Global analysis and economics IV : Finiteness and stability of equilibria with general consumption sets and production

Among other things a global version of the fundamental theorem of welfare economics is proved. One starts with a pure exchange economy with fixed total resources where hypotheses of differentiability, convexity, and monotonicity are made on the utility functions. Let be the set of price equilibria where the initial allocation coincides with the final one. Then the map which assigns to such a price equilibrium, the corresponding allocation is a diffeomorphism (a complete correspondence) between and the set of Pareto Optima.     

Global analysis and economics III: Pareto Optima and price equilibria

Among other things a global version of the fundamental theorem of welfare economics is proved. One starts with a pure exchange economy with fixed total resources where hypotheses of differentiability, convexity, and monotonicity are made on the utility functions. Let ? be the set of price equilibria where the initial allocation coincides with the final one. Then the map which assigns to such a price equilibrium, the corresponding allocation is a diffeomorphism (a complete correspondence) between ? and the set of Pareto Optima.     

Strategy-proofness, core, and sequential trade

We extend the Shapley-Scarf (1974) model - where a finite number of indivisible objects is to be allocated among a finite number of individuals - to the case where the primary endowment set of an individual may contain none, one, or several objects and where property rights may be transferred (objects inherited) as the allocation process unfolds, under the retained assumption that an individual consumes at most one object. In this environment we analyze the core of the economy and characterize the set of strategy-proof and Pareto efficient mechanisms. As an alternative approach, we consider property rights implicitly defined by a strategy-proof and Pareto efficient mechanism and show a core property for the mechanism-induced endowment rule.Received: 19 February 2004, Accepted: 14 April 2005, JEL Classification: C71, C78, D71, D78We would like to thank two anonymous referees for valuable comments. Financial support from The Swedish Council for Research in the Humanities and Social Sciences is gratefully acknowledged by Lars-Gunnar Svensson. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged by Bo Larsson.     

Communication complexity and stability of equilibria in economies and games

The theory of decentralized allocation mechanisms introduced by Leonid Hurwicz enabled economists to analyze the implications of requiring an allocation mechanism to perform well over a range of possible economic environments. One of the earliest major results in this theory was the formalization and proof of Hayek’s famous assertion that the competitive market mechanism minimizes the communication needed to achieve Pareto efficient allocations. The informational efficiency theorem spawned a large literature on communication complexity in allocation mechanisms. This paper provides an exposition of some results on the communication required to make equilibria locally stable, and the possibility of eliciting the required communication in allocation mechanisms and games.     

Monetary general equilibrium with transaction costs

Commodity money arises endogenously in a general equilibrium model with separate budget constraints for each transaction. Transaction costs imply differing bid and ask (selling and buying) prices. The most liquid good—with the smallest proportionate bid/ask spread—becomes commodity money. General equilibrium may not be Pareto efficient. If zero-transaction-cost money is available then the equilibrium allocation is Pareto efficient. Fiat money is an intrinsically worthless instrument. Its positive price comes from acceptability in paying taxes, and its use as a medium of exchange is based on low transaction cost.     

On strong representations of games by social choice functions

Games in characteristic function form are used to model an allocation of decision power among individuals involved in a voting situation. The problem of strong representation is to find a strategically acceptable social choice function that entails the allocation of power prescribed by a given game. Within the class of non-weak characteristic function games, we fully characterize the games that admit a strong representation. We apply this result to Peleg's problem of strong representation of simple games. Our results indicate that a strong representation requires significantly more than has been recognized in the literature.     

Optimal mechanisms for siting noxious facilities

We study Bayesian mechanism design in the context of the siting of noxious facilities. Under incomplete information, we characterize optimal mechanisms facilitating the siting and cost sharing of the facility. These mechanisms are allocatively and Pareto efficient. However, it appears that transfers occur when the good is not provided. This result is due to the weakening of the incentive notion to Bayesian–Nash equilibrium and to the balanced budget condition. This phenomenon disappears if the setting is perfectly symmetric.      

A characterization of the existenceof optimal dominant strategy mechanisms

This paper provides two theorems which characterize the domains of valuation functions for which there exist Pareto efficient and truth dominant strategy mechanisms (balanced Groves mechanisms). Theorem 1 characterizes the existence of balanced Groves mechanisms for a general class of valuation functions. Theorem 2 provides new balance-permitting domains of valuation functions by reducing the problem of solving partial differential equations to the problem of solving a polynomial function. It shows that a balanced Groves mechanism exists if and only if each valuation function in the family under consideration can be obtained by solving a polynomial function with order less than , where n is the number of individuals. Received: 5 January 1997 / Accepted: 25 May 1999     

Trading equilibrium in a public good economy with smooth preferences and a mixed measure space of consumers

Lindahl and Nash equilibria are often used in the theory of public good. Shitovitz and Spiegel (1998) present an example of 2-person economy with one private good and one pure public good, where the core efficient Lindahl allocation does not Pareto dominate the (inefficient) Nash allocation. In this paper we introduce the new concept of Trading equilibrium for a general public good economy with smooth preferences and a mixed measure space of consumers. We obtain that this economy admits a unique Trading equilibrium. Moreover, the Trading equilibrium induces a core allocation that strictly Pareto dominates the Nash allocation.     

