International trade in genetically modified products

This paper investigates competition between two markets that sell close substitutes: a traditional product and a genetically modified (GM) product. Tightening an import quota on the GM product raises the prices of both goods and hurts consumers. Two scenarios are considered under free trade: Cournot–Nash equilibrium and Stackelberg equilibrium. A Stackelberg type monopolist produces more, and the competitive traditional firms produce less, than in Cournot–Nash equilibrium. In the long run, an import ban on the GM product does not help competitive producers of the genetically modified organism (GMO)-free products but benefits only the landowners in Europe.     

Rent Seeking and Allocative Efficiency

This paper considers a rent‐seeking game (specifically, a winner‐takes‐all contest) with incomplete information. By allowing for sequential moves, a Bayesian‐Stackelberg equilibrium can be constructed. It can be shown that, at the Bayesian‐Stackelberg equilibrium, it is always possible that the allocative efficiency argument fails. That is, there are cases in which the Stackelberg follower is more efficient but loses the contest. Using a specific class of distributions, it is also shown that sometimes the corrupt official will choose the Bayesian‐Stackelberg equilibrium over the Bayesian‐Nash equilibrium in order to maximise the expected bribe revenue. That is, when designing the rules of the rent‐seeking game, the dynamic nature of competition will be taken into account.     

A note on Stackelberg competition

This note investigates a Stackelberg–Nash competition model. We determine the conditions under which the leaders may achieve better profits than the followers when all firms compete on quantity in a two stage game. We focus on the properties of the followers’ best response functions. It is shown that the Stackelberg equilibrium may coincide with the Cournot equilibrium. In addition, the followers may achieve higher profits than the leaders. Such results put forward the working and the consequences of strategic complementarities. These results are illustrated with three examples.     

Public input competition

Public investment in infrastructure may help create agglomeration economies, by attracting mobile factors such as skilled labour. Competition among regions in public investment can then be destructive. This paper analyzes the Nash equilibria to a simple model of public input competition. Even though the regions are assumed identical, the equilibrium may not be symmetric. The problem with non-cooperative behaviour is not (only) that regions invest too much, but that too many regions may choose to invest. Depending on the parameter values, the Nash equilibrium may be efficient, may be inefficient or may not exist (at least not in pure strategies). Better mobility among regions leads to more aggressive competition. The analysis suggests that rents from public investment may be dissipated by governments' competition to attract mobile factors.     

文化创意产品的版权博弈分析

以人的创造力和知识创新为核心要素的文化创意产业日益成为未来经济增长的动力源泉。在深入了解文化创意产业的内涵及特征的基础上，为促进这一新兴产业更快更好地发展，本文研究了文化创意产业主体之间为占有市场，选择对创意产品采取竞争或激励措施的博弈问题。本文的研究发现：纳什均衡中，文化创意产品的版权博弈双方为了自身收益最大化会独立进行价值投入；斯坦克尔伯格均衡中，版权受让商的价值投入与版权让与商的努力水平成正比，与价值投入成本成反比，双方在纳什均衡条件下投入较少，而各自的均衡期望收益在斯坦克尔伯格均衡条件下更高。     

MARKET PRICE MECHANISMS AND STACKELBERG GENERAL EQUILIBRIA: AN EXAMPLE

This paper considers Stackelberg competition in a general equilibrium framework with a productive sector. The working of market power and the configurations of strategic interactions are complexified by the presence of a leader. Two market price mechanisms are studied: one is associated with the Stackelberg–Walras equilibrium and the other is linked to the Stackelberg–Cournot equilibrium. Throughout the example of a two commodity economy, several results are obtained about equilibria mergings and about welfare comparisons.     

Pricing decisions in a dual channels system with different power structures

This paper investigates the effect of product substitutability and relative channel status on pricing decisions under different power structures of a dual exclusive channel system where each manufacturer distributes its goods through a single exclusive retailer but two goods are substitute. A linear demand based on the utility function of a representative consumer is assumed, and three game scenarios(Manufacturer Stackelberg, Retailer Stackelbeg and Vertical Nash) are examined under symmetric and asymmetric related channel status. It is shown that no power structure is always the best for the entire supply chain though all members on supply chain have incentive to lead the Stackelberg game. Meanwhile, the vertical Nash game is an equilibrium for the members, however, a Prisoner's dilemma necessarily incurs for the entire supply chain because the Retailer Stackelberg or the Manufacturer Stackelberg can gain the better performance than that in vertical Nash for the entire supply chain when the product substitutability is moderate or higher and the asymmetric relative channel status is moderate, while consumers always get the most welfare from the vertical Nash game.     

