An extremely simple proof of the K-K-M-S Theorem

Summary.  An extremely simple proof of the K-K-M-S Theorem is given involving only Brouwer’s fixed point theorem and some elementary calculus. A function is explicitly given such that a fixed point of it yields an intersection point of a balanced collection of sets together with balancing weights. Moreover, any intersection point of a balanced collection of sets together with balancing weights corresponds to a fixed point of the function. Furthermore, the proof can be used to show -balanced versions of the K-K-M-S Theorem, with -balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to by Billera can be even weakened. Received: January 22, 1996; revised version June 9, 1996     

On Kakutani's fixed point theorem,the K-K-M-S theorem and the core of a balanced game

Summary We provide elementary proofs of Scarf's theorem on the non-emptiness of the core and of the K-K-M-S thoerem, based on Kakutani's fixed point theorem. We also show how these proofs can be modified to apply a coincidence theorem of Fan instead of Kakutani's fixed point theorem, for some additional simplicity.The results presented here were first reported in Shapley (1987) and Vohra (1987). A version of our proof of Theorem 1 has also been presented in a recent book by C.D. Aliprantis, D.J. Brown and O. Burkinshaw,Existence and Optimality of Competitive Equilibria (1989) Springer-Verlag. We are grateful to Ky Fan, Wanda Gorgol, Tatsuro Ichiishi and Ali Khan for comments on earlier drafts. Vohra's research has been supported in part by NSF grant SES-8605630.     

A simple proof of K-K-M-S theorem

Summary We give a simple proof of the K-K-M-S theorem based on the Kakutani fixed point theorem, the separation theorem for convex sets and the Berge maximum theorem.The author is grateful to Gerard Debreu for his advice and to Tatsuro Ichiishi, Michael Todd, Rajiv Vohra, Nicholas Yannelis, Lin Zhou and two anonymous referees for their comments. The original version of this note was written in the fall 1992 while the author was visiting the Department of Economics, University of California at Berkeley.     

Open gaps,metrization and utility

Summary It is shown that each of the Debreu Open Gap Theorem and the Debreu Continuous Utility Representation Theorem can be used in order to prove the other. Furthermore, it is proved that the classical Alexandroff-Urysohn Metrization Theorem implies Debreu's Continuous Utility Representation Theorem and, thus, all known results on the existence of continuous utility functions.     

An Optimal IPO Mechanism

We analyse the optimal Initial Public Offering (IPO) mechanism in a multidimensional adverse selection setting where institutional investors have private information about the market valuation of the shares, the intermediary has private information about the demand, and the institutional investors and intermediary collude. Theorem 1 states that uniform pricing is optimal (all agents pay the same price) and characterizes the IPO price in terms of conditional expectations. Theorem 2 states that the optimal mechanism can be implemented by a non-linear price schedule decreasing in the quantity allocated to retail investors. This is similar to IPO procedures used in the U.K. and France. Relying on French IPO data we perform a GMM structural estimation and test of the model. The price schedule is estimated and the conditions characterizing the optimal mechanism are not rejected.     

On mixed markets with asymmetric information

In asymmetric information exchange economies involving both non-negligible and negligible agents, one should expect the failure of the private Core-Walras Equivalence Theorem. This paper shows that if “large” traders are similar to each other, then they lose their market power and hence the Equivalence Theorem can be restored. We also investigate on weaker equivalences among Walrasian expectations allocations, Aubin private core and private core allocations of the original mixed economy and the atomless one associated to it, without the assumption that all atoms are of the same type. Furthermore, extensions of Hervés-Moreno-Yannelis and Schmeidler Theorems (compare Hervés et al. in J Math Econ 41:844–856, 2005a; Schemidler in Econometrica 40:579–580, 1972) are given for differential information economies in which the feasibility constraints are imposed with an equality (exact feasibility).     

Network formation and stable equilibrium

We study the non-cooperative formation of a (directed) network that builds upon one-way immediate links. Our novel feature is that we require circular paths of links for productive activities. This captures more clearly the higher level of coordination that is often required for network formations than models such as those of Jackson and Wolinsky [A strategic model of social and economic networks, J. Econ. Theory 71 (1996) 44-74] and Bala and Goyal [A non-cooperative model of network formation, Econometrica 68 (2000) 1181-1229], in that in our model a single agent's unilateral action is limited in affecting the network structure. We completely characterize the class of Nash equilibria by showing that the minimality of a graph is both necessary and sufficient (Theorem 1). We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996). We show that stable equilibria are a wheel, a trivial network, or a sub-wheel partitioned network (Theorem 2). We modify the Bala and Goyal (2000) dynamic process with inertia, and obtain the convergence to stable equilibria regardless of the initial state (Theorem 3).     

