Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g∈ G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

Farsightedly stable networks

A set of networks G is pairwise farsightedly stable (i) if all possible farsighted pairwise deviations from any network g G to a network outside G are deterred by the threat of ending worse off or equally well off, (ii) if there exists a farsighted improving path from any network outside the set leading to some network in the set, and (iii) if there is no proper subset of G satisfying conditions (i) and (ii). A non-empty pairwise farsightedly stable set always exists. We provide a full characterization of unique pairwise farsightedly stable sets of networks. Contrary to other pairwise concepts, pairwise farsighted stability yields a Pareto dominant network, if it exists, as the unique outcome. Finally, we study the relationship between pairwise farsighted stability and other concepts such as the largest pairwise consistent set and the von Neumann–Morgenstern pairwise farsightedly stable set.     

International Environmental Agreements—The Role of Foresight

The present paper attempts to bridge the gap between the cooperative and the non-cooperative approach employed to examine the size of stable coalitions, formed to address global environmental problems. We do so by endowing countries with foresightedness, that is, by endogenizing the reaction of the coalition’s members to a deviation by one member. We assume that when a country contemplates withdrawing or joining an agreement, it takes into account the reactions of other countries ignited by its own actions. We identify conditions under which there always exists a unique set of farsighted stable IEAs. The new farsighted IEAs can be much larger than those some of the previous models supported but are not always Pareto efficient.     

Stable cartels revisited

Summary. This paper analyzes cartel stability when firms are farsighted. It studies a price leadership model á la D Aspremont et al. (1983), where the dominant cartel acts as a leader by determining the market price, while the fringe behaves competitively. According to D Aspremont et al. s (1983) approach a cartel is stable if no firm has an incentive to either enter or exit the cartel. In deciding whether to deviate or not, a firm compares its status quo with the outcome its unilateral deviation induces. However, the firm fails to examine whether the induced outcome will indeed become the new status quo that will determine its profits. Although the firm anticipates the price adjustment following its deviation, it ignores the possibility that more firms may exit (or enter) the cartel. In other words, the firm does not consider the fact that the outcome immediately induced by its deviation may not be stable itself. We propose a notion of cartel stability that allows firms to fully foresee the result of their deviation. Our solution concept is built in the spirit of von Neumann and Morgensterns (1944) stable set, while it modifies the dominance relation following Harsanyis (1974) criticism. We show that there always exists a unique, non-empty set of stable cartels.Received: 20 August 2002, Revised: 11 August 2004, JEL Classification Numbers: C79, D43, D49, L13.On page 921, the final paragraph as well as the two references by Rothschild were inserted.This revised version was pulished in February 2005.I would like to thank Joseph Greenberg, Licun Xue, Daniel Arce M. and Curtis Eberwein for their helpful suggestions on an earlier draft. I am indebted to an anonymous referee for his very constructive comments.     

A note on cartel stability and endogenous sequencing with tacit collusion

We use the concept of cartel stability defined by d’Aspremont et al. (Can J Econ 16(1):17–25, 1983) to obtain that the sequence of play between the cartel and the fringe affects cartel stability in a quantity-competition setting where firms tacitly collude. We also prove that an endogenous sequence of play between a cartel and a fringe depends on the discount factor. If the discount factor is large enough, the cartel and the fringe simultaneously choose quantities since the stable cartel may contain more firms under simultaneous play than under cartel leadership. This is due to the fact that under simultaneous play cartel firms have incentives to participate in the cartel because otherwise no collusion is possible.      

Cartel Stability in a Delivered Pricing Oligopoly

Using the spatial price discrimination framework, the relationship between the locations of firms and their ability to collude is investigated. Gupta and Venkatu (2002) show that in a duopoly model agglomeration at one point is the most stable location. We find that agglomeration stabilizes the cartel when there are three firms, too. When there are more than three firms, however, agglomeration of all firms is never the most stable location. With four firms, the following location pattern produces the most stable cartel: two firms at one point and the other two at the farthest point from the first two.     