Voracity, growth, and welfare

This paper explores some implications of the comparison between feedback Nash and Stackelberg equilibria for growth and welfare in a ‘voracity’ model. We show that, as compared to the Nash equilibrium, the Stackelberg equilibrium involves a lower growth rate, while it leaves both the leaders and the followers better off, i.e., the Stackelberg equilibrium is Pareto superior to the Nash equilibrium.     

WELFARE ANALYSIS OF PRIVATIZATION IN A MIXED MARKET WITH BARGAINING

The author analyzes the welfare effects of privatization in a mixed duopoly model in which the wage rate for the privatized firm is determined by Nash bargaining beforehand. The evaluations are based on three-stage privatization frameworks respectively under two regimes: Cournot competition and a public firm acting as a Stackelberg leader. The author finds that the optimal degrees of privatization from the viewpoint of social welfare may be different for various types of competition. The article also shows that even optimal privatization set by a welfare-maximization government may not guarantee welfare improvement, owing to the interference of wage bargaining. (JEL D60, D78, L32, L33 )     

Nonexclusionary input prices under quantity competition: vertical integration,foreclosure and sabotage

A vertically integrated provider is a monopoly supplier of an input essential for its rival to produce downstream output. Market exclusion in the form of inefficient foreclosure or sabotage can arise when input prices are, respectively, ‘too high’ or ‘too low’ relative to the downstream price. The range of nonexclusionary input prices within which neither form of market exclusion arises is determined by displacement ratios. The safe harbour range of downstream-to-upstream ‘price-cost’ margin ratios is decreasing in the degree of product homogeneity and approaches a single ratio in the limit as the products become perfectly homogeneous. The bounds of nonexclusionary input prices are markedly wider under Bertrand–Nash competition than they are under Stackelberg competition.     

The Optimal Privatization Policies under an International Mixed Duopoly

This paper explores the socially optimal privatization policies under the setting of international mixed duopoly. We find that partial privatization is socially optimal under Cournot competition and private leadership competition, whereas full nationalization is socially optimal under public leadership competition. Moreover, the equilibrium social welfare under private leadership competition is higher than that observed under Cournot competition and that observed under private leadership competition, which differs from the findings of Matsumura ( 2003b ). We also show that the endogenous timing game has a subgame perfect Nash equilibrium outcome, under which the government chooses a partial privatization policy, and private leadership competition emerges as the optimal output decision sequence of firms. An important policy implication from this paper is that the government should partially privatize the public firm and facilitate the emergence of private leadership competition in an international mixed market.     

技术创新扩散补贴机制研究——基于微分博弈分析

运用微分博弈纳什反馈均衡(Feedback Nash Equilibrium)和Stackelberg反馈均衡(Feedback Stackelberg Equilibrium)对技术创新扩散过程中,采用时间定量补贴和投入比例补贴的两种补贴机制进行了研究。通过研究,我们发现在采用时间定量补贴的微分博弈中,纳什反馈均衡和Stackelberg反馈均衡相同,则先行动者无先动优势,补贴机制没有达到目标。而在改进的采用投入比例补贴机制中,存在唯一的Stackelberg反馈均衡:领导者是先采用者,跟随者是后采用者,则该博弈具有先动优势,从而达到了提高潜在采用者采用积极性的补贴目的。     

The Role of Central Government in Tax Competition Between Heterogenous Regions

This paper analyzes the role of central government in a Nash tax competition between two heterogenous regions, which differ in their endowments of two production factors. Regional governments use a source-based unit tax on mobile capital to finance their public service expenditures. The central government employs excise subsidies and lump-sum taxes to induce the two regions to efficient resource allocations. We answer to the question that whether the central government can induce an efficient equilibrium, and investigate the effects of endowments difference on the optimum subsidy rates. We find that there exists a unique tax rate under which the efficiency is achieved. We identify the set of endowment allocations for which the subsidy rate to one region is higher (or lower) than the subsidy rate to the rival. The large poor region receives a higher subsidy than the small rich region, but the subsidy to the small poor region may be higher or lower than that to the large rich region. [H2]     

