Spatial discrimination: Bertrand vs. Cournot with asymmetric demands

This paper develops a barbell model a la Hwang and Mai [Hwang, H., and C.C. Mai, 1990, Effects of spatial price discrimination on output, welfare, and location, American Economic Review 80, 567–575.] with homogeneous product and asymmetric demands to compare prices, aggregate profits and social welfare between Cournot and Bertrand competition, and to analyze the firms' equilibrium locations. It focuses on the impacts of the spatial barrier generated from transport costs, and the market size effect resulting from asymmetric demands. It shows that the market-size effect is crucial in determining firms' locations under Cournot competition, but insignificant under Bertrand competition. Moreover, the equilibrium price of the large market and the aggregate profits are lower but the social welfare is higher under Cournot competition than under Bertrand competition if one of the markets is sufficiently large and the transport cost is high.     

基于成本差异的最佳贸易与产业政策选择

本文讨论了存在成本差异的第三国市场模型的最佳贸易与产业政策选择问题，讨论了社会成本和私人成本、本国和外国成本差异情况下的Cournot竞争和Bertrand竞争的情况。本文发现，在Cournot竞争下，政府首先行动时，当政府基金影子价格低于4／3时，政府对出口进行补贴，并且本国越有成本优势，补贴越高，补贴的利润转移效应越大；当政府基金影子价格高于4／3时，政府对出口征收出口税，且本国越有成本优势，征税越多。在Bertrand竞争下，当政府先行动时，对出口征收出口税；当政府后行动时，对出口进行补贴。当本国企业具有劣势时，事后补贴是最佳政蓑。     

Price versus quantity in a duopoly with network externalities under active and passive expectations

This study examines the endogenous choice of strategic contracts in a duopoly composed of firms that produce goods with network externalities with some sort of compatibility. We adopt two types of expectations—active and passive—as consumers' expectations for each firm's equilibrium market share. In addition, we take into account the managerial case and entrepreneurial case with and without separation between ownership and management, as firms' internal structures. We derive the properties in the Cournot competition and the Bertrand competition as the equilibrium market structures under both passive and active expectations under imperfectly compatibility of networks.     

Endogenous vertical structure and trade policy in an import-competing market

We examine the endogenous determination of a vertical market in an import-competing market with import tariff. We show that if firms commit to vertical organization before the government's commitment to trade policy, the home and foreign firms choose vertical separation and vertical integration, respectively, at equilibrium under Bertrand competition. Under Cournot competition, the subgame perfect Nash equilibrium entails both firms separating their retailers. Comparing profits between Bertrand competition to Cournot competition, we find that upstream manufacturer's profit can be higher under Bertrand competition with integration than under Cournot competition with separation when comparing foreign upstream manufacturer's profit.     

Quantity precommitment and price-matching

We study the effects of price-matching in a capacity-constrained duopoly setting. We show that no firm does worse at any pure equilibrium under price-matching relative to Bertrand, but as capacity increases, one or both firms do better relative to Bertrand. If the firms choose their capacities simultaneously before making pricing decisions, then the effect of price-matching varies with the cost of capacity. Specifically, when the cost is “high” price-matching either (i) has no effect on the market price, i.e., the market price associated with the pure SPEs is the Cournot one, or (ii) weakly decreases the market price relative to Cournot. Furthermore, when the cost is “low” price-matching leads to a set of (pure) SPE prices that includes the Cournot price in the interior. Therefore, price-matching does not necessarily benefit the firms when firms select their capacities before competing in price.     

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.     

Disclosure Policy in a Mixed Market

This paper investigates the optimal disclosure strategy for private information in a mixed duopoly market, where a state-owned enterprise (SOE) and a joint-stock company compete to supply products. I construct a model where the two firms compete in either quantity or price, and uncertainty is associated with either marginal cost or market demand. The model identifies the optimal disclosure strategies that constitute a perfect Bayesian equilibrium by type of competition and uncertainty. In Cournot competition, both firms disclose information under cost uncertainty, while only the SOE or neither firm discloses information under demand uncertainty. Alternatively, in Bertrand competition, only the joint-stock company discloses information under cost uncertainty or demand uncertainty. Recently, developed countries have required the same level of disclosure standards for SOEs as for ordinary joint-stock companies. The findings described in this paper warn that such mandatory disclosure by SOEs can trigger a reaction by joint-stock companies, putting the economy at risk of a reduction in welfare.     

Disclosure Regulation in Duopoly Markets: Proprietary Costs and Social Welfare

Abstract

The argument of proprietary costs is commonly used by firms to object against proposed disclosure regulations. The goal of this paper is to improve our understanding of the welfare consequences of disclosure in duopoly markets and to identify market settings where proprietary costs are a viable argument for firms to remain silent. We, therefore, solve the optimal disclosure strategies and distinguish two different potentially costly effects of disclosing private information: the strategic information effect and the market information effect. We identify the market settings for which a regulator prefers to impose disclosure regulation so as to maximise consumer surplus or total surplus. Regulation may be necessary because (i) the increase in welfare outweighs proprietary costs to the firms, or (ii) firms are trapped in a prisoners' dilemma. The first primarily applies to Bertrand competition with demand uncertainty and, to a lesser extent, to Cournot competition. The second applies primarily to Cournot competition and Bertrand competition with cost uncertainty.     

Do firms choose overcapacity or undercapacity in a vertical structure?