Farmer Brown v. Rancher Wyatt: Teaching the Coase Theorem

The Coase Theorem is a fundamental tenet of environmental economics and is taught to thousands of principles of microeconomics students each year. Its counterintuitive conclusion, that a Pareto optimal solution can result between private parties regardless of the initial allocation of property rights over a scarce resource, is difficult for students to understand. By using a mock trial that centers on a property dispute, students can be taught how the Coase Theorem works in practice with minimal preparation. The strong assumptions on which the Coase Theorem relies also can be included to show why the theorem may not hold. By using a unique, active learning technique, students will be more engaged and may have a better understanding of a difficult but seminal theory of economics.     

A reconsideration of the problem of social cost: Free riders and monopolists

Summary. One version of the Coase Theorem is, If property rights are fully allocated, competition leads to efficient allocations. This version implies that the public goods problem can be solved by allocating property rights fully. We show that this mechanism is not likely to work well in economies with global externalities because the privatized economy is highly susceptible to strategic behavior: The free-rider problem manifests itself as a complementary monopoly problem in an associated private goods economy. Thus, our work relates the validity of the Coase Theorem to the literature on the incentives for strategic behavior in economies with complementarities. Received: 12 May 1999; revised version: 9 July 1999     

Some general results on the metric rationalization for social decision rules

The purpose of this paper is twofold. First, to provide a transparent characterization of the family of metrizable social decision rules. Second, to provide the necessary and sufficient conditions for a reasonable metric rationalization. Theorem 1 establishes that the class of metrizable social decision rules is uniquely characterized by a variant of the well-known Pareto condition. Theorem 2 establishes that positional rules can be characterized in terms of a special class of additively decomposable quasi-metric rationalizations. Theorem 3 characterizes strong positional rules in terms of reasonable metric rationalizations.     

积极财政政策执行效果及隐忧问题研究——H省执行情况个案分析

基于凯恩斯主义国民收入决定理论 ,通过对H省经济运行数据的实证模拟 ,分析H省积极财政政策的执行情况 ,并结合H省省情和我国国情 ,我们得到了九个基本命题 :命题 1∶H省经济处于投资陷阱之中 ,因而货币政策无效 ,财政政策充分有效。命题 2∶H省的财政政策乘数为 5 596,投资需求拉动乘数为 2 3 945,消费需求拉动乘数为2 2 0 1 5,财政支出回馈乘数为 0 2 2 66。命题 3∶H省国债转贷与补助资金拉动的经济增长率为 :1 988年 0 6个百分点 ,1 999年 0 9个百分点 ,2 0 0 0年 0 6个百分点 ,2 0 0 1年 0 5个百分点。命题 4:乘数愈大 ,积极财政政策的效果愈大 ,但积极财政政策退出造成的负作用也愈大 ,总需求和经济增长对积极财政政策的依赖程度也愈强。命题 5,民营化程度愈低 ,投资的利率弹性愈低 ,货币政策愈无效 ,反之亦然。命题 6,民营化程度愈低 ,财政依赖程度愈强 ,反之亦然。命题 7:我国的积极财政政策必然会退出 ;退出的最佳方式是淡出 ;维持现有国债规模是淡出的最可能的形式 ,是一个聚点均衡。命题 8:H省的民营化程度低于全国的平均水平 ,财政依赖程度高于全国的平均水平 ,自主性增长动力尤显不足。命题 9:如果没有激励民间投资的有效措施出台 ,积极财政政策淡出将使H省经济增长速度下滑。     

The irreversibility effect in environmental decisionmaking

We provide a new, more general, definition for the irreversibility effect and demonstrate its relevance to problems involving environmental and other decisions under uncertainty. We establish several analytical and numerical results that suggest both that the effect holds more widely than generally recognized, and that an existing result (Epstein’s Theorem), giving a sufficient condition for determining whether the effect holds, can be applied more widely than previously indicated, in particular to problems involving intertemporally nonseparable benefit functions. We further show that a low elasticity of intertemporal substitution will however result in failure of the effect.      

