Open core and quasi-equilibria with lower semi-continuous preferences

Summary. This note introduces a new concept of core –open core, using which it shows a quasi-equilibrium existence result in an economy where consumers' preference relations are assumed to be lower semi-continuous, but not necessarily to have open lower sections nor to be open valued, such as the lexicographic ordering. As an application, a competitive equilibrium existence result without non-satiation assumption is proved. Received: October 28, 1996; revised version: November 4, 1997     

Transitive closure, proximity and intransitivities

Summary. Assignments of weak orders to complete binary relations are considered. Firstly, it is shown that assigning the transitive closure of a complete binary relation does not always assign the closest weak order according to any reasonable metric on complete binary relations. It is then shown that the assignment of a weak order to a complete binary relation assigns its transitive closure if and only if it assigns the closest weak order according to a particular distance function that is not a metric. This permits more direct comparisons between the Transitive Closure Rule and other rules such as the Slater Rule.Received: 10 March 2002, Revised: 19 July 2002, JEL Classification Numbers: D70, D71. Correspondence to: Christian KlamlerPreliminary versions of this paper have been presented at a seminar in Graz University, at the CEPET Annual Workshop in Economic Theory, at the South-East Theory and Trade meetings and at the meetings of the European Public Choice Society and the Public Choice Society. We are grateful to all participants. Helpful communications with John Conlon, Wulf Gaertner, Christian Gehrke, Hannu Nurmi, Howard Petith and Don Saari are also gratefully acknowledged. Comments by a referee greatly improved the paper and are much appreciated.     

Choice under complete uncertainty: axiomatic characterizations of some decision rules

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules. Received: August 20, 1998; revised version: November 3, 1999     

Quasi-equilibria in Banach spaces with lower semi-continuous preferences

Summary. This paper establishes a general result on the existence of non-trivial quasi-equilibria for economies with infinitely many commodities, in which consumers preferences are assumed to be lower semi-continuous, but not necessarily to have open lower sections nor to be open valued. Such preference relations include the lexicographic orderings. In addition, production technologies are not required to satisfy free disposal condition.Received: 25 May 2004, Revised: Received: 25 May 2004; revised version: September: 14, 2004, JEL Classification Numbers: D51, D61, D62.I am grateful to Professors Sho-Ichiro Kusumoto, Atsushi Kajii, Yoshihiko Otani, Zaifu Yang and one anonymous referee for their helpful commente and suggestions.     

Evolutionary stability and lexicographic preferences

We explore the interaction between evolutionary stability and lexicographic preferences. To do so, we define a limit Nash equilibrium for a lexicographic game as the limit of Nash equilibria of nearby games with continuous preferences. Nash equilibria of lexicographic games are limit Nash equilibria, but not conversely. Modified evolutionarily stable strategies (Binmore and Samuelson, 1992. J. Econ. Theory 57, 278–305) are limit Nash equilibria. Modified evolutionary stability differs from “lexicographic evolutionarily stability” (defined by extending the common characterization of evolutionary stability to lexicographic preferences) in the order in which limits in the payoff space and the space of invasion barriers are taken.     

Necessity conditions in voting theory

In this paper we take some concepts of necessity conditions in voting theory first developed by Inada, Sen, and Pattanaik and refine those concepts to deal with the more commonly discussed case of fixed numbers of voters. These new concepts are then applied to the study of domain restrictions designed to yield quasitransitive and transitive social preference relations. Along the way, a conjecture of Pattanaik is settled.     

Lexicographic choice under variable capacity constraints

In several matching markets, to achieve diversity, agents' priorities are allowed to vary across an institution's available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined ordering of the seats, called a (capacity-constrained) lexicographic choice rule. We provide a characterization of lexicographic choice rules and a characterization of deferred acceptance mechanisms that operate based on a lexicographic choice structure under variable capacity constraints. We discuss some implications for the Boston school choice system and show that our analysis can be helpful in applications to select among plausible choice rules.     

Remarks on the first welfare theorem with nonordered preferences

A strong convexity assumption is used to establish the first fundamental theorem of welfare economics using the strong definition of Pareto optimality without assuming that the weak preference relations are complete or transitive. An example demonstrates that Debreu's (Proc. Nat. Acad. Sci., 40 (1954), 588–592) nonsatiation and convexity assumptions are insufficient to establish the result in the absence of transitivity.     

Epistemic equivalence of extended belief hierarchies

In this paper, we introduce a notion of epistemic equivalence between hierarchies of conditional beliefs and hierarchies of lexicographic beliefs, thus extending the standard equivalence results of Halpern (2010) and Brandenburger et al. (2007) to an interactive setting, and we show that there is a Borel surjective function, mapping each conditional belief hierarchy to its epistemically equivalent lexicographic belief hierarchy. Then, using our equivalence result we construct a terminal type space model for lexicographic belief hierarchies. Finally, we show that whenever we restrict attention to full-support beliefs, epistemic equivalence between a lexicographic belief hierarchy and a conditional belief hierarchy implies that an arbitrary Borel event is commonly assumed under the lexicographic belief hierarchy if and only if it is commonly strongly believed under the conditional belief hierarchy. This is the first result in the literature directly linking common assumption in rationality (Brandenburger et al., 2008) with common strong belief in rationality (Battigalli and Siniscalchi, 2002).     