This study investigates capacity choice in a vertical structure in which each downstream firm makes its capacity decision, then a monopolistic upstream firm proposes the input price or two-part tariff contract. Finally, each downstream firm chooses its output (or price). Contrary to the conventional wisdom that both firms hold excess capacity in an Cournot competition, we find that each downstream firm always chooses undercapacity regardless of both the nature of goods and the competition modes. Second, we also show that capacity efficiency is higher under Cournot competition than under Bertrand competition. Third, even though there are double marginalization distortion and rent-extracting effect, we can achieve the monopoly equilibrium of the vertically integrated firm though two-part tariff contract.     

On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms’ production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.     

Efficiency loss in a Cournot oligopoly with convex market demand

We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature.     

Learning cycles in Bertrand competition with differentiated commodities and competing learning rules

This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.     

Accreditation in a differentiated duopoly

Accreditation is increasingly important worldwide; however, some industries have higher accreditation rates than others. We suggest a duopoly model to discuss how market characteristics affect the incentive for firms to seek accreditation. The discussion relates to the effects accreditation might have on the costs and demands in the markets, the degree of product differentiation (addressing both substitutable and complementary goods), type of competition (various Cournot and Bertrand games), and welfare for society. It follows that markets with high accreditation rates are either characterized by fierce competition (price competition in substitutable goods) or by a high degree of coordination (complementarity).     

Correlated equilibria in homogeneous good Bertrand competition

We show that there is a unique correlated equilibrium, identical to the unique Nash equilibrium, in the classic Bertrand oligopoly model with homogeneous goods and identical marginal costs. This provides a theoretical underpinning for the so-called “Bertrand paradox” as well as its most general formulation to date. Our proof generalizes to asymmetric marginal costs and arbitrarily many players in the following way: The market price cannot be higher than the second lowest marginal cost in any correlated equilibrium.     

External bargaining versus internal manipulation: A theory of managerial delegation

Does the competition mode influence the delegation decisions of the firm owners? By constructing a vertical negotiation game model, we find that under Cournot competition in the downstream market, the downstream firm's owner will not choose delegation, whereas under Bertrand competition, the downstream firm's owner will choose delegation. If the product substitution is relatively large, the adoption of delegation management by the owners of downstream firms under Bertrand competition will bring higher profits. It further shows that compared with the situation of no delegation, delegation management may reverse the social welfare ranking under Bertrand and Cournot competitions.     

Robust results on the sharing of firm-specific information: Incentives and welfare effects

Contrary to much of the existing literature, we obtain robust and clear-cut results for the incentives and welfare effects of information sharing when information is firm-specific. We show that firms’ incentives to share this type of information are aligned with social welfare. Whenever revealing information is the dominant strategy (such as for Cournot firms revealing costs or Cournot and Bertrand firms revealing demand), it is socially beneficial. Only cost information in Bertrand competition will not be revealed but this is socially desirable, too. These findings are independent of distributional assumptions on random shocks and signals and hold for general asymmetric oligopoly with any mixture of substitute, complementary and independent goods.     

Price and Quantity Competition in a Differentiated Duopoly with Upstream Suppliers

This paper analyzes the noncooperative game on the choice of strategic variable to set in duopoly in the presence of an upstream market for the input. For the case of labor input, the analysis shows that if the wage is the result of decentralized firm-union bargain, a duopoly producing substitutes may choose to compete either in the quantity space or in the price space, depending upon the distribution of bargaining power in the wage negotiation and the union's relative preference over the wage. For the case of input suppliers as profit-maximizing firms, the paper shows that a vertically differentiated duopoly may prefer to compete either in the quantity space or in a mixed strategy setting where the high-quality firm plays price and the low-quality firm plays quantity, depending upon the extent of substitutability, the degree of vertical product differentiation and the distribution of bargaining power in the input price negotiation.     

Market Structure and the Demand for Free Trade

We examine a heterogenous goods duopoly model, wherein governments simultaneously and noncooperatively choose whether or not to provide subsidies for their firms and then firms noncooperatively choose output levels, either sequentially or simultaneously. We find that government trade policy and market structure are interdependent. First, the trade regime alters traditional firm preferences over sequential versus simultaneous play. Second, different market structures influence governments' preferences about free trade versus subsidies. Further, if one of the firms is a potential leader, allowing for endogenous market structure generates equilibrium outcomes that sometimes reinforce, and sometimes counter, traditional results in the strategic trade literature .     

Endogenous mergers under multi-market competition

This paper examines a simple model of strategic interactions among firms that face at least some of the same rivals in two related markets (for goods 1 and 2). It shows that when firms compete in quantity, market prices increase as the degree of multi-market contact increases. However, the welfare consequences of multi-market contact are more complex and depend on how two fundamental forces play out. The first is the selection effect, which acts to increase welfare, as shutting down the relatively more inefficient firm is beneficial. The second opposing effect is the internalisation of the Cournot externality effect; reducing the production of good 2 allows firms to sustain a higher price for good 1. This works to increase prices and, therefore, decrease consumer surplus (but increase producer surplus). These two effects are influenced by the degree of asymmetry between markets 1 and 2 and the degree of substitutability between goods 1 and 2.     

基于cournot Model与Bertrand Model寡头竞争模型的药品最优定价策略

本文将竞争博弈模型引用到药品定价策略中,分别从制造商利润最大化,销售商利润最大化以及总体药品市场价值最大化的角度,研究了在Cournot Model下,制造商应该对销售商采取如何定价策略,而销售商应该如何应对才能达到总体利润最大化;在Bertrand Model下,论证多个药品制造商应该采取一体化的价格管理体系,并在文章最后给出Cournot Model以及Bertrand Model的寡头竞争模型在药品流通渠道管理中的应用。