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.     

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.     

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.     

Harmonic symmetries of imperfect competition on circular city

Taking location as given, we study imperfect competition on a circular city. In Bertrand oligopoly, we identify price harmonics as a function of firm unit costs and locations. The sum of oligopoly profits is larger when costs and/or locations are more dispersed in the ‘dihedral majorization’ sense. This also tends to be the case in which prices are more variable. We study how phase shifts between cost parameters and inter-firm distance parameters change production and oligopoly profits. An exact characterization of production patterns is developed in terms of the eigenvalues for what we call the price harmonics matrix. The same techniques are applied to Cournot oligopoly with spatial externalities on circular city. Solutions are compared with first-best. Production patterns can differ markedly when cost spillovers are negative.     

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).     

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.     

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。     

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.     

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.     

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.     

Differentiated Duopoly with Asymmetric Costs

In this paper, we compare Bertrand and Cournot equilibria in a differentiated duopoly with linear demand and cost functions. We extend the Singh and Vives (1984) model by allowing for a wider range of cost and demand (product quality) asymmetry between firms. Focusing on the case of substitute goods, we show that both the efficient firm's profits and industry profits are higher under Bertrand competition when asymmetry is strong and/or products are weakly differentiated. Therefore, Singh and Vives's ranking of profits between the two modes of competition is reversed in a sizeable portion of the relevant parameter space. Contrary to the standard result with symmetric firms, we also show that product differentiation can reduce both the efficient firm's and industry profits, implying that a local incentive towards less differentiation may arise.     

Welfare impacts of a non-profit firm in mixed commercial markets

Utilizing a model that allows for the welfare of the commercial NPO’s stakeholders directly in terms of their consumer surplus, and indirectly in terms of NPO profits, we explore the impact of changes in the NPO’s “social concern” for consumers on market efficiency. Three separate Cournot mixed market scenarios are analyzed: competition between the NPO and a private for-profit firm, competition between the NPO and a public firm, and a market scenario that includes all three firms. We find that the technical efficiency of the NPO vis-à-vis the profit maximizer is crucial in determining whether social welfare rises or falls as the NPO places more weight on their stakeholders’ surplus. In particular, if the NPO is less technically efficient than the profit maximizer or public firm, somewhat paradoxically social welfare may fall as the NPO shows a greater social concern for consumers. In other words, a movement away from pure profit maximizing behavior by a NPO may well be detrimental in these mixed commercial markets. We also show the additional sources of revenue available to a NPO may decrease the overall welfare in these mixed market situations.     

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.     

Information Acquisition and Strategic Disclosure in Oligopoly

I study the incentives of oligopolists to acquire and disclose information on a common demand intercept. Because firms may fail to acquire information even when they invest in information acquisition, firms can credibly conceal unfavorable news while disclosing favorable news. Firms may earn higher expected profits under such a selective disclosure regime than under the regimes where firms commit to share all or no information. In particular, this holds under both Cournot and Bertrand competition, if the firms have sufficiently flat information acquisition cost functions. For steeper cost functions Cournot duopolists prefer strategic disclosure, if their goods are sufficiently differentiated.     

Backward Integration by a Dominant Firm

This paper studies the welfare consequences of a vertical merger that raises rivals' costs when downstream competition is a la Cournot between firms with constant asymmetric marginal costs. The main result is that such a vertical merger can nevertheless improve welfare if it involves a downstream firm whose cost is low enough. This is because by raising the input price paid by the nonmerging firms the merger shifts production away from those relatively inefficient producers in favor of the more efficient firm. Yet, there is a trade-off between the gain in productive efficiency and the loss in consumers' surplus caused by the higher downstream price that follows a higher input price. It is also shown, through an example, that this result extends to price competition with differentiated products.     

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.     

连接外部性、横向联盟和市场竞争

分析了横向关系的双寡头企业具有连接外部性条件下的联盟决策,得出结论,横向企业的联盟降低了企业自身的成本,同时也降低了竞争对手的成本,具有正的连接外部性。企业先决定是否联盟,然后在市场上进行竞争;证实了市场竞争比较缓和时,横向企业联盟;市场竞争比较激烈时,横向企业不联盟。当存在产品差异化时,结论仍然不变;比较了企业联盟决策和社会计划者决策,论证得出市场竞争比较缓和时,企业和社会计划者联盟决策一致;市场竞争比较激烈时,企业联盟决策背离社会计划者的决策。     

Pricing Experience Goods: The Effects of Customer Recognition and Commitment

In a two‐period model of nondurable experience goods, we compare the profit and social welfare effects of behavior‐based price discrimination (BBPD) and price commitment (PC) (relative to time‐consistent pricing) in a monopoly. We find that when the static, full‐information monopoly price is higher (lower) than the mean consumer valuation, PC yields higher (lower) profits and social welfare than BBPD. We also identify the market conditions under which BBPD does not increase firm profits and provide an explanation as to when the firm should discriminate against its first‐time and repeat customers, respectively.     

Price and Quantity Contracts in a Mixed Duopoly with a Socially Concerned Firm

I study the endogenous choice of a price or quantity contract in a mixed duopoly with a socially concerned firm, which maximizes a combination of profit and consumer welfare. Equilibria with price and quantity contracts might co‐exist; welfare under price competition might be lower than under quantity competition; the firms' profit ranking might be different from that of a private duopoly or mixed duopoly with a public firm. Hence, if a firm follows a social strategy, the optimal market strategy crucially depends on the levels of social concern and competition in the market. The presence of socially concerned firms may change the mode of competition. Copyright © 2014 John Wiley & Sons, Ltd.     

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.