Endogenous City Formation with Production Externalities: Existence of Equilibrium

I show that equilibria exist in closed city‐system models with production externalities if firms' production possibilities vary continuously with the source of the externality, are constant returns to scale in own inputs, include inaction, and satisfy free disposal; if firms have to employ their own inputs to produce output; if there is a finite number of firm types; and if some standard conditions on preferences and endowments are satisfied. This is the first model to include production externalities in the fully general equilibrium framework required for endogenous city formation. Thus, this result provides formal support for the conjecture that production externalities lead to urban agglomeration.     

Consumption Externalities,Habit Formation and Equilibrium Efficiency*

We analyze the welfare properties of the competitive equilibrium in a capital accumulation model where individual preferences are subject to both habit formation and consumption spillovers. Using an additive specification for preferences, according to which the argument in the utility function is a linear combination of present and past values of own consumption and consumption spillovers, we analyze the circumstances under which these spillovers are a source of inefficiency. It is shown that consumption externalities have to interact with habits in order to generate an inefficient dynamic equilibrium. Finally, we characterize optimal tax policies aimed at restoring efficient decentralized paths.     

团队生产的纳什均衡及合作博弈空间

本文在霍姆斯特姆所做贡献的基础上认为团队生产问题在本质上等同于囚徒困境问题,并指出霍姆斯特姆的实施强制契约的解决方法存在逻辑漏洞,在现实社会中一般是无效的.本文依据社会经济人个人效用最大化的条件定义了团队生产的合作战略博弈空间,合作战略博弈空间的均衡极点(即个人效用最大化点)就是团队生产收益分配博弈的纳什均衡解.如果个人收益的总和等于集体收益的最优值,那么个人理性与集体理性之间就达到统一,处于帕累托最优状态,即不存在道德风险;反之,则说明存在道德风险.并给出了在团队生产中通过改变合作战略博弈空间达到帕累托最优的一个特例,指出了科学合理地改变合作战略博弈空间在社会经济发展中的重要作用     

Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium

We define a class of games with discontinuous payoffs that we call shared resource games and establish a pure strategy Nash equilibrium existence theorem for these games. We then apply this result to a canonical game of fiscal competition for mobile capital. Other applications are also discussed. Our result for the mobile capital game holds for any finite number of regions, permits general preferences over private and public goods, and does not assume that production technologies have a particular functional form, or are identical in all regions, or satisfy the Inada condition at zero.     

东北亚自由贸易区三方博弈的纳什均衡解

通过可计算一般均衡模型,对中、日、韩三国间建立自由贸易区的各种可能形式进行模拟分析,在博弈分析框架下得出包含中日韩三国的自由贸易区三方博弈的纳什均衡解;三国中任何一国通过与其他两国分别建立双边自由贸易区所建立的轴心-边陲型FTA是不可行的;建立中日韩FTA不仅能使三国的福利得到提高,而且能促进部分产业在区域外市场上的竞争力提升。     

On the Number of Pure Strategy Nash Equilibria in Random Games

How many pure Nash equilibria can we expect to have in a finite game chosen at random? Solutions to the above problem have been proposed in some special cases. In this paper we assume independence among the profiles, but we allow either positive or negative dependence among the players' payoffs in a same profile. We provide asymptotic results for the distribution of the number of Nash equilibria when either the number of players or the number of strategies increases. We will show that different dependence assumptions lead to different asymptotic results. Journal of Economic Literature Classification Number C72.     

Nash Equilibria in Pure Strategies

We consider an n ‐person non‐zero‐sum non‐cooperative game in normal form, where the strategy sets are some closed intervals of the real line. It is shown that if the pay‐off functions are continuous on the whole space and if for each pay‐off function the smallest local maximum in the strategy variable is a global maximum, then the game possesses a pure strategy Nash equilibrium.     

Farmers’ Adoption of Irrigation Technologies: Experimental Evidence from a Coordination Game with Positive Network Externalities in India

Electric irrigation contributes to food security in rural India, but deteriorating electrical infrastructures threaten the functioning of farmers’ pump sets. This problem could be solved through investments in energy‐efficient technologies. However, network externalities create a coordination problem for farmers. We develop a framed field experiment to study the effects of group size, leading by example, and payoff structures on the ability to coordinate technology adoption investments. The experiment is based on a game that combines features of a step‐level public goods game and a critical mass game. Our findings show that smaller groups more frequently coordinate on payoff‐superior equilibria and that higher payoffs lead to more investments. Contrary to previous studies, leading by example reduces investments but has no effect on efficiency. Building on this analysis, we discuss possible bottom‐up solutions to the energy crisis in rural India.     

Equilibrium in a Market Game

This paper studies the equilibrium of an exchange economy with the same number of agents and commodities. It is shown that under rather mild conditions on demand the market have a price equilibrium—independently of the divisibility of the commodities. The result extends Gale’s equilibrium theorem for indivisible commodities to the case where some commodities are perfectly divisible. The proof is based on a topological lemma contained in previous paper of one of the authors.     

An Experimental Education Market with Positive Externalities

A graphical approach shows that in order for the tax revenue to increase, following a reduction in the marginal rate, the increase of aggregate supply must be greater the lower the price level elasticity of aggregate demand.     

