness of the obtained results.

Competition between branded and nonbranded firms and its impact on welfare

AbstractWe examine a quantity competition among branded and nonbranded firms. The market comprises two consumer segments: one purchases only branded products (the high‐end market), while the other segment's consumers purchase less expensive products (the low‐end market). When branded firms take actions sequentially, we show that the branded leader has an incentive to restrict its quantity to avoid entering the low‐end market. As the follower recognizes this incentive, it can restrict the leader by implementing a quantity constraint, which is affected by the number of nonbranded firms. We find that both the branded leader and follower could benefit from the nonbranded firms and that the leader prefers to have more nonbranded firms in the market than the follower does. Furthermore, we show that the free entry of nonbranded firms could negatively affect total surplus as well as consumer surplus even without any costs, because of the premium pricing of branded products.