The Core of a Coalitional Production Economy Without Ordered Preferences

It is shown that the core of a coalitional production economy with a balanced technology (Bohm [1974]) is nonempty, even if the consumers have preferences which are intransitive, provided the preferences are convex and continuous. Since such preferences cannot be represented by utility functions, this result does not follow from the nonemptiness of the core of a characteristic function game. Rather, the approach is closer to that of Ichiishi's [1981] social coalitional equilibrium

Reduced Form Auctions Revisited

This note uses Farkas’s Lemma to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite

On Equilibria of Excess Demand Correspondences

A new lemma on the existence of maximal elements of binary relations is proved and applied to a revealed preference relation on price vectors. The resulting maximal elements are equilibrium prices. This technique allows one to generalize results of Aliprantis and Brown [1982], Neuefeind [1980], and Geistdoerfer-Florenzano [1982]

Social Welfare Functions for Economic Environments with and without the Pareto Principle

Social welfare functions for private goods economies with classical preferences are considered. It is shown that every social welfare function satisfying a weak nonimposition condition and the independence of irrelevant alternatives axiom is of one of the following forms. It is either null or the class of decisive coalitions is an ultrafilter or the class of anti-decisive coalitions is an ultrafilter

More on Harsanyi's Utilitarian Cardinal Welfare Theorem

If individuals and society both obey the expected utility hypothesis and social alternatives are uncertain, then the social utility must be a linear combination of the individual utilities, provided the society is indifferent when all its members are. This result was first proven by Harsanyi [4] who made implicit assumptions in the proof not actually needed for the result (see [5]). This note presents a straightforward proof of Harsanyi's theorem based on a separating hyperplane argument

An Impossibility Theorem for Spatial Models

This paper examines the implications for social welfare functions of restricting the domain of individual preferences lo type-one preferences. Type-one preferences assume that each person has a most preferred alternative in a euclidean space and that alternatives are ranked according to their euclidean distance from this point. The result is that if we impose Arrow's conditions of collective rationality, IIA, and the Pareto principle on the social welfare function, then it must be dictatorial. This result may not seem surprising, but it stands in marked contrast to the problem considered by Gibbard and Saiterthwaite of finding a social-choice function. With unrestricted domain, under the Gibbard-Satterthwaite hypotheses, choices must be dictatorial. With type-one preferences this result has been previously shown not to be true. This finding identifies a significant difference between the Arrow and the Gibbard-Satterwaite hypothesis

Noncooperative Games, Abstract Economies, and Walrasian Equilibria

The introduction of an additional player to serve as coordinator in an N-person abstract economy leads in a natural way to an N+1-person noncooperative game. Sufficient conditions on the abstract economy are considered which lead to the existence of equilibrium in the resulting game and hence for the abstract economy

A Core Existence Theorem for Games Without Ordered Preferences

[Introduction] To a large extent the cooperative theory of games has an altogether different appearance from the noncooperative theory. The noncooperative theory generally deals with games in either extensive form or normal form, while the cooperative theory is usually described in characteristic function form. One of the central concepts in the cooperative theory is that of the core, which is the set of utility allocations which no coalition can improve upon. This notion of the core and of the characteristic function form of a game depends heavily on the existence of a utility representation for players' preferences. Recently Gale and Mas-Colell [3] and Shafer and Sonnenschein [6] have proven theorems on the existence of a Nash equilibrium for noncooperative games in normal form in which the players' preferences over strategy vectors are not necessarily complete or transitive and so may fail to have a utility representation. Thus it might appear that the noncooperative theory is applicable in environments where the cooperative theory is not. In order to formulate theorems in the cooperative theory of games which can be applied to environments in which players may have nonordered preferences, the characteristic function must be reformulated in terms of physical outcomes as opposed to utility outcomes. The players' preferences can then be expressed in terms of the physical outcomes without the use of a utility function

Preferences Over Solutions to the Bargaining Problem

There are several solutions to the Nash bargaining problem in the literature. Since various authors have expressed preferences for one solution over another, we find it useful to study preferences over solutions in their own right. We identify a set of appealing axioms on such preferences that lead to unanimity in the choice of solution, which turns out to be the solution of Nash

Dutch Book Arguments and Subjective Probability

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