Cournot-Walras equilibria in markets with a continuum of traders

Summary In a model with a nonatomic continuum of traders some of which behave strategically while the others remain price-takers, the set of Cournot-Walras equilibria coincides with the set of Walras equilibria. This property is no longer valid when the strategic agents are represented by atoms.It is a pleasure to acknowledge the stimulating discussions we had with R. Amir about the question examined in the present work.     

Oligopoly in markets with a continuum of traders: An asymptotic interpretation

This paper tries to make relevant for a finite economy the results of Shitovitz on the “pricing-out” of cores of economies with a non-atomles measure space of agents. It is hoped that the comparison of the two sets of results will shed light on the interpretation and modeling of a “large” trader.     

Agglomeration in a vertically-related oligopoly

This paper examines the location of three vertically-linked firms. In a spatial economy composed of two regions, a monopolist firm supplies an input to two consumer goods firms that compete in quantities. It is concluded that agglomeration is more likely to occur when the ratio between the transport cost of the intermediate good and the transport cost of the final good is higher. If this proportion is low, the likelihood of an agglomeration decreases with transport costs. If the ratio has an intermediate value, a non-monotonic pattern is obtained that is different from Krugman and Venables (1995).Received: October 2004, Accepted: March 2005, JEL Classification: C68, F12, F15, R12, R13This paper had the support of the Research Unit on Complexity in Economics (UECE). The author wishes to thank Masahisa Fujita, Armando Pires and an anonymous referee for helpful comments. The usual disclaimer applies.     

Debt as a collusive device in an oligopoly supergame

This paper explores the impact of debt holdings on the output decisions of firms in an oligopoly supergame with stochastic demand fluctuations. It is demonstrated that when perfect collusion is not feasible then there exist circumstances in which increased debt holdings may facilitate tacit collusion. This occurs because higher debt levels act as a credible commitment device which lowers the payoffs accruing to a firm when it defects from the tacitly collusive equilibrium. It is further shown that in these circumstances firms may have an incentive to hold debt for strategic purposes which promote collusion.     

Stable market structures from merger activities in mixed oligopoly with asymmetric costs

This paper examines endogenous merger formations in a mixed oligopoly. Applying the core as a solution concept, we analyze which market structure(s) remain(s) stable when three firms—two symmetric private firms and one inefficient public firm—are allowed to merge with each other in a mixed Cournot industry. We show that according to the value of the marginal cost of the public firm, there always exists a pair of share ratios of the owners of both the (pre-merged) public firm and the (pre-merged) private firm such that the market structure with the merger between the public firm and one private firm belongs to the core. When the initial market structure is a mixed triopoly, it can only be blocked when one public firm and one private firm merge. Furthermore, we conduct a similar analysis in a general mixed oligopoly with one public firm and n private firms.      

Communication in financial markets with several informed traders

This paper investigates the incentives for informed traders in financial markets to reveal their information truthfully to the public. In the model, a subset of traders receive noisy signals about the value of a risky asset. The signals are composed of a directional component (“high” vs. “low”) as well as a precision component that represents the quality of the directional component. Between trading periods, the informed agents make public announcements to the uninformed traders. With a sufficiently large number of informed traders, an equilibrium exists in which the directional components are credibly revealed, but not the precision components. Even though the informed traders retain some of their rivate information, the post-communication estimate of the asset value converges in probability to the full-information estimate as the number of informed traders increases. The paper is based on a chapter of my Ph.D. thesis at the University of Western Ontario and was circulated previously under the title “Public Communication Devices in Financial Markets.” I thank my dissertation committee Arthur Robson, Hari Govindan, and Al Slivinski for their guidance and support. I also thank Murali Agastya, Roland Benabou, Philippe Grégoire, Rick Harbaugh, Mike Peters, an anonymous referee and an associate editor, and seminar participants at various universities and conferences at which this paper was presented.     

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

Focusing on foreign ownership in the private firm, we examine the Cournot-Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot-Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot-Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.     

Optimal pollution control in a mixed oligopoly with research spillovers

We study optimal pollution abatement under a mixed oligopoly when firms engage in emissions‐reducing research and development (R&D) with imperfect appropriation. The regulator uses a tax to curb emissions. Results show that in a mixed oligopoly, the public firm has positive emissions reduction in equilibrium; however, emissions reductions of the private firm could be positive or zero. Under certain conditions, the optimal pollution tax is positive; otherwise, the tax reverts to a subsidy. Comparing mixed and private duopolies, privatisation leads to reductions in R&D and output, but to an increase in overall emissions, so privatisation tends to make the environment worse.     