How to Select a Dual Nash Equilibrium

The paper analyzes situations, generalizing the duopoly problem, where two identical players are allowed with two control variables each, all of them linked through two non-strategic private constraints. Four dual equilibria are then obtained when each agent selects one leading variable to optimize and adjusts the other, and these equilibria are compared in a meta-game. For a simplified class of continuous games with linear constraints, it is shown that one symmetric dual equilibrium dominates the others and is the only perfect equilibrium of the metagame. The latter result holds locally for all quasi-concave utility functions and globally for all homogeneous ones, always keeping linear constraints. However, it is no longer valid in discrete games where the implicit constraints are not linear. Journal of Economic Literature Classification Numbers: C72, D43.     

浅析知识产权保护中混合策略纳什均衡模型的应用

知识产权保护不但受制于立法的完善和执法的力度,而且取决于自觉维权的意识和守法的环境。我国企业和科研机构知识产权保护意识薄弱,缺乏维护自身合法权益的能力,尊重他人知识产权的观念尚未形成社会主流。本文运用博弈论方法,分析了一个知识产权保护博弈案例中的混合策略纳什均衡解,得出从增加知识产权主体自觉维权意识和加大侵权者成本两方面实现知识产权有效保护的结论。     

On Equilibrium Dynamics Under Externalities in a Model of Economic Development

This paper studies a discrete-time version of a model of economic development proposed by Lucas, in which the average stock of human capital produces a positive externality in the production of the physical capital good. It establishes the existence of equilibrium programmes from arbitrary initial conditions, and of an equilibrium steady-state programme. The principal results are concerned with the global dynamic behaviour of equilibrium programmes off the steady state. They show that the asymptotic growth rates of consumption, physical and human capital on any equilibrium programme will equal the growth rates of the respective variables along the equilibrium steady state
JEL Classification Numbers: C62, D90, O41     

Gains From Trade in a Cournot–Nash General Equilibrium

It is shown that, in a context of Cournot–Nash general equilibrium, free trade is potentially gainful for each trading country. No restrictions are placed on the numbers of products, factors of production or countries, or on the nature of returns to scale. Moreover, preferences, techniques and factor endowments can differ from agent to agent.
JEL Classification Numbers: F10, F12, F13, F15.     

Mixed-strategy equilibria in the Nash Demand Game

In the Nash Demand Game, each of the two players announces the share he demands of an amount of money that may be split between them. If the demands can be satisfied, they are; otherwise, neither player receives any money. This game has many pure-strategy equilibria. This paper characterizes mixed-strategy equilibria. The condition critical for an equilibrium is that players’ sets of possible demands be balanced. Two sets of demands are balanced if each demand in one set can be matched with a demand in the other set such that they sum to one. For Nash’s original game, a complete characterization is given of the equilibria in which both players’ expected payoffs are strictly positive. The findings are applied to the private provision of a discrete public good.     

The Gains from Trade in a Cournot–Nash Trading Equilibrium

It has recently been suggested by several authors that a Cournot–Nash free‐trade equilibrium might leave each country worse off than under autarky, in apparent contradiction of earlier findings. In the present note it is shown that the suggestion is typically based on self‐contradictory assumptions and is therefore unacceptable.     

中国股票市场机构与散户的均衡策略及实证研究

证券市场作为一个政府、交易所、上市公司、机构和散户多方参与的博弈竞技场,各方必然要观察各参与方的行为策略并据此制定己方的行动战略。由于目前中国证券市场尚无做空机制,且股票供应紧俏,很多股票交易中都有机构主力参与的痕迹。机构利用信息和资金优势,在政策法律允许的范围内,尽力推高股价以诱使散户追涨是其最优策略的理性选择。而散户在信息严重不对称的劣势下,其后验信念的修正往往会受到机构信号的误导,博弈所要求的最优策略行动实际上是很难达到的,故个体投资者无疑是证券市场最大的受害者。     

Stable Provision vs. Cournot–Nash Equilibria in Pure Public Good Economies

Shitovitz and Spiegel (1998, Journal of Economic Theory 83 , pp. 1–18) demonstrated that in pure public good economies, for some consumers the Lindahl consumption bundles can be inferior (utility-wise) to their Cournot–Nash allocation. In this paper, we prove that in any finite pure public good economy there exists a core allocation that is unanimously preferred, utility-wise, by all consumers over their Cournot–Nash consumption bundles.     

Coalition and Party Formation in a Legislative Voting Game

We examine a legislative voting game where decisions are to be made over both ideological and distributive dimensions. In equilibrium legislators prefer to make proposals for the two dimensions together, despite having preferences that are separable over the two dimensions. The equilibria exhibit interaction between the ideological and distributive dimensions, and the set of legislators who approve winning proposals does not always consist of ideologically adjacent legislators. There is more than one ideological decision that has a positive probability of being proposed and approved. We show that legislators can gain from forming political parties, and consider examples where predictions can be made about the composition of parties. Journal of Economic Literature Classification Numbers: D72, C71, C78.     

On the Existence and Uniqueness of Pure-Strategy Nash Equilibrium in Asymmetric Rent-Seeking Contests

There can be three types of heterogeneity among players in a rent‐seeking contest. First, effectiveness of player's effort on the winning probabilities may differ among players. Secondly, players may evaluate the rent or prize of the rent‐seeking contest differently. Thirdly, players may face different financial constraints. This article proves under standard assumptions in the literature that there exists a unique pure‐strategy Nash equilibrium in a general asymmetric rent‐seeking contest with these three types of heterogeneity among players.