QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

The Economics of International Policy Coordination*

One aspect of reforming the world monetary system is the issue of designing a set of ‘rules of the game’ within which countries can pursue their own national objectives and yet which still leads to some form of global coordination of macroeconomic policies. The issue of strategic interactions between countries has recently received some analytical insights with the application of game theory to the economics literature on interdependence between countries. The purpose of this paper is to survey these recent applications of static and dynamic game theory to the question of international policy coordination. It also surveys the results of the few empirical attempts to measure the potential gains to coordination.     

后危机时代人民币汇率大国博弈研究

后危机时代,美国、日本、德国、巴西与中国展开了一场大国汇率博弈。这些大国寄希望通过人民币升值来转嫁危机,提振本国经济。然而,各国在全球的位势差异决定了其不同的策略选择。面对不断升级的人民币汇率大国博弈,中国必须学会用政治乃至国家竞争的战略眼光来看待问题的实质,继续按照主动性、可控性和渐进性原则来推动汇率形成机制改革,拒绝人民币“被升值”。     

Leadership in Public Good Provision: A Timing Game Perspective

We address in this paper the issue of leadership when two governments provide public goods to their constituencies with cross‐border externalities as both public goods are valued by consumers in both countries. We study a timing game between two different countries: before providing public goods, the two policymakers non‐cooperatively decide their preferred sequence of moves. We establish conditions under which a first‐ or second‐mover advantage emerges for each country, highlighting the role of spillovers and the complementarity or substitutability of public goods. As a result, we are able to prove that there is no leader when, for both countries, public goods are substitutable. When public goods are complements for both countries, each of them may emerge as the leader in the game. Hence a coordination issue arises. We use the notion of risk‐dominance to select the leading government. Finally, in the mixed case, the government for whom public goods are substitutable becomes the leader.     

Austrian Economics and Game Theory: A Stocktaking and an Evaluation

I discuss the merits and drawbacks of game theory in economics from the perspective of Austrian economics. I begin by arguing that Austrians have neglected game theory at their peril, and then suggest that game theoretic reasoning could be one way of modelling key Austrian insights. However, admittedly some aspects of game theory don't square easily with Austrian economics. Moreover, a major stumbling block for an Austrian acceptance of game theory may lie in the traditional Austrian resistance to formal methods.     

A NOTE ON SEMIPARAMETRIC ESTIMATION OF FINITE MIXTURES OF DISCRETE CHOICE MODELS WITH APPLICATION TO GAME THEORETIC MODELS*

We view a game abstractly as a semiparametric mixture distribution and study the semiparametric efficiency bound of this model. Our results suggest that a key issue for inference is the number of equilibria compared to the number of outcomes. If the number of equilibria is sufficiently large compared to the number of outcomes, root‐n consistent estimation of the model will not be possible. We also provide a simple estimator in the case when the efficiency bound is strictly above zero.     

A note on allocations attainable through nash equilibria

This note reexamines the issue of attaining efficient resource allocations as noncooperative equilibria of a strategic game. Contrary to the spirit of earlier work on this subject, it is shown that there is an entire class of choice rules, aside from the Walrasian one, which are implementable in Nash equilibrium stategies.     

The Paper River Revisited: A Common Property Externality Exercise

The author describes a modified version of the Paper River exercise that appeared in this journal in the Spring 1999 issue. The original game was designed to illustrate the application of the Coase theorem for solving an externality problem. In the Paper River, pairs of students share a single productive resource: small pieces of paper. At question is who has the rights to the paper. The author presents a modified version of the game that retains many of the same elements from the original, but the students work in groups rather than in pairs. Doing so increases the transaction costs associated with negotiating a solution. In addition, the productive resource is common property, so property rights are difficult to establish. These difficulties make a Coasian solution more difficult but make the simulation more realistic.     

Credible communication and cooperation: Experimental evidence from multi-stage Games

It is well known that communication often serves as a facilitator for cooperation in static games. Yet, communication can serve entirely different purposes in dynamic settings as communication during the game may work as a means for renegotiation, potentially undermining the credibility of cooperative strategies. To explore this issue, this paper experimentally investigates cooperation and non-binding communication in a two-stage game. More specifically, two treatments are considered: one with only pre-play communication and one where subjects can also communicate intra-play between the stages of the game. The results highlight a nontrivial difference concerning the effects of pre-play communication between the two treatments. Sending or receiving pre-play messages has a positive and significant effect on cooperation if there is no possibility of intra-play communication. However, this effect is significantly reduced when when intra-play communication is allowed. The results suggest that the credibility of pre-play messages may depend crucially on future communication opportunities.     

Influence and the discretionary allocation of several prizes

When a decision process involves discretion, it may also be open to influence by various actors. If a single prize is at issue, then this influence can be modelled in the context of a rent-seeking game. However, the basic rent-seeking model needs to be extended in order to examine the amount of influence exerted when more than one prize is at stake. In this paper, we investigate the effect of several factors which may affect rent-seeking in this multi-prize framework but are not accounted for in single-prize models; examples here are the number of prizes, the division of the prize mass and the distribution mechanism which is employed.     

A three way equivalence

In view of the well known core equivalence results in atomless economies, coincidence of market game equilibrium allocations with competitive allocations is tantamount to a three way equivalence between market game mechanisms, competitive equilibria and the core. Based on this idea we study equilibrium refinements of market games, which allow us to use the core equivalence machinery in order to provide an exact market game characterization of competitive equilibria.     