On price taking behavior in a nonrenewable resource cartel–fringe game

We consider a nonrenewable resource game with one cartel and a set of fringe members. We show that (i) the outcomes of the closed-loop and the open-loop nonrenewable resource game with the fringe members as price takers (the cartel–fringe game à la Salant, 1976) coincide and (ii) when the number of fringe firms becomes arbitrarily large, the equilibrium outcome of the closed-loop Nash game does not coincide with the equilibrium outcome of the closed-loop cartel–fringe game. Thus, the outcome of the cartel–fringe open-loop equilibrium can be supported as an outcome of a subgame-perfect equilibrium. However the interpretation of the cartel–fringe model, where from the outset the fringe is assumed to be price taker, as a limit case of an asymmetric oligopoly with the agents playing Nash–Cournot, does not extend to the case where firms can use closed-loop strategies.     

On the possibility of welfare-enhancing hard core cartels

The conventional wisdom is that cartels which merely lead to lower production levels and higher prices are detrimental to social welfare. This paper explores the extent to which this is generally valid. We derive necessary and sufficient conditions for the existence of a hard core cartel that is beneficial for firms and society at large. Considering both strong (with side payments) and weak (without side payments) hard core cartel contracts, we find that (i) both strong and weak welfare-enhancing cartels exist when at least one firm makes a loss on part of its sales in competition, (ii) a welfare-enhancing strong cartel exists whenever there is a difference in unit cost at competitive production levels, and (iii) a welfare-enhancing weak cartel exists when the profit margin on all sales is positive and the cost difference is sufficiently large.     

Endogenous Cartel Formation

This paper investigates the endogenous formation of cartels in a supergame framework in which cheating on the cartel agreement results in the ejection of only the defector from the cartel while collusion continue s amongst the non-cheating members. A more sophisticated notion of cartel stability than has been analysed hitherto is developed here, and it is shown that cartels are even less stable than they are generally believed to be. When firms produce heterogeneous goods and set prices, cartels comprising a small fraction of the industry's firms are shown to be viable. The emergence of two or more cartels within the same industry is seen not only to be a distinct possibility but also to be quite likely     

政府产品创新补贴下的企业R＆D策略选择

为了研究在政府产品创新补贴政策下企业的R＆D策略选择问题,建立了双寡头市场中面向工艺R＆D的三阶段博弈模型：第一阶段政府以社会福利最大为目标选择产品创新补贴率;第二阶段企业进行R＆D投资以降低生产成本;第三阶段企业在产品市场中进行古诺竞争。根据双寡头在第二和第三阶段是否合作,给出了研发竞争、研发卡特尔、技术共享联盟和研究共同体等四种R＆D策略,得到了相应的政府最优R＆D补贴率。研究表明：从企业的R＆D投入和产品产量的角度看,当溢出效应较高时,研发竞争策略优于研发卡特尔策略;当溢出效应较低时,研发卡特尔策略优于研发竞争策略。研发卡特尔策略与研发竞争策略相比,研发卡特尔更能推动企业利润的提高并且可以改善社会总福利。从产品产量、企业利润和社会总福利最大化角度考虑,研究共同体为四种策略中的最优策略。     

Asymmetric Research Joint Ventures and Market Concentration

This paper studies two asymmetric R&D cooperation structures. In the first structure some firms in an industry organize a research joint venture (RJV) cartel while the remainder engage in independent R&D. In the other structure, each firm joins one of a number of competing RJV cartels. The findings indicate that cooperative R&D may lead to a more concentrated post-innovation industry than standard R&D competition owing to the technology advantage of the (large) cartel obtained from R&D co-operation. Under certain conditions these asymmetric structures are more efficient, but they result in a redistribution of income towards the firms in the (large) cartel.
JEL Classification Numbers: D43, L13, O31.     

产品差异与技术差距影响研发溢出的理论探讨

在传统研发溢出效应假设基础上，通过技术差距将溢出效应与产品差异有机联系起来，并通过构建双寡头企业两阶段博弈模型对研发卡特尔、生产卡特尔、完全合作等不同形式合作联盟的均衡水平和福利变化进行分析比较。研究证实：当企业间技术差距较小时，完全合作或研发卡特尔能有效提高企业利润和社会福利；而当技术差距较大时，研发阶段的合作不仅无法激励企业进行研发投入，还会抑制企业创新的积极性。此外，与完全合作相比，局部合作具有更强的稳定性和可持续性，尤其是在产品差异程度较大的情况下，研发卡特尔最为稳定。     