A note on Kuhn’s Theorem with ambiguity averse players

Kuhn’s Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrates the limits of Kuhn’s Theorem in an environment with ambiguity averse players who use a maxmin decision rule and full Bayesian updating.     

Repeated games with one-memory

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an ε-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.     

Optimal mixed taxation,credit constraints,and the timing of income tax reporting

We study optimal income and commodity tax policy with credit‐constrained low‐income households. Workers receive an even flow of income during the tax year, but report their incomes and make tax payments (receive transfers) at the end of the year. They spend their disposable income on multiple commodities over the year. We show that differentiated subsidies on commodities can be optimal even if the Atkinson–Stiglitz Theorem conditions apply. When the optimal policy leaves low‐income households with binding credit constraints, it may be optimal to subsidize differentially the good that they consume in higher proportion. Uniform subsidies would also relax the credit constraint, but would be more costly to the government since they would equally benefit unconstrained households. Numerical examples suggest that commodity tax differentiation increases with basic needs and with the interest rate at which government borrows.     

VOTING,LOBBYING, AND THE DECENTRALIZATION THEOREM

This paper revisits the well‐known fiscal “Decentralization Theorem” by relaxing the role of the assumption that governments are benevolent, while retaining the assumption of policy uniformity. If, instead, decisions are made by majority voting, the theorem fails. Specifically, (i) centralization can welfare‐dominate decentralization even if there are no externalities and regions are heterogeneous and (ii) decentralization can welfare‐dominate centralization even if there are positive externalities and regions are homogeneous. Similar results are obtained if a benevolent government is subject to lobbying. Hence, the Decentralization Theorem is not robust to relatively minor deviations away from the benchmark of a purely benevolent government.     

Candidate stability and nonbinary social choice

Summary. The requirement that a voting procedure be immune to the strategic withdrawal of a candidate for election can be formalized in different ways. Dutta, Jackson, and Le Breton (Econometrica, 2001) have recently shown that two formalizations of this candidate stability property are incompatible with some other desirable properties of voting procedures. This article shows that Grether and Plott's nonbinary generalization of Arrow's Theorem can be used to provide simple proofs of two of their impossibility theorems. Received: August 15, 2001; revised version: March 11, 2002 RID="*" ID="*" Parts of this article were previously circulated in somewhat different form in a working paper with the same title by the second author. We are grateful to Michel Le Breton and an anonymous referee for their comments. Correspondence to:J.A. Weymark     

Free‐Riding and the Provision of Public Goods in the Family: A Laboratory Experiment*

We examine the provision of family public goods using experimental economics methods. With sufficient altruism and shared resource arrangements, families can provide the efficient level of family public goods. Becker's Rotten Kid Theorem asserts that transfers from altruistic parents will induce children to maximize family income even if children are not altruistic toward other family members. Consistent with altruism, parents and children contributed more to a public good when in groups with family members than when in groups with strangers. In contrast to the predictions of the Rotten Kid Theorem, however, children's behavior fell short of maximizing family income.     

When Does Everyone Contribute in the Private Provision of Local Public Goods?

When does everyone genuinely contribute in the private provision of a local public good? We first introduce a monotonic condition to characterize the relationship between the structure of the network that underlie the noncooperative game of private provision of local public goods on the one hand, and the preferences of the agents on the other, showing that the monotonic condition is a sufficient and necessary condition of existence of a distributed Nash equilibrium (DNE) in which each agent exerts a positive amount of effort to provision of the public good (Theorem 1). We then study the number of equilibria, and, by using the monotonic condition, characterize the condition under which the DNE set is a singleton, a continuum, or null (Theorem 2). As it turns out, the structure of the network and the agents’ preferences jointly shape the effort profile in the provision of local public goods.     

Corrigendum to “Stable matchings and preferences of couples” [J. Econ. Theory 121 (1) (2005) 75–106]

We correct an omission in the definition of the domain of weakly responsive preferences introduced in [B. Klaus, F. Klijn, Stable matchings and preferences of couples, J. Econ. Theory 121 (2005) 75–106] or KK05 for short. The proof of the existence of stable matchings [KK05, Theorem 3.3] and a maximal domain result [KK05, Theorem 3.5] are adjusted accordingly.