Duopoly competitions with capacity constrained input

This paper focuses on the duopoly substitutability product with an upstream input subjected to capacity constraints. The effects of capacity constraints are captured. Combining competition effect with constraint effect, some interesting conclusions are reached. First, the relationship between capacity constraints and firm size is addressed. We argue that the capacity constraints reduce market size difference and price difference under Cournot. Second, under the Stackelberg case, the existence of solution is proved, and Stackelberg competitions enlarge firm-size difference and price difference if the more efficient firm plays the leading position. When the weaker firm plays the leading position, the conclusions depend on the total capacity. Finally, under the Stackelberg case, when the stronger firm plays the leading position, the firm-size difference and price difference decrease with total input under capacity constraints, which is contrary to the conclusions under Cournot competitions.     

中国四类地区工业用地供给研究*——来自新经济地理学的解释

本文基于工业用地供给模型,修改了多样性偏好假定,并将中国按照工业发展程度分成四类地区,分析四类地区政府在GDP考核目标下的工业用地供给策略。通过求解纳什均衡的近似解析解,笔者发现,处于工业发展初级阶段的地区,倾向于多供给土地,形成小规模企业;反之亦然。同时本文证明了在同样的劳动力规模下,交易成本高、同质性竞争激烈、技术水平低下的地区会供给更多的工业用地。这为提升工业用地使用效率指明了方向。     

Stackelberg thresholds in network routing games or the value of altruism

It is well known that the Nash equilibrium in network routing games can have strictly higher cost than the optimum cost. In Stackelberg routing games, where a fraction of flow is centrally-controlled, a natural problem is to route the centrally-controlled flow such that the overall cost of the resulting equilibrium is minimized.We consider the scenario where the network administrator wants to know the minimum amount of centrally-controlled flow such that the cost of the resulting equilibrium solution is strictly less than the cost of the Nash equilibrium. We call this threshold the Stackelberg threshold and prove that for networks of parallel links with linear latency functions, it is equal to the minimum of the Nash flows on links carrying more optimum flow than Nash flow.Our approach also provides a simpler proof of characterization of the minimum fraction that must be centrally controlled to induce the optimum solution.     

Stackelberg Beats Cournot — On Collusion and Efficiency in Experimental Markets

We report on an experiment designed to compare Stackelberg and Cournot duopoly markets with quantity competition. We implement both a random matching and a fixed-pairs version for each market. Stackelberg markets yield, regardless of the matching scheme, higher outputs than Cournot markets and, thus, higher efficiency. For Cournot markets, we replicate a pattern known from previous experiments. There is stable equilibrium play under random matching and partial collusion under fixed pairs. We also find, for Stackelberg markets, that competition becomes less intense when firms remain in pairs but we find considerable deviations from the subgame perfect equilibrium prediction which can be attributed to an aversion to disadvantageous inequality.     

A graphic representation of the Nash and Lindahl equilibria in an economy with a public good

In an economy with a public good the noncooperative Nash equilibrium and the cooperative Lindahl equilibrium are represented graphically. The Nash equilibrium is shown to be non-optimal, while the Lindahl equilibrium is shown to be optimal. Simple stability analyses are undertaken. Finally, the two equilibria are compared. It appears that more public good will be allocated in the Lindahl than in the Nash equilibrium, and that in a sufficiently large economy a transition from a Nash to a Lindahl equilibrium will be advantageous for everyone.     

Public capital and imperfect competition

In this paper we consider a macroeconomic model in which public capital is a productive input and there is monopolistic competition in the product market. We analyze the effects of a permanent variation in public capital investment both in the short and in the long run. Finally, we show that the optimal provision of public capital under imperfect competition is higher than that associated with the first-best policy.     

The trade paradox persists under excise taxes

Brander and Krugman (1983) and Sertel (1988) followed by Krugman (1989), showed two sides of a ‘trade paradox’: The paradox in competition, viz. that opening trade (or increasing competition) may cause welfare to decline, and the paradox in efficiency, viz. that an increase in unit transport cost may increase welfare. In this paper, we consider the situation in an environment where interventionist trade policies are not permitted but each country is sovereign to impose an excise tax (or subsidy). The paradoxes persist under equilibrium excise taxes, reckoned both at the non-cooperative (Nash or dominant strategy) equilibrium and at the cooperative solution among tax-imposing authorities maximizing welfare. We also see that the paradoxes persist in a taxless environment where market equilibrium is Stackelberg rather than Cournot.