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Lexicographic composition of abstract games
(2010-01-18)
In this paper we begin by obtaining a necessary and sufficient condition for a quasi transitive binary relation to be transitive. Then we obtain necessary and sufficient conditions for the lexicographic composition of two ...
Consequence of chernoff and outcasting and solutions for abstract games
(2010-01-16)
The purpose of this paper is to prove by induction the theorem (in Aizerman and Malishevski [1981]) that a choice function which satisfies Chernoffs axiom and Outcasting can always by expressed as the union of the solution ...
Preservation of proximity and merging functions
(2010-01-16)
In this paper we are interested in a property due to Baigent (1987) called proximity preserving. In the conventional model of voting theory it was proposed by Baigent that aggregation procedures should be proximity preserving ...
One dimensional kakutani's fixed point theorem: a classroom capsule
(2010-01-16)
A feature of the study of such problems which is difficult to miss is that there is a clear dichotomy between the analytical methodology concerning the study of problems of fair division of just one commodity and the ...
Axiomatic characterisation of weighted voting operator
(2010-01-18)
A federation voting operator allows a finite set of coalitions to unilaterally elect any outcome. There are several special types of federation voting operators, all of which share a property: the candidates are assigned ...
Note on characterising the median
(2010-01-16)
Consider the situation where one has to choose one among three differently priced birthday cakes, to give to a friends. It is very likely, that in the absence of strong personal reasons, one would select the cake whose ...
One dimensional Kakutani's fixed point theorem in problems of fair division: a classroom capsule
(2010-01-16)
In this paper, we provide a simple proof of the one-dimensional version of the Kakutani s fixed point theorem, which is required to prove the existence of a Walrasian equilibrium in a two commodity multi-agent economy where ...
Abstract games admitting stable solutions
(2010-01-16)
An abiding problem in choice theory has been one of characterizing those choice functions which are obtained as a result of some kind of optimization. Specifically, the endeavour has concentrated largely on finding a binary ...
Threshold and median rank solutions for transitive abstract games
(2010-01-16)
In this paper we consider solutions defined on the class of transitive games. A solution is said to be a threshold solution, if for every subgame there exists an alternative such that the solution set for the subgame ...
Indirect utility extension: axiomatic characterizations
(2010-01-18)
In this paper, we first provide several axiomatic characterizations of the indirect utility extension. The general problem we are interested in this paper is of the following variety: We are given a finite universal set ...