The Effects of Issue Salience on Political Decision-making

Game-theoretic models of political decision-making regard policy outcomes as a combined result of actor preferences and institutions. This paper explores the effects of adding relative issue salience to the analysis. I focus on non-cooperative models of complete and perfect information that are based on the concept of structure-induced equilibrium (Shepsle in Am J Polit Sci 23(1):27–59, 1979). Assuming a progressive agenda-setter and two conservative voters, I show how a change of the relative issue salience for players in a game results in a different equilibrium outcome in a political decision-making body.     

政府农村公共项目投资决策失范的诱因研究

政府农村公共项目投资决策失范是普遍存在的现象,要解决这一问题必须找出导致这种失范产生的诱因。对于该问题的研究,要抓住一个主线,就是利益。导致该决策失范的诱因,除决策程序外,更重要的是作为投资主体的政府追求自身利益所导致的对农村公共利益的偏差,以及令这一问题更加复杂化的政府内部博弈行为。从利益偏差、内部博弈和决策过程角度对决策失范的诱因进行了研究,这种分析框架对于其他领域政府行为的研究也有一定的借鉴意义。     

A Dynamic Tiebout Theory of Voluntary vs. Involuntary Provision of Public Goods

This paper considers a dynamic model of Tiebout-like migration between communities that utilize distinct allocation procedures for public goods. At issue is whether voluntary or compulsory procedures are more likely to prevail over time. We model infinitely lived individuals who make repeated, sequential location decisions over one of two communities. Each community uses a distinct mechanism for allocating public goods. The first is one in which contributions are given voluntarily by the citizenry of the community. The second is a compulsory scheme by which individuals are taxed proportionately to wealth with the tax determined by a majority vote. Opportunities to accumulate wealth exist via accumulation of public capital.
The Markov Perfect equilibria of the dynamic game are studied. Our main result shows that when accumulated wealth converges to a steady state, individuals' locational choices eventually "select" the involuntary provision mechanism. This holds despite the fact that unanimous location in the voluntary provision community may in many cases remain as a Nash equilibrium of the static game each period. We also describe conditions under which voluntary provision survives. These conditions require that accumulation of capital fails to decrease wealth dispersion over time. The results are shown to be consistent with findings relating inequality to school choice.     

Coordination and the Provision of Discrete Public Goods by Correlated Equilibria

The strategic analysis of the private provision of a discrete public good has shown the existence of multiple Nash equilibria with the efficient number of players voluntarily contributing. However the coordination issue is left unexplained by this literature. The experimental evidence shows that communication among players is helpful in achieving cooperation. We claim that, from the theoretical point of view, this is equivalent to playing correlated equilibria in an extended public good game with communication, modeled as Chicken. We characterize such equilibria as feasible coordination mechanisms to achieve public goods provision in the general contribution game. We further introduce a second kind of game characterized by payoff externalities that may persist after the minimal threshold of contributors is achieved. While it is easy to show the existence of Pareto efficient correlated equilibria in the first game, in the second one players face incentive problems such that a first best cannot always be an equilibrium. Nevertheless there exist correlated equilibria that can qualify as incentive efficient mechanisms, once free riding is seen as a moral hazard issue. Finally, with an example, we discuss the impact of coalition formation in our framework.     

企业培训策略选择的博弈分析

企业对员工进行培训,可以提高员工的生产率,从而为企业带来更丰厚的利润,然而却又面临着员工跳槽的风险.企业为了挽留经过培训的员工,给予其较高的薪资待遇,结果给企业带来巨大的成本,甚至仍然留不住关键人才.笔者运用信号博弈的方法分析企业在员工培训方面的决策问题,得出多种均衡结果.     

A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

结构化多人博弈的分析框架

结构化多人博弈是一种把博弈方嵌入到具体的社会关系之中,在两两博弈的基础上求解整体博弈均衡状态的分析框架。和现有的合作博弈(Cooperative Game Theory)、网络博弈(Network Games)、进化图论(Evolutionary Graph Theory,EGT)、计算博弈论(Computational Game Theory)等多人博弈分析框架相比,结构化博弈既有和它们相似的地方,也有非常重要的差别。结构化博弈更适合用来分析政治问题和社会现象中的多人博弈局面。作为最简单的情况,本文先给出了一个三人结构化博弈的一般分析框架,然后根据这个分析框架对传统的联盟博弈进行了新的分析,发现经典的"三人分300元"博弈事实上有稳定的均衡解,即三人各分100元。作为一个简单的应用,文章分析了三个国家之间的"战争-同盟博弈",我们发现该博弈有两个稳定的均衡解,在这两个稳定的均衡解中,超级大国和小国总是选择结盟,而小国总是选择和地区大国进行战争。从这两个例子可以看出,结构化多人博弈在分析复杂的政治、经济、社会问题上具有传统博弈论方法所不具备的很多优势,其获得的均衡解也更符合社会实际。     

A Noncooperative Quantity‐Rationing Theory of Transboundary Pollution

We study a remedy for the problem caused by international transfrontier pollution. Our results are derived from the analysis of a noncooperative game model of the determination of emissions in a quantity‐rationing setting. We model the emission capping negotiations using the best response dynamic process and provide natural conditions under which the process has a unique and globally asymptotically stable stationary point. We then analyze the link between type profiles and the stationary points of the negotiation process to derive various comparative statics results and the type‐contingent ordering of emission allocations. These results are used to study the investment strategies that nations can use prior to the negotiations in order to manipulate the equilibrium emission caps.