Implementation of Pareto efficient allocations

This paper considers Nash implementation and double implementation of Pareto efficient allocations for production economies. We allow production sets and preferences are unknown to the planner. We present a well-behaved mechanism that fully implements Pareto efficient allocations in Nash equilibrium. The mechanism then is modified to fully doubly implement Pareto efficient allocations in Nash and strong Nash equilibria. The mechanisms constructed in the paper have many nice properties such as feasibility and continuity. In addition, they use finite-dimensional message spaces. Furthermore, the mechanism works not only for three or more agents, but also for two-agent economies.     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

Price discrimination and the location choice of a durable goods monopoly

Delivered pricing by a spatial monopoly amounts to third degree price discrimination. Well known results in spatial economics show that the monopolist location choice is efficient under delivered pricing and generally inefficient under mill pricing. By contrast, the present paper shows that if the monopolist sells a durable good, the location is also inefficient under delivered pricing.     

Endogenous household interaction

Most econometric models of intrahousehold behavior assume that household decision making is efficient, i.e., utility realizations lie on the Pareto frontier. In this paper, we investigate this claim by adding a number of participation constraints to the household allocation problem. Short-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize under (inefficient) Nash equilibrium. Long-run constraints ensure that each spouse obtains a utility level at least equal to what they would realize by cheating on the efficient allocation and receiving Nash equilibrium payoffs in all successive periods. Given household characteristics and the (common) discount factor of the spouses, not all households may be able to attain payoffs on the Pareto frontier. We estimate these models using a Method of Simulated Moments estimator and data from one wave of the Panel Study of Income Dynamics. We find that both short- and long-run constraints are binding for sizable proportions of households in the sample. We conclude that it is important to carefully model the constraint sets household members face when modeling household allocation decisions, and to allow for the possibility that efficient outcomes may not be implementable for some households.     

基于交换理论思考第三方物流的良性发展

利用交换理论,研究了制造业和第三方物流业融合时形成的契约曲线．提出了双方在合作过程中由于帕累托效率配置点背后的无差异曲线原因．造成双方改变动力不足的观点。结合福利经济学第一、第二定理,深入分析了目前第三方物流业在市场上处于的地位和不利局面。依据模型分析,提出了政府应该强化政策扶持、设置政策扶持时问限制．鼓励第三方物流自身壮大,以及强化双方的学习曲线融合效应等对策,     

Efficiency and monotonicity of bargaining solutions

A continuity axiom for bargaining solutions is introduced, which is satisfied by all Pareto optimal and continuous (in the Hausdorff metric) solutions. It is shown by two examples how this axiom can be used to characterize solutions having certain kind of monotonicity properties. One of the solutions is the lexicographic maximin solution. The other is the lexicographic extension of the Kalai-Smorodinsky solution. The former is an efficient (Pareto optimal) extension of the symmetric proportional solution. The latter is an efficient extension of the Kalai-Smorodinsky solution.     

The allocation of a shared resource within an organization

Many resources such as supercomputers, legal advisors, and university classrooms are shared by many members of an organization. When the supply of shared resources is limited, conflict usually results between contending demanders. If these conflicts can be adequately resolved, then value is created for the organization. In this paper we use the methodology of applied mechanism design to examine alternative processes for the resolution of such conflicts for a particular class of scheduling problems. We construct a laboratory environment, within which we evaluate the outcomes of various allocation mechanisms. In particular, we are able to measure efficiency, the value attained by the resulting allocations as a percentage of the maximum possible value. Our choice of environment and parameters is guided by a specific application, the allocation of time on NASA's Deep Space Network, but the results also provide insights relevant to other scheduling and allocation applications. We find (1) experienced user committees using decision support algorithms produce reasonably efficient allocations in lower conflict situations but perform badly when there is a high level of conflict between demanders, (2) there is a mechanism, called the Adaptive User Selection Mechanism (AUSM), which charges users for time and yields high efficiencies in high conflict situations but, because of the prices paid, in which the net surplus available to the users is less than that resulting from the inefficient user committee (a reason why users may not appreciate ‘market solutions’ to organization problems) and (3) there is a modification of AUSM in which tokens, or internal money, replaces real money, which results in highly efficient allocations without extracting any of the users' surplus. Although the distribution of surplus is still an issue, the significant increase in efficiency provides users with a strong incentive to replace inefficient user committees with the more efficient AUSM.     

A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.     

The Walras core of an economy and its limit theorem

The Walras core of an economy is the set of allocations that are attainable for the consumers when their trades are constrained to be based on some agreed price system, such that no alternative price system exists for any sub-coalition that allows all members to trade to something better. As compared with the Edgeworth core, both coalitional improvements and being a candidate allocation for the Walras core become harder. The Walras core may even contain allocations that violate the usual Pareto efficiency. Nevertheless, the competitive allocations are the same under the two theories, and the equal-treatment Walras core allocations converge under general conditions to the competitive allocations in the process of replication.     

Perturbed utility and general equilibrium analysis

We study general equilibrium theory of complete markets in an otherwise standard economy with each household having an additive perturbed utility function. Since this function represents a type of stochastic choice theory, the equilibrium of the corresponding economy is defined to be a price vector that makes its mean expected demand equal its mean endowment. We begin with a study of the economic meaning of this notion, by showing that at any given price vector, there always exists an economy with deterministic utilities whose mean demand is just the mean expected demand of our economy with additive perturbed utilities. We then show the existence of equilibrium, its Pareto inefficiency, and the upper hemi-continuity of the equilibrium set correspondence. Specializing to the case of regular economies, we finally demonstrate that almost every economy is regular and the equilibrium set correspondence in this regular case is continuous and locally constant.