Continuous representation of Von Neumann–Morgenstern preferences

This paper considers a continuous representation of preference relations satisfying Grandmont's (1972) Expected Utility Hypothesis. We equip the preferences with the topology of closed convergence, then we show the existence of a jointly continuous expected utility function and consider its uniqueness. Furthermore, we construct an embedding map of the preferences into the set of expected utility functions.     

Representing complete and incomplete subjective linear preferences on random numbers

We show that preferences on random numbers which satisfy certain natural properties can be represented, in the setting of topological vector spaces, by a suitable family of continuous previsions which is, in a sense, unique. Moreover, for most commonly used spaces of random numbers, we establish that one can derive these preferences, via an expectation operator, from a suitable family of probabilities (whether or not finitely additive). Mathematics Subject Classification (2000): 06A06, 62C05, 91B06 Journal of Economic Literature Classification: D11, D81     

Similarity of information and behavior with a pointwise convergence topology

A topology on the space of information is defined which makes the latter a complete separable metric space. In this metric, set-theoretic convergent sequences of information converge, and the set of finite partitions of the state space is dense. This topology is weaker than the one studied by Allen. In addition, an expected utility maximizing consumer's demand for commodities is a continuous function of his information, and this topology is the weakest one with that property.     

Social decision for a measure society

Preference aggregation is here investigated for a society defined as a measure space of individuals and called a measure society. Individual preferences are represented through continuous vnm utilities. It is shown that aggregating preferences in an utilitarian way for any kind of measure society is possible under adapted Pareto conditions.     

A continuous double implementation of the constrained Walras equilibrium

We provide a continuous and feasible double implementation of the Walras equilibrium. In our game form the set of traders is partitioned intok subsets,k>-2, and for each member of the partition there is an (outside) auctioneer. Also, each agent announces a price-allocation pair so that all agents become price takers. The outcome allocation is defined as the feasible (and budget balanced) allocation which is closest to the aggregate announced allocation. No assumptions are made on the preferences of the traders.     

Uniform allocation and reallocation revisited

Thomson (1995a) proved that the uniform allocation rule is the only allocation rule for allocation economies with single-peaked preferences that satisfies Pareto efficiency, no-envy,one-sided population-monotonicity, and replication-invariance on a restricted domain of single-peaked preferences. We prove that this result also holds on the unrestricted domain of single-peaked preferences. Next, replacing one-sided population-monotonicity by one-sided replacement-domination yields another characterization of the uniform allocation rule, Thomson (1997a). We show how this result can be extended to the more general framework of reallocation economies with individual endowments and single-peaked preferences. Following Thomson (1995b) we present allocation and reallocation economies in a unified framework of open economies. Received: 20 February 1999 / Accepted: 15 February 2000     

A note on the space of preference relations

The space of irreflexive, transitive, and continuous binary relations of R^l endowed with the topology of closed convergence, and subsets of defined by various other properties of the relations are investigated. It is shown that the subsets defined by properties, which one often assumes in general equilibrium theory, have nice topological properties such as compactness or G₈-ness.     

Limited arbitrage is necessary and sufficient for the existence of an equilibrium

In Chichilnisky (Working Paper No. 586, 1991), Chichilnisky (Working Paper No. 650, 1992) and Chichilnisky (Economic Theory, 1995, 5, 79–108), I introduced the concept of a global cone and used it to define a condition on endowments and preferences, ‘limited arbitrage’, which I showed to be necessary and sufficient for the existence of a competitive equilibrium. In response to a comment (Monteiro et al., Journal of Mathematical Economics, 1997, 26, 000-000), I show here that the authors misunderstood my results by focussing on brief announcements which cover other areas, social choice (Chichilnisky, American Economic Review, 1994, 427–434 and algebraic topology (Chichilnisky, Bulletin of the American Mathematical Society, 1993, 29, 189–207), rather than on the publication which contains may proofs on equilibrium. The comment's example is irrelevant to my results in Chichilnisky (Economic Theory, 1995, 5, 79–108) because it starts from different conditions. Limited arbitrae is always necessary and sufficient for the existence of a competitive equilibrium, with or without short sales, with the global cones as I defined them, and exactly as proved in Chichilnisky (Economic Theory, 1995, 5, 79–108).     

Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.     

Median unbiased estimates for M.L.R.-families

Summary Lehmann [p. 83] has shown that some families of probability measures with monotone likelihood ratios (m.l.r.) admit median unbiased estimates which are optimum in the sense that among all median unbiased estimates they minimize the expected loss for any loss function which assumes its minimal value zero for the “true” parameter value and is nondecreasing as the parameter moves away from the true value in either direction. This very strong optimum property was proved under the assumption that all probability measures of the m.l.r.-family have continuous distribution functions, that they are mutually absolutely continuous and that each element of the support is the median of somep-measure of the family. This result does therefore not cover important cases such as the binomial families or thePoisson family. The purpose of the present paper is to show the existence ofrandomized median unbiased estimates with the same optimum property for m.l.r.-families which are closed and connected with respect to the strong topology. Such families are always dominated. We do, however, neither assume that thep-measures are mutually absolutely continuous nor that the distribution functions are continuous. We remark that the use of randomized estimates is indispensable here because nonrandomized median unbiased estimates do not always exist in the general case.     

Economies with a mean demand function

The present paper shows one way to look at G. Debreu and W. Hildenbrand's conjecture that certain atomless economies have mean demand functions. We conclude within the continuity framework that an economy gives rise ‘in general’ to a continuous mean demand function, and that the class of all atomless economies is ‘big’ in the space of all economies with a continuous mean demand function. The same problems are reconsidered within the framework of a space of differentiable preferences at the end.     