Finite-dimensional utilities

Summary. Sufficient axioms are identified for the existence of a finite- dimensional quasilinear utility function whose lexicographically ordered vectors preserve a decision maker's preference order on a mixture set . It is shown that those axioms are also necessary for the linear lexicographic representation when the underlying set is a mixture space. Received: August 20, 1998; revised version: December 14, 1998     

In Defense of DEFECT

The one-state machine that always defects is the only evolutionarily stable strategy in the machine game that is derived from the prisoners' dilemma, when preferences are lexicographic in complexity. This machine is the only stochastically stable strategy of the machine game when players are restricted to choosing machines with a uniformly bounded complexity. Journal of Economic Literature Classification Numbers: C70, C72.     

Problems in valuing the benefits of biodiversity protection

This paper considers two problems in valuing the benefits of biodiversity protection. These are, firstly, that preferences for biodiversity protection may be lexicographic rather than utilitarian. The more individuals for whom this is true, the less is cost-benefit analysis validated as a means of decision making for biodiversity protection, since lexicographic preferences are incompatible with the Kaldor-Hicks Compensation Test. Secondly, people may be poorly informed about the meaning of biodiversity, complicating the use of contingent valuation as a means of measuring preservation benefits. This paper first discusses the meaning of biodiversity, and trends in diversity over time. We offer some empirical evidence with regard to lexicographic preferences; consider the implications of having poorly-informed consumers; and then report the results of a contingent valuation study of biodiversity protection with varying levels of information. We find that willingness to pay for biodiversity protection increases with the level of information provided.We thank David Pearce, participants at a seminar at University College London, and two referees for comments on earlier versions of this paper.     

Lexicographic compositions of multiple criteria for decision making

This paper considers two distinct procedures to lexicographically compose multiple criteria for social or individual decision making. The first procedure composes M binary relations into one, and then selects its maximal elements. The second procedure first selects the set of maximal elements of the first binary relation, and then within that set, chooses the maximal elements of the second binary relation, and iterates the procedure until the Mth binary relation. We show several distinct sets of conditions for the choice functions representing these two procedures to satisfy non-emptiness and choice-consistency conditions such as contraction consistency and path independence. We also examine the relationships between the outcomes of the two procedures. Finally we investigate under what conditions the outcomes of each procedure are independent of the order of lexicographic application of the criteria.     

Preference revelation with a limited number of indifference classes

Suppose that g is a strategy-proof social choice rule on the domain of all profiles of complete and transitive binary relations that have exactly m indifference classes. If and the range of g has three or more members, then g is dictatorial. If m = 2, then for any set X of feasible alternatives, there exist non-dictatorial and strategy-proof rules that are sensitive to the preferences of every individual and which have X as range.     

An axiomatic definition of the leximin

For a class of multicriterion decision making problems the set of lexicographic minimax in a set of alternatives with regard to the given criterion functions is characterized by six axioms: symmetry, independence of irrelevant alternatives, domination, separability, convexity, and monotone transformation. Each of the axioms is independent of the rest.     

Characterization of the existence of maximal elements of acyclic relations

Summary. We obtain a sufficient condition for the existence of maximal elements of irreflexive binary relations that generalizes the theorem of Bergstrom and Walker by relaxing the compactness condition to a weaker one that is naturally related to the relation. We then prove that the sufficient conditions used both in the Bergstrom-Walker Theorem and in our generalization provide a characterization of the existence of maximal elements of acyclic binary relations. Other sufficient conditions for the existence of maximal elements obtained by Mehta, by Peris and Subiza and by Campbell and Walker are shown to be necessary too. Received: May 28, 1997; revised version: October 5, 2000     

Efficiency First or Equity First? Two Principles and Rationality of Social Choice

This paper formalizes two different principles to socially rank allocations under efficiency-equity trade off. The efficiency-first social preference relation ranks an allocation x higher than an allocation y if and only if (i) x is Pareto-superior to y or (ii) x and y are Pareto-noncomparable and x is equity-superior to y. The equity-first social preference relation reverses the order of application of the two criteria. We show that the efficiency-first relation may have a cycle, whereas the equity-first relation is transitive. We also characterize and compare the sets of maximal elements for these social preference relations in the Edgeworth box and examine the nonemptiness of the sets. Journal of Economic Literature Classification Numbers: D71, D63, D61.     

Determinants of household savings in China and their role in quasi‐money supply1

This study derives household saving potential empirically from econometric models of Chinese urban and rural household consumption and uses this potential to explain household bank deposits. Model simulations are performed to analyse the effects of interest rates, income and income uncertainty on the saving potential and the bank deposits. The bank deposits variable is then used to explain quasi‐money supply. High bank absorption of household savings is found to account mainly for the rapid growth in quasi‐money, which in turn explains the exceptionally high M2/GDP ratio. Households’ savings are largely predictable from their regular consumption.     

能够为母公司创利的IBM实验室

多年来IBM不但是世界获得专利最多的高技术企业，而且它的实验室能为母公司盈得巨额利润，本文总结了该公司的成功经验，主要是：（一）研发资金雄厚；（二）有一大批高水平的科学家；（三）研发以市场为导向；（四）从管理体制上确保研发的经济效益；（五）强调基础研究的重要作用。（六）突出计算机服务业；（七）利用公关造势。     

论经济法律关系的二元结构与二重性--一种整体主义解释

经济法律关系是法律关系体系中的一种,是指由经济法调整而产生的经济有机体整体(通常以国家的各种机关为代表)与功能个体(通常指在市场经济中生产经营活动的个人或组织)及功能个体相互间的权利(职权)义务(职责)关系。经济法律关系的显著特性是:二元结构及二重性。二元结构是指,经济法律关系是由两种性质完全不同的权利义务体系构成:其一是,作为社会经济整体代表的经济机关在经济法律活动中形成的权利义务体系;其二是,作为经济功能个体的权利义务体系。二重性是指,经济法主体的同一行为,因其角色二重性,同时处于两重法律关系中,有两重不同的权利义务。