Hotelling was Right

This paper proves existence of a subgame perfect equilibrium in Hotelling's original (unidimensional city, linear transportation costs, uniform distribution of the consumers, two firms with identical and constant marginal cost, perfectly inelastic demand) location–price game such that in the location subgame the location choices of the firms are pure and identical. The result can be extended to variations of the original setup (multidimensional city, nonlinear transportation costs, nonuniform distribution of consumers, many firms with identical and constant marginal costs, two or more firms with nonidentical but constant marginal costs).     

基于二阶段博弈的碳排放权分配机制研究

建立了政府和两企业之间的一主两从Stackelberg博弈模型和企业之间的差异Bertrand价格博弈模型,将两者结合成一个二阶段博弈模型。对政府和企业之间的博弈行为以及决策变量之间的关系进行分析。研究证明碳排放交易市场可以通过每个企业的边际减排成本均等化实现排放权最终的优化配置,而政府通过确定碳排放权的初始分配比例实现社会的公平性。最后通过数据分析了环境污染程度、企业的减排技术对在均衡条件下的企业效益、政府决策偏好和社会公平性的影响。     

Dynamics in research joint ventures and R&D collaborations

We investigate the short- and long-term effects of different types of R&D collaborations on firms, consumers, and the industry. To that end, we consider a differentiated-product market in which firms compete à la Bertrand and invest in process innovation in order to lower the production cost over time. Investments are stochastic and there can be cartelization or competition strategies among firms at the moment of making the decision on the amount to invest in R&D. Our results show that in equilibrium, the long-run welfare is larger under a research joint venture than under other environments. Discounted present value profits increase with the level of the spillover but there are asymmetries that depend on the firms’ asymmetry on marginal costs.     

Strategic Invasion in Markets with Switching Costs

We investigate the role of consumer switching costs in a three-stage model in which the entrant and the incumbent firm set prices sequentially and then the consumers decide from which firm to buy. We characterize the unique subgame perfect equilibrium and find that even an entrant with a higher marginal cost may profitably invade part of the market due to the existence of switching costs. Switching costs benefit both firms but harm consumers. This model is used to understand pricing behavior in the US telecommunications industry.     

A market game with symmetric limit orders

We extend the market game with symmetric limit orders studied in Weyers (2003, 2004) to a many-good setup. Our limit orders are symmetric in terms of payment and determine a unique consistent price system for every strategy profile. The limit orders studied in the previous literature—see Dubey (1982), Simon (1984) and Mertens (2003)—share none of these properties. It is shown that three mild market-thickness conditions imply that the set of symmetric Nash equilibrium outcomes coincides with the set of price-taking equilibrium outcomes. First, the Dubey and Shubik (1978) refinement is used to eliminate no-trade as an equilibrium. Second, any price-taking equilibrium has trade in each market. Third, there are at least two agents of each type, where a type is determined by preferences and endowments. The last two conditions enable applying the Bertrand argument. This paper thus provides new insights to Bertrand’s (1883) classic critique of Cournot and the associated problem of capacity constraints raised by Edgeworth (1897).     

Workers' enterprises in price competition

Extending earlier equivalence results for perfect competition and for (imperfect) quantity competition, here it is shown that in price competition, too, the behavior of a workers‘ enterprise (defined by the coincidence of its workers with its partners) is tamed by the worker-partnership market so as to be identical with that of a twin entrepreneurial firm. Thus, not only is Bertrand–Nash equilibrium unaltered when an entrepreneurial firm is replaced by its workers’ enterprise twin, but such a replacement also leaves Bertrand-von Stackelberg equilibrium intact whether we switch the leader or a follower from one form of ownership/management to the other.     

Stackelberg equilibrium with multiple firms and setup costs

I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of identical leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium exists. Besides showing existence I characterize the equilibrium set and provide a number of results that contribute to the applied literature. As the number of leaders increases, leaders produce more and eventually they deter entry. Leaders produce more than the Cournot best reply, but they may underinvest in entry deterrence. As the number of followers increases, leaders become more aggressive. When this number is large, if leaders can produce the limit quantity and at the same time have market power, then they deter entry.     

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.     

Intermediation in Search Markets

In markets, in which exchange requires costly search for trading partners, intermediaries can help to reduce the trading frictions. This intuition is modeled in a framework with heterogeneous agents, who have the choice between intermediated exchange and search accompanied by some bargaining procedure. The equilibria of such a game are characterized. In the case of a monopolistic intermediary, the tradeoff between the bid-ask spread and the costs of delay during private search determine the intermediary's clientele. In equilibrium the monopolist charges a positive spread. Traders with large gains from trade prefer to deal with him, whereas traders with relatively low gains from trade engage in search. In case of competition among intermediaries, the classical Bertrand result obtains, and bid and ask prices converge to the (unique) Walrasian equilibrium price. Thus, in the confines of the model, the Walrasian auctioneer of the market under consideration can be replaced by competing intermediaries. In addition a multiplicity of subgame perfect Nash equilibria emphasizes the coordination problems inherent in models of intermediation.     

