Modification of Semivalues for Games with Coalition Structures

Consideration of reference systems for semivalues leads us to a global representation of the action of a semivalue on a game. Using this representation, we show how to modify semivalues to take account of coalition structures on the player set. The players' allocations according to a semivalue, including a modified semivalue, can be computed by means of products of matrices obtained from the multilinear extension of the game.     

On the gearing adjustment. An axiomatic approach

The gearing adjustment is approached axiomatically. The gearing adjustment defines a capital maintenance concept; the revaluation criteria compatible with it are investigated. It is proved that one and only one kind of revaluation criterion is compatible with the gearing adjustment.     

Knots and blanks: The pragmatic foundation of logical principles

Logical principles, in particular the law of noncontradiction and the law of exclusion of middle term, play different roles at different levels of discourse: valid formulae in an axiomatic calculus, methodological requirements (of consistency and completeness) for formalized systems. When postulated as formal laws, —pvp and —(p·—p), they are totally interdefinable and equivalent as well (DeMorgan's transformations are proof of this). If postulated as methodological requirements, the principles are not equivalent, although they could still be said in some sense to be interdefinable (the existence of consistent yet incomplete systems shows that the requirements are not equivalent; still, completeness of a system can be defined in terms of consistency of another system which keeps a definite relationship with the first one).There exists a third level of discourse: scientific praxis. At this level, the principles come even farther apart: they neither have the same logical value nor is one definable in terms of the other. However, they keep a family resemblance which justifies our dealing with them jointly. Let us call the principles at this level pragmatic imperatives. They deal with paradoxes, which are of two types: knots (conflicts) and blanks (gaps in the scientific pattern). The left-hand pragmatic imperative says: Be intolerant with knots, try to remove (dissolve) them. The right-hand pragmatic imperative says: Try to remove (fill) all blanks. The knot-removing and the blank-dissolving imperatives are prior to and more important than the laws of noncontradiction and excluded middle and the requirements of consistency and completeness. Logical principles are not prime categories: pragmatic imperatives are primordial.     

Potential and probable pathological gamblers: Where do the differences lie?

A large proportion of adolescents engage in gambling activities and the prevalence of pathological gambling is high. This study presents a factor analysis of responses from 122 college students who obtained a score of 3 or greater on the South Oaks Gambling Screen (SOGS), the most widely used instrument to identify probable and potential pathological gamblers. The analysis showed five dimensions: Illegal Behaviors, Heavy Gambling, Eating Disorders, Parentally Modelled/Less Impulsive, and Worry. Analyses revealed that except for the Eating Disorders factor, all factors clearly differentiated the probable from potential pathological gamblers, as identified by the SOGS. Results raise important questions about the relationship of pathological gambling to other psychopathological or antisocial behaviors. Thus the probable pathological gambler category represents a wide-ranging behavioral profile that goes beyond gambling per se. Avenues for future research as well as clinical implications are discussed.This research was partially supported by grants from Le Fonds Richelieu, le Conseil Québécois de la Recherche Sociale and the Social Sciences and Humanities Research Council of Canada.     

Some advances in the study of the compatibility of three bivariate copulas

Summary In this paper we study the problem of the compatibility of three bivariate copulas, i.e., we look for conditions which allow us to assure the existence of a three-copula whose two-dimensional margins are given. As a particular case, we seek conditions for two bivariate copulasC ₁ andC ₂ under whichC ₂[C₁ (x, y), z] is a three-copula. We specifically study the compatibility of the copulasM, W andII with other copulas both in general and in the particular case. We also study the compatibility of a two-copula with convex linear combinations of other two-copulas. Several examples illustrate the results obtained in each case, and some applications are given.     

Agenda control in coalition formation

Theoretical models of government formation in political science usually assume that the head of state is non-strategic. In this paper, we analyze the power of an agenda setter who chooses the order in which players are recognized to form coalitions in simple games. We characterize those sets of players which can be imposed in the equilibrium coalition and show that the only decisive structures where the agenda setter can impose the presence of any minimal winning coalition are apex games, where a large player forms a winning coalition with any of the small players. Keywords: Government Formation, Agenda Control, Coalitional Bargaining, Finite Bargaining Rules. Received: 26 January 2001/Accepted: 31 July 2001     

A note on closure of the ILR and DLR classes under formation of coherent systems

In this paper, we give the closure of the class of increasing likelihood ratio (ILR) life distributions under the formation of certain coherent systems with independent and identically distributed components, and particularly in k-out-of-n systems. Some possible definitions of its dual class (DLR) are discussed and results about the closure are given. Furthermore, we include examples which show that these two aging classes are not closed under formation of special coherent systems. This work has been supported by Ministerio de Ciencia y Tecnologia, Grants PB96-1105 and BFM2000-0362.