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.     

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.     

OLIGOPOLY GAMES AND THE COURNOT–BERTRAND MODEL: A SURVEY

Traditional oligopoly models hold that firms compete in the same strategic variable, output (Cournot) or price (Bertrand). Alternatively, a hybrid model allows some firms to compete in output and other firms to compete in price, also known as the Cournot–Bertrand model. When the choice of strategic variable is endogenous, the established dominant strategy is output competition. A growing body of work demonstrates, however, that the Cournot–Bertrand outcome can be a subgame‐perfect Nash equilibrium in the presence of market asymmetries. Observations of real‐world markets consistent with Cournot–Bertrand behavior bolster justification for the model and have stimulated an impressive and evolving literature on advances and applications. We lay out the roots of the Cournot–Bertrand model and explore a number of model developments. We categorize 12 primary models in the literature based on alternative assumptions. In particular, some authors consider when the timing of play as well as the choice of strategic variable are endogenous. Altogether, this research identifies when Cournot–Bertrand behavior can emerge in a dynamic setting and under alternative market conditions. We also review the Cournot–Bertrand model applications in the fields of international economics, industrial organization, labor, and public economics. We expect the literature to continue to expand in the future.     

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.     

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.     

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.     

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。     

Product Differentiation and Upstream-Downstream Relations

This paper examines the relationship between a differentiated downstream market and a specialized upstream market. We analyze three different types of vertical relation between the upstream and downstream sectors when the upstream market supplies specialized and complementary inputs to a downstream product-differentiated market. The first is the benchmark case of decentralized markets, the second is a network of alliances among upstream suppliers, and the third is partial vertical integration. We identify the perfect equilibrium for a symmetric model in each case and show that there is no simple relationship between the degree of connection between upstream and downstream firms and profitability. The key factor affecting prices and the relative profitability of the different market organizations is the degree of product differentiation among the downstream firms, because it affects the intensity of competition among upstream suppliers. We show that vertical foreclosure is not an equilibrium strategy.     

Effect of Overconfidence on Cournot Competition in the Presence of Yield Uncertainty

This study investigates the effects of overconfidence on a Cournot competition subject to yield uncertainty. We consider one of two firms to be overconfident, whereas the other is completely rational and derive the Nash equilibrium to compare with that when both firms are completely rational. Through this comparison and analysis, we establish that (i) the relationship between a firm's overconfidence and the likelihood of that firm developing a monopoly in the market is positive; (ii) a rational firm always suffers a loss because of its competitor's overconfidence in a Cournot competition; and (iii) an overconfident firm does not benefit constantly from its overconfidence, although overconfidence results in permanent, increased, and more aggressive market sharing in competitions. Copyright © 2016 John Wiley & Sons, Ltd.     

The relationship between product market competition and unemployment with profit sharing

We investigate the implications of product market imperfections on negotiated wages and equilibrium unemployment under profit sharing. We show that intensified product market competition reduces equilibrium unemployment in a strictly monotonic way when the trade union's bargaining power exceeds the profit share. If the profit share exceeds the trade union's bargaining power, the effect of product market competition is ambiguous: there is a threshold for the benefit–replacement ratio above (below) which intensified product market competition increases (decreases) equilibrium unemployment. The profit share and the union's bargaining power affect the wage mark-up, and thereby equilibrium unemployment, in different directions.     

Delegation and Incentives under Evolutionarily Stable Conjectures

Existing results show that in a homogenous Cournot duopoly, commitment by delegation harms profit. This conclusion presupposes that market conduct is the same whether incentives are aggressive or accommodating. We study delegation and incentives under evolutionarily stable conjectures and show how performance pay co‐determines market conduct. In fact, in equilibrium with evolutionarily stable conjectures, we show that commitment through delegation leads to a profit increase. Manipulation of managerial incentives produces less competition and therefore benefits firms' owners even in symmetric homogenous oligopoly. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

Downstream Competition, Foreclosure, and Vertical Integration

This paper analyzes the effect of competition among downstream firms on an upstream firm's payoff and on its incentive to integrate vertically when firms in both segments negotiate optimal contracts. We argue that as downstream competition becomes more intense, the upstream firm obtains a larger share of a smaller downstream industry profit. The upstream firm may encourage downstream competition (even excessively) in response to high downstream bargaining power. The option of vertical integration may be a barrier to entry downstream and may trigger strategic horizontal spinoffs or mergers. We extend the analysis to upstream competition.     

Strategic Delegation and Vertical Integration

This paper proposes a game‐theoretic model to analyze owners' vertical integration choices if they delegate pricing decisions to their managers. We find that all three vertical structures are possible Nash equilibrium outcomes. If the products are weak substitutes, then the outcome is that both owners adopt vertical integration. When the products are close substitutes, both owners adopt vertical separation in equilibrium. When substitution between the products is medium, the coexistence of vertical integration and vertical separation is the equilibrium outcome, and the owner corresponding to vertical separation offers exactly a profit‐maximization contract to his or her manager under this situation. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Long-Term or Short-Term Managerial Incentive Contracts

This paper deals with the strategic role of the temporal dimension of contracts in a duopoly market. Is it better for a firm to sign long-term incentive contracts with managers or short-term contracts? For the linear case, with strategic substitutes (complements) in the product market, the incentive variables are also strategic substitutes (complements). It is shown that a long-term contract makes a firm a leader in incentives, while a short-term contract makes it a follower. We find that, under Bertrand competition, in equilibrium one firm signs a long-term contract and the other firm short-term incentive contracts; however, under Cournot competition, the dominant strategy is to sign long-term incentive contracts.     

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).     

Vertical externality and strategic delegation

This paper examines the effects of vertical externality generated by the upstream monopoly on the incentives that owners of competing downstream firms give their managers. It is shown that the introduction of the upstream monopoly may have significant effects on the incentive schemes for the downstream firms' managers. In particular, it is shown that in equilibrium, each owner obtains the simple Nash equilibrium outcome regardless of the mode of competition (quantity or price) in the downstream market. Copyright © 2002 John Wiley & Sons, Ltd.