Nash-implementation of competitive equilibria via a bounded mechanism

We deal with the problem of providing incentives for the implementation of competitive outcomes in a pure-exchange economy with finitely many households. We construct a feasible price-quantity mechanism, which fully implements Walras equilibria via Nash equilibria in fairly general environments. Traders’ preferences need neither to be ordered nor continuous. In addition, the mechanism is such that no pure strategy is weakly dominated, hence is bounded (in the sense of Jackson 1992). In particular it makes no use of any integer game.     

Multiple equilibria in two-sector monetary economies: An interplay between preferences and the timing for money

In this paper, we study the occurrence of local indeterminacy in two-sector monetary economies. We consider a general MIUF model with two alternative timings in monetary payments: the Cash-In-Advance timing, in which the cash available to buy goods is money in the consumers’ hands after they leave the bond market but before they enter the goods market, and the Cash-After-the-Market timing, in which agents hold money for transactions after leaving the goods market. We consider three standard specifications of preferences: the additively separable formulation, the Greenwood–Hercovitz–Huffman (GHH) (Greenwood et al., 1988) formulation and the King–Plosser–Rebelo (KPR) (King et al., 1988) formulation. First, we show that for all the three types of preferences, local indeterminacy occurs under the CIA timing with a low enough interest rate elasticity of money demand. Second, we show that with the CAM timing, although determinacy always holds under separable preferences, local indeterminacy can occur with GHH and KPR preferences. We thus prove that compared to aggregate models, two-sector models provide new rooms for local indeterminacy when non-separable standard preferences are considered.     

Neighboring information and distributions of agents' characteristics under uncertainty

This paper proposes a topological structure for information. Specifically, information is considered an arbitrary sub-σ-field of the σ-field (of measurable subsets of states of the world) which represents events. A complete metric is defined on the space of all equivalence classes of sub-σ-fields; its uniformity is the same for all probability measures (on the abstract measurable space of states of the world and events) which are uniformly absolutely continuous. With this topology, economic behavior depends continuously on the agent's information; demand functions under uncertainty are jointly continuous in utilities, endowments, and information. Moreover, the value of information is a continuous function of the information sub-σ-field. Technical properties of the topology are also given.     

Anonymity and continuous social choice

Continuity of social choice is reformulated in terms of the quotient topology on profiles of individual preferences induced by the equivalence class corresponding to anonymity. It is shown that Chichilnisky's impossibility continues to hold.     

A non-parametric approach to smoothing by aggregation over preferences

A distributional dispersion condition on C² monotone preferences, defined by unit normals to indifference surfaces, yields a C⁰ mean demand function when one integrates over such suitably diffuse consumers with convex preferences, regardless of the distribution of their initial endowments. For non-convex preferences, the dispersion condition implies that at any price vector, individual demands are finite sets for almost every agent. A stronger dispersion condition, involving both utility functions and unit normals, yields C⁰ mean demand functions with monotone non-convex preferences.     

Further remarks on totally ordered representable subsets of Euclidean space

We introduce the property of ? -norm-boundedness on totally ordered subsets of Euclidean spaces. We show that when a closed subset X of the Euclidean space ⁿ, endowed with a continuous total order ?, is ? -norm-bounded, the order topology and the induced Euclidean topology must coincide on X. This generalizes a recent result by Beardon, proved on connected totally ordered subsets of Euclidean space, because on totally ordered closed subsets of ⁿ connectedness is a particular case of ? -norm-boundedness. We also analyze necessary and sufficient conditions for the coincidence of both topologies, and discuss some extension to the infinite-dimensional context.     

Evaluating asset‐pricing models using the Hansen–Jagannathan bound: a Monte Carlo investigation

We use recent statistical tests, based on a ‘distance’ between the model and the Hansen–Jagannathan bound, to compute the rejection rates of true models. For asset‐pricing models with time‐separable preferences, the finite‐sample distribution of the test statistic associated with the risk‐neutral case is extreme, in the sense that critical values based on this distribution deliver type I errors no larger than intended—regardless of risk aversion or the rate of time preference. We also show that these maximal‐type‐I‐error critical values are appropriate for both time and state non‐separable preferences and that they yield acceptably small type II error rates. Copyright © 2002 John Wiley & Sons, Ltd.     

On the Economics of Moral Preferences

Abstract . The long‐standing critique of the “economic model of man” has gained new impetus, not least due to the broadening research in behavioral and experimental economics. Many of the critics have focused on the apparent difficulty of traditional rational choice theory to account for the role of moral or ethical concerns in human conduct, and a number of authors have suggested modifications in the standard model in response to such critique. This article takes issue with a quite commonly adopted “revisionist” strategy, namely, seeking to account for moral concerns by including them as additional preferences in an agent's utility function. It is argued that this strategy ignores the critical difference between preferences over outcomes and preferences over actions, and that it fails to recognize that “moral preferences” belong in the second category. Preferences over actions, however, cannot be consistently accounted for within a theoretical framework that focuses on the rationality of single actions. They require a shift of perspective, from a theory of rational choice to a theory of rule‐following behavior.     

Equilibria in large economies with a separable Banach commodity space and non-ordered preferences

The purpose of this paper is to provide an existence result of equilibria for economies with a measure space of agents, a non-trivial production sector and an infinite dimensional commodity space. The commodity space is modeled by an ordered separable Banach space whose positive cone has a non-empty interior. The discretization approach proposed in this paper, allows us to extend the existence results in Khan and Yannelis [Equilibrium in markets with a continuum of agents and commodities. In: Khan, M.A., Yannelis, N.C. (Eds.), Equilibrium Theory in Infinite Dimensional Spaces. Springer, Berlin, 1991] and Podczeck [Economic Theory 9 (1997) 585] to economies with a non-trivial production sector and with possibly non-ordered but convex preferences as well as partially ordered (possibly incomplete) but non-convex preferences.