Taxation under oligopoly in a general equilibrium setting

Taxation under oligopoly is analyzed in a general equilibrium setting where the firms are large relative to the size of the economy and maximize the utility of their shareholders. Assuming that preferences are either identical and homothetic or identical and quasi‐linear, then the oligopoly model is an aggregative game, which greatly simplifies the comparative statics for the effects of taxation. This novel analysis of taxation leads to a number of counterintuitive results that challenge conventional wisdom in microeconomics. A lump‐sum tax may increase the price of the oligopolistic good and decrease welfare whereas a profits tax may decrease the price of the oligopolistic good and increase welfare. A profits tax is shown to be superior to a lump‐sum tax. Furthermore, in line with conventional wisdom, total tax revenue is always higher with an ad valorem tax than with a specific tax that leads to the same price for the oligopolistic good.     

Changes in the firms behavior after the opening of markets of allowances

This paper focuses on the influence on the general equilibrium of an economy of the opening of markets of allowances, such as the European Union Emission Trading Scheme. Assuming there existed an equilibrium before the opening of allowances’ markets, we describe the changes in the firms behavior which guarantee that an equilibrium can be reached in the enlarged economy. Hence we describe under which conditions the economy can undergo the opening of markets of allowances. This paper is a substantial improvement of previous work in collaboration with Alexandrine Jamin (Jamin and Mandel 2006).The author is grateful to Professor Jean-Marc Bonnisseau for his guidance and to an anonymous referee whose comments led to substantial improvements of the paper.     

Welfare effects of competitive lobbying efforts in international oligopoly markets

Conventionally, rent-seeking activities have been considered to deteriorate social welfare and to distort resource allocation. This paper examines whether rent-seeking behavior can improve social welfare by focusing on the welfare effects of firms’ competitive lobbying efforts when governments can impose market entry regulation against foreign firms. We demonstrate that competitive lobbying efforts can improve social welfare when such lobbying efforts are directed to reduce market entry barriers. In addition, social welfare can be maximized when the government shows the maximum sensitivity to the foreign firm's political contributions while maintaining competitive market structure. Moreover, it is shown that the dominant strategy for a domestic firm is to allocate more resources to R&D sectors while it is optimal for foreign firms is to exert more efforts in lobbying to reduce the market entry barriers when a government makes political economic approach in market entry regulations.     

Managerial incentives and the decision to hire managers in markets with public and private firms

This paper considers the managerial incentive contract when public and private firms compete in the same market. Social welfare is enhanced when all firms hire managers, but for different reasons than when all firms are privately owned. Incentives to hire managers differ in private and public firms; in equilibrium, only private firms hire managers.     

The equilibrium of the bargaining game and core convergence theorem on an exchange economy with limited traders

Debreu and Scarf (1963), Hildenbrand (1974), Aumann (1964), Dierker (1975), Bewley (1973), and others have shown that the core of an exchange economy with infinitely many or finitely many traders converges. However, an exchange economy does not always consist of infinitely many or finitely many traders. This note provides proof of the core convergence theorem on an exchange economy with limited traders by a bargaining game methodology. The main contribution of this note is to innovate the equilibrium solution to the bargaining game in the exchange economy. In this note, the concept of common payoff is introduced; in the bargaining game of a coalition on its common payoff, all coalition members will get the same distribution, thus the distribution scheme of the cooperation surplus of the exchange economy is determined. This note shows that the bargaining game among the traders on the distribution of the cooperation surplus will make the pure exchange economy with limited traders converge to the Walrasian equilibrium, all the allocations other than the Walrasian equilibrium will be eliminated from the core of this economy.     

Signaling in markets with two-sided adverse selection

Summary. The paper analyzes an economy with two-sided adverse selection, focusing on equilibria that satisfy a refinement based on the notion of strategic stability. In the familiar case of one-sided adverse selection, agents reveal all of their private information as long as the contract space is rich enough. However, with two-sided adverse selection, the sufficient conditions for separation are much stronger. Received: September 3, 1999; revised version: December 3, 1999     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

Summary. Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo -algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved. Received: October 29, 2001; revised version: April 24, 2002 RID="*" ID="*" Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent's macro workshop at Stanford. We are grateful to him and Felix Kübler in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape. Correspondence to: P.J. Hammond     

A biased firm in a market with complementary products. A note on the welfare effects

We analyse a duopoly setting with complementary products, in which a firm has a bias about its absolute advantage. We show that the bias can internalize parts of the negative externality that the complementarity of goods creates implying a higher producer's surplus. Moreover, we analyse additional conditions, which lead to an increase in the consumer's surplus. Counterintuitively, we show that the presence of a bias can lead to a positive welfare effect.     

Endogenous Timing in a Mixed Oligopoly with Foreign Competitors: the Linear Demand Case

We introduce foreign private firms into the model of Pal (1998) and investigate the impact of the introduction of foreign private firms on the endogenous timing in a mixed oligopoly in the linear demand case. We find that the public firm chooses to be a follower of all domestic private firms and that the public firm chooses not to be a leader of all foreign private firms, which is in contrast to Matsumura (2003).