ON THE SUSTAINABILITY OF COLLUSION IN A DIFFERENTIATED OLIGOPOLY WITH A CARTEL AND A FRINGE

We discuss the effects of the existence of non‐colluding (fringe) firms on cartel sustainability. We obtain, using trigger strategies, that with product differentiation collusion is always more easily sustained when firms compete in prices than when firms compete in quantities. This is true basically because (i) price competition is more intense than quantity competition, and (ii) fringe firms exacerbate the fact that cartel firms have more incentives to deviate from the agreement under quantity competition. This result reverses previous findings where, in the absence of fringe firms, product differentiation plays a crucial role in determining the effectiveness of price or quantity competition in sustaining collusion.     

Optimality and Natural Selection in Markets

We ask if natural selection in markets favors profit-maximizing firms and, if so, is there a difference between the predictions of models which assume all firms are profit maximizers and the predictions of models which explicitly take account of population dynamics in the market. We show that market selection favors profit maximizing firms, but we also show that the long-run behavior of evolutionary market models is nonetheless not consistent with equilibrium models based on the profit-maximization hypothesis. Dynamic equilibrium paths with market selection are not Pareto optimal, nor even asymptotically optimal. The discrepancy arises because the dynamics created by firm evolution causes prices to vary over time and the resulting dynamical system need not have stable steady states.     

Intertemporal market division:: A case of alternating monopoly

In this paper, we report on an equilibrium with market dominance that exists in a simple two-firm model that features neither entry barriers nor sophisticated punishment strategies. This equilibrium induces an intertemporal market division in which the two firms alternate as monopolists - despite the fact that the model also sustains a Cournot duopoly. Even when initially both firms are active in the market, the alternating monopoly reveals itself rather quickly. Moreover, it Pareto dominates the Cournot equilibrium - as it is close to the cartel outcome. Several examples of what well may be such alternating monopolies are presented.     

Time-consistent fiscal policy and heterogeneous agents

This paper characterizes the time-consistency properties of the set of Pareto efficient (or second best) fiscal policies, in a two-class, stochastic economy similar to that in [Judd, K.L., 1985, Redistributive taxation in a simple perfect foresight model, Journal of Public Economics 28, 59–83]. The key finding is that the continuation of any Pareto efficient policy is always Pareto efficient. Hence, to require any policy revision to be approved by unanimity safeguards the time consistency of efficient fiscal policy. I also show that any Pareto efficient policy from a timeless perspective can be rendered time consistent by a policymaker whose objective function is given by a utilitarian social welfare function with precise welfare weights. These results link the policymaker's equity considerations with the credibility of efficient fiscal policy.     

When imperfect collusion is profitable

This paper studies cartel stability under the assumption that member firms can choose intermediate degrees of collusion as well as the joint-profit-maximizing solution in determining the quota to be produced by each firm. After showing that firms can increase the number of participants by decreasing the degree of collusion, I prove that individual members' profits are maximized when firms choose a (possibly low) degree of collusion such that all firms in the industry want to take part in the cartel. More precisely, if the number of firms in the industry is four or less, then all of them want to take part in the cartel even if the maximum degree of collusion is chosen (i.e., the monopoly output is produced); if the number of firms is greater than four, firms will still create an industry-wide cartel but they will produce a higher quantity than the monopoly output.     

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (in A Econ Rev, 95(4), 913–935, 2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable. Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence. In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.     

Firm-specific information and explicit collusion in experimental oligopolies

We experimentally study the effect of information about competitors’ actions on cartel stability and firms’ incentives to form cartels in Cournot markets. As in previous experiments, markets become very competitive when individualized information is available and participants cannot communicate. In contrast, when communication is possible, results reverse: markets become less competitive and cartels become more stable when individualized information is available. We also observe that the extra profits that firms obtain thanks to the possibility to communicate are higher when individualized information is present, suggesting that firms have greater incentives to form cartels in that situation.     

COMPETITION POLICY AND CARTEL SIZE

This article examines endogenous cartel formation in the presence of a competition authority. Competition policy is shown to make the most inclusive stable cartels less inclusive. In particular, small firms that might have been cartel members in the absence of a competition authority are no longer members. Regarding the least inclusive stable cartels, competition policy can either decrease or increase their size and, in the latter case, the collusive price can rise.