The quasilinearity of certain composite functionals associated to the celebrated Schwarz’s inequality for inner products is investigated . Applications for operators in Hilbert spaces are given as well. 1. Introduction Let X be a linear space over the real or complex number …eld K and let us denote by H (X) the class of all positive semi-de…nite Hermitian forms on X; or, for simplicity, nonnega...

We prove a recent conjecture of Duchêne and Rigo, stating that every complementary pair of homogeneous Beatty sequences represents the solution to an invariant impartial game. Here invariance means that each available move in a game can be played anywhere inside the game board. In fact, we establish such a result for a wider class of pairs of complementary sequences, and in the process generali...

A solution function for convex transferable utility games encourages the grand coalition if no player prefers (in a precise sense defined in the text) any coalition to the grand coalition. We show that the Shapley value encourages the grand coalition in all convex games and the τ -value encourages the grand coalitions in convex games up to three (but not more than three) players. Solution funct...

Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solution requires careful analysis: only some of the solutions are stable in the sense that no group of a...

When we are constantly and simultaneously bombarded with various types of sensory inputs, how do we make decisions or motor outputs to deal with the world in a meaningful manner? This is a central issue in multisensory integration. One example of such type of processing is eating, as placing food in one's mouth provides taste, olfactory and somatosensory (texture, temperature) information (Verh...

In a recent article, Douven and Williamson offer both (i) a rebuttal of various recent suggested sufficient conditions for rational acceptability and (ii) an alleged ‘generalization’ of this rebuttal, which, they claim, tells against a much broader class of potential suggestions. However, not only is the result mentioned in (ii) not a generalization of the findings referred to in (i), but in co...

As shown by Peleg, the core of market games is characterized by nonemptiness, individual rationality, superadditivity, the weak reduced game property, the converse reduced game property, and weak symmetry. It was not known whether weak symmetry was logically independent. With the help of a certain transitive 4-person TU game it is shown that weak symmetry is redundant in this result. Hence the ...

Bundling of products is very prevalent in the marketplace. For example, travel and a rental car (Dolan, 1987), music systems come as a bundle packages include airfare, lodging, and a rental car. Considerable economic of the speakers, amplifier, stereo, and graphic equalizer, and research has focused on the change in profits and consumer surplus that razors and razor blades are routinely sold to...

In this paper we give an axiomatic characterization of three families of measures of success de…ned by Laruelle and Valenciano (2005) for voting rules. Key words: collective decision-making, voting rules, axiomatization 1. Introduction The aim of this paper is to provide an axiomatization of the measures of success in voting rules. We look for a set of axioms, that is, assumptions that, whateve...

We explain why and how to deal with the definition, acceptability, computation and management of risk in a genuinely multitemporal way. Coherence axioms provide a representation of a risk-adjusted valuation. Some special cases of practical interest allowing for easy recursive computations are presented. The multiperiod extension of Tail VaR is discussed. 1. NEW QUESTIONS WITH MULTIPERIOD RISK R...