Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

Winner-take-all price competition

Summary. We analyze an oligopoly model of homogeneous product price competition that allows for discontinuities in demand and/or costs. Conditions under which only zero profit equilibrium outcomes obtain in such settings are provided. We then illustrate through a series of examples that the conditions provided are “tight” in the sense that their relaxation leads to positive profit outcomes. Received: April 7, 2000; revised version: September 14, 2000     

Competition with Congestible Networks

We analyse competition between two network providers when the quality of each network depends negatively on the number of customers connected to that network. With respect to price competition we provide a sufficient condition for the existence of a unique pure strategy Nash equilibrium. Comparative statics show that as the congestion effect gets stronger quantities will decrease and prices increase, under both Bertrand and Cournot competition. In an example with endogenous capacities it turns out that equilibrium capacities are at first increasing and then decreasing in the strength of congestion. Furthermore, capacities are higher under Cournot competition. Welfare comparisons between Bertrand and Cournot competition are unambiguous for fixed capacities, but may turn around for endogenous capacities.     

Price and quantity competition under free entry

This paper complements that of Cellini et al. (Cellini, R., Lambertini, L., Ottaviano, G. I. P., 2004. Welfare in a differentiated oligopoly with free entry: A cautionary note. Research in Economics, 58:125–33.), which shows that Cournot competition may generate higher welfare compared to Bertrand competition in an economy with free entry. Unlike them, we provide a more general proof for this result and show that Cournot competition generates higher welfare compared to Bertrand competition when the products are sufficiently differentiated. If the products are close substitutes, welfare is higher under Bertrand competition. We show that these qualitative results hold whether or not number of varieties increases market size. We also show when the active firms earn higher profits under Bertrand competition compared to Cournot competition.     

考虑港口收费管制的进出口贸易竞争研究

考虑港口的收费管制因素,建立了进出口贸易竞争模型。该模型由一个出口国和两个进口国组成,且各国都拥有一个港口,位于出口国的两家公司均向两个进口国销售商品,并在各个进口国展开市场竞争（古诺竞争或伯川德竞争）,各贸易国的港口根据其是否存在价格管制确定港口收费。针对进出口公司的每种竞争模式,得到了不同的港口收费管制组合下各贸易国的港口收费、港口利润和社会福利,并将竞争均衡结果进行了比较。研究发现： （1）在进出口公司古诺竞争模式下,若三个贸易国的港口都无收费管制（有收费管制）且进出口产品的差异较大 （小）时,各贸易国的社会福利和港口利润均更高; （2）在进出口公司伯川德竞争模式下,若进出口产品的差异较大 （小）,则出口国的港口利润主要取决于港口收费 （贸易量）,而进口国恰好相反; （3）当进出口产品的差异较大 （小）时,进出口公司在古诺 （伯川德）竞争模式下各贸易国的社会福利、港口利润以及港口使用费都更高。     

On the efficiency of indirect taxes in differentiated oligopolies with asymmetric costs

This paper shows that unit taxation can be welfare superior to ad valorem taxation in asymmetric and differentiated oligopolies if the goods are sufficiently differentiated, the cost variance is sufficiently large and the ad valorem tax rate is sufficiently high. Moreover, this result holds under either Cournot competition or Bertrand competition.      

The sale of small firms: a multidimensional analysis

Summary. This paper endogeneizes the security voting structure in an auction mechanism used to sell a small firm. The design of security voting structure allows the seller to choose between two objectives which are not mutually consistent. If the seller wants to maximize his revenue, he should retain some shares to benefit from the future dividends generated by the acquirer. At the opposite, if he wants to sell his firm to the most efficient candidate, he should sell all the shares. Received: July 4, 2001; revised version: October 31, 2002 RID="*" ID="*" The paper has benefited from a number of comments from the anonymous referees. Correspondence to: C. At     

Equilibrium selection in coordination games with simultaneous play

Summary. We apply the dynamic stochastic framework proposed in recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games payoffs, and hence best replies, are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be made stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Received: February 12, 2001; revised version: October 29, 2001     

Endogenous market segmentation with heterogeneous agents

Summary. An explanation is provided for the evolution of segmented marketplaces in a pairwise exchange economy. Large traders operating in a pairwise exchange market prefer to meet other similar traders, because this enables them to trade their endowments in a smaller number of encounters. Large and small traders, however, cannot be distinguished a priori, and the existence of the small traders imposes a negative externality on the large traders. We show that, under conditions which are not very restrictive, establishing a separate market (perhaps with an entry fee) designated for the large traders induces the two types of traders to segment themselves. However, this segmentation is not necessarily welfare improving. Received: January 12, 2001; revised version: July 17, 2002 RID="*" ID="*" I wish to thank the participants in the Friday Theory Workshop at the University of Sydney, and the participants at the 17th Australian Theory Workshop at the University of Melbourne for comments and discussion. John Hillas and Stephen King pointed out an omission in an earlier version, and Catherine de Fontenay and Hodaka Morita made extensive comments on earlier drafts. This work was initiated while I was a short-term visitor at the University of Southern California.     

A note on Bossert,Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules”

Summary. Recent work by Bossert, Pattanaik and Xu provides axiomatic characterizations of some decision rules for individual decision making under complete uncertainty. This note shows that, in the case of two of these rules, they do not satisfy one of the axioms used for their characterization. A counterexample illustrating this fact is provided, as well as an alternative way to characterize the two rules under consideration, mantaining as far as possible the original axioms proposed by Bossert, Pattanaik and Xu. Received: November 3, 2000; revised version: March 1, 2002 RID="*" ID="*" I am grateful for the encouragement and support of Professor Prasanta Pattanaik. I thank also the suggestions of two anonymous referees. This work was made during an academic visit to the Department of Economics of the University of California in Riverside (UCR). The visit was possible thanks to an invitation by the UCR and the financial support of the Public University of Navarra, the Government of Navarra, and the CICYT (SEC96-0858).     