基于伯川德推测变差的有限理性动态寡头博弈的复杂性

本文在具有伯川德推测变差的推测变差模型的基础上,引入参与人的基本有限理性的动态产量调整行为,构建出动态调整系统,论证了企业调整速度在稳定域内时,静态伯川德推测变差均衡仍可作为稳定的动态均衡而实现。并用数值仿真的方法说明了当企业的产量调整速度不在稳定域内时,经济系统将会出现倍周期分岔或混沌等复杂动态。     

Spatial competition with free entry, Chamberlinian tangencies, and social efficiency

Free entry in Löschian spatial competition leads to a tangency between each firm's negatively sloped average revenue and the downsloping portion of average costs—as in Chamberlin's monopolistic competition. It is generally concluded that this equilibrium involves too many inefficiently small firms. However, this conclusion is incorrect. The difference between price and firm marginal production costs in spatial equilibrium is just sufficient to cover the additional marginal cost of output resulting from availability of multiple locations. This Chamberlinian tangency does not imply inefficiency, because it does not include all the social costs and benefits resulting from spatial competition.     

A model of population distribution,traffic congestion,and neighborhood crowding in a circular city

An idealized static equilibrium model of a circularly symmetric city is presented. The model allows one to compute the spatial distribution of residences, given certain simple and plausible assumptions about the “costs” of transport, housing and neighborhood crowding. The model is chosen so as to guarantee that in first approximation, the residential population distribution which would be considered optimal by a perfect planner is identical to the distribution reached in a push-shove, laissez-faire equilibrium. This aspect of the construction is shown to be related in a simple way to the familiar “external diseconomy” situation in which a free resource is allocated among alternative uses by equating average, rather than marginal products. The existence of an infinite class of models in which the associated planner's optimum and laissez-faire equilibria are equivalent follows naturally from the standard theory of the private and social costs of highway congestion. The model leads naturally to exponentially falling population distributions which exhibit an “urban-suburban” dichotomy, to a particular overall city size, and to an optimal allocation of land between transport and residential uses.     

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.     

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.     

Oligopoly firms with quantity-price strategic decisions

An agent-based model is used to determine market equilibrium with price-setting firms in an oligopoly market. The agent-based model is designed to match the experimental rules that Brandts and Guillen (J Ind Econ 55:453–474, 2007) used with human subjects. Their model uses posted prices and advance production of a perishable good. When the marginal cost is zero, the analytical Bertrand solution is almost perfect competition. When the marginal cost is nonzero, the game does not have a theoretical equilibrium in pure strategies. The agent-based model results show that with one or two firms, prices are at or near the monopoly level, which matches the human experiments. With four firms, prices are always at the perfectly competitive level when particle swarm optimization is used. Results using a genetic algorithm, however, are noisier than those using the particle swarm optimization, and the genetic algorithm falls short of the competitive solution. The triopoly market changes from mostly monopoly to a price in between monopoly and perfect competition when a marginal cost is added. The computerized agents tend to overproduce so that profits are negative in the three- and four-firm cases when production is costly. While the prices in the simulation are close to those observed in experiments with human subjects, the inefficiency due to overproduction is much greater in the agent-based model results. This result suggests that human agents are able to reach solutions, perhaps through social norms, that are missed by the simple agent-based rules used here.     

The economics of property taxes and land values: The elasticity of supply of structures

Land values are explained by diminishing returns to a variable factor, structure, added to fixed land. The total cost minimizing structural density determined by land value, occurs where the marginal cost of increased density equals the average cost of structure plus land. Structural demand prices equal marginal costs in equilibrium determining land demands. A general equilibrium land price establishes the uses, prices and densities of structures. A simple method of calculating structure supply elasticity and the incidence and deadweight loss of property taxes is developed. Differing property tax rates are found to be efficient.     

An examination of the equilibrium specification and structure of production for Canadian telecommunications

Multiple-output models of Canadian telecommunications production are estimated under different production equilibria. A specification test is conducted between the short- and long-run equilibrium models and the long-run equilibrium is rejected. In order to capture the nature of the disequilibrium, a dynamic cost of adjustment model is estimated for Bell Canada. There are significant adjustment costs and it is estimated that for $1.00 of marginal capital costs the carrier must incur an additional cost of $0.30 to install the new capital into the production process.     

Is having a unique equilibrium robust?

We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n  -player finite games with a unique correlated equilibrium is open, while this is not true of Nash equilibrium for n>2$n>2$. The crucial lemma is that a unique correlated equilibrium is a quasi-strict Nash equilibrium. Related results are studied. For instance, we show that generic two-person zero-sum games have a unique correlated equilibrium and that, while the set of symmetric bimatrix games with a unique symmetric Nash equilibrium is not open, the set of symmetric bimatrix games with a unique and quasi-strict symmetric Nash equilibrium is.     

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.