Efficiency and options on the market index

Summary. In a static exchange economy, when all the endowments are issued as securities on a stock exchange, Pareto optimal allocations may be reached by trading options on the market index (see Breeden and Litzenberger (1978)). We extend this result when some of the risks cannot be exchanged on the market. Options on an appropriate index, which typically differs from the market index, depending on the correlation of the non-tradable risks with the exchanged securities, are still an appropriate tool to support a (constrained) efficient equilibrium. This suggests that the recent development of derivatives based on interest rates may be an efficient way to reach a Pareto optimal allocation of risks. Received: June 16, 1997; revised version: July 25, 1997     

Delegation and polarization of platforms in political competition

Summary. We consider a model of political competition among two ideological parties who are uncertain about the distribution of voters. The distinguishing feature of the model is that parties can delegate electoral decisions to candidates by nomination. It is shown that if the credible platform commitments of the candidates is feasible, then at least one of the parties nominates in equilibrium to a candidate who has an ideology that is more radical than the delegating party's ideology. In a variety of circumstances, this, in turn, yields a polarization of equilibrium policy choices of the candidates. It is thus argued formally here that strategic nomination of the candidates may well be one of the major reasons behind the well documented observation that the platforms associated with the political parties in two-party democracies are often surprisingly polarized. Received: January 10, 2002; revised version: May 8, 2002 RID="*" ID="*" We thank Alberto Alesina, Levent Ko?kesen, Antonio Merlo, Ronny Razin, Vijay Krishna, Alessandro Lizzeri, and seminar participants at Alicante, Columbia, Copenhagen, and NYU for helpful comments. We also thank an anonymous referee for its useful suggestions. A good fraction of this research was conducted while Ok was a visitor in the Department of Economics at University of Alicante; he thanks for the kind hospitality of this institution. We gratefully acknowledge the financial support from the Spanish Ministry of Education through grant CICYT BEC2001-0535 (Faulí-Oller) and BEC2001-0980 (Ortu?o-Ortín). Correspondence to:I. Ortu?o-Ortin     

Choice under complete uncertainty: axiomatic characterizations of some decision rules

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules. Received: August 20, 1998; revised version: November 3, 1999     

On competition and endogenous firm efficiency

Summary. Conventional wisdom holds that product market competition disciplines firms into efficiency of operation. However, in a well known paper, Martin (1993) has shown that in a linear Cournot setting (with costs determined first and product market competition taking place in a second stage) the exact opposite obtains – a larger number of firms competing in the market implies lower firm efficiency. The note clarifies further the links between market structure and efficiency. Specifically, it argues why (and how) the result derived by Martin (1993) depends upon the assumptions made regarding the structure of demand and nature of conjectures held by firms as to their rivals' behavior. An illustrative counter-example (with Bertrand behavior and non-linear demand) in which entry increases efficiency is provided as well. Received: March 2, 2000; revised version: September 19, 2000     

A new look for Stackelberg-Cournot equilibria in oligopolistic markets

Summary. This note deals with Cournot type oligopolies in which the market clearing price occasionally may be non-unique. A Stackelberg leading producer is present. Given that setting we explore continuity properties of the followers' reaction and provide sufficient conditions for existence of equilibrium. Received: June 20, 2000; revised version: April 24, 2001     

Limit-pricing as Bertrand equilibrium

Summary. We consider a Bertrand duopoly model with increasing returns to scale where one of the firms have a cost advantage and prices vary over a grid. We find that typically more than one equilibria exist. However, there are only two perfect equilibria. Moreover, as the size of the grid becomes small, both these equilibria converge to the limit-pricing outcome. Received: February 25, 2000; revised version: January 9, 2001     

Non-cooperative games with a continuum of players whose payoffs depend on summary statistics

Summary. We consider static non-cooperative games with a continuum of small players whose payoffs depend on their own actions and finitely many summary statistics of the aggregate strategy profile. We prove the existence of an equilibrium in pure strategies without any convexity restrictions on payoffs or the common action space. We show that this result applies to a broad class of monopolistic competition models. Received: April 13, 2001; revised version: December 18, 2001 RID="*" ID="*" The result in this paper generalizes a result in my PhD dissertation supervised by M. Ali Khan and Joe Harrington. I thank them for support and encouragement. I also thank Sung Kim, Bruce Nanney, Ashvin Rajan, Kali Rath, and an anonymous referee for comments. The usual disclaimer applies.     

Uncertainty and insurance in strategic market games

Summary. For perfectly competitive economies under uncertainty, there is a well-known equivalence between a formulation with contingent goods and one with state-specific securities followed by spot markets for goods. In this paper, I examine whether this equivalence carries over to a particular form of imperfect competition. Specifically, I look at three Shapley-Shubik strategic market games: one with contingent commodities, one with Arrow securities traded under imperfect competition and one with Arrow securities traded under perfect competition. First I compare the feasibility constraints of these three games. Then I compare their equilibrium sets. As in Peck and Shell (1989), the only common equilibria between the first and the second game are those which involve no transfer of income across states. However, if the securities markets are competitive, then the set of equilibria of the contingent commodities game and the securities game coincide. Received: June 16, 1997; revised version: April 30, 1998