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Simple games in Łukasiewicz calculus and their cores

Petr Cintula, Tomáš Kroupa (2013)

Kybernetika

We propose a generalization of simple coalition games in the context of games with fuzzy coalitions. Mimicking the correspondence of simple games with non-constant monotone formulas of classical logic, we introduce simple Łukasiewicz games using monotone formulas of Łukasiewicz logic, one of the most prominent fuzzy logics. We study the core solution on the class of simple Łukasiewicz games and show that cores of such games are determined by finitely-many linear constraints only. The non-emptiness...

Small perturbations with large effects on value-at-risk

Manuel L. Esquível, Luís Dimas, João Tiago Mexia, Philippe Didier (2013)

Discussiones Mathematicae Probability and Statistics

We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.

Smooth solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...

Smooth Solutions of systems of quasilinear parabolic equations

Alain Bensoussan, Jens Frehse (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear Hamiltonian seems to be...

Social network evolution and actor oriented models. Applications in the fields of friendship formation, decision making, emergence of cooperation, and coalition formation

Evelien P. H. Zeggelink (1997)

Mathématiques et Sciences Humaines

We present an overview of different actor oriented models of network evolution, that have been developed in the last couple of years. The models are constructed in different fields of application and all have in common that the emergence of network structure is directly or indirectly of interest. Each model is based on a set of actors and a set of behavioral rules of these actors, resulting in interaction mechanisms and the coming into existence of some network pattern of relationships. Actors vary...

Solidarity and cooperative bargaining solutions

Naoki Yoshihara (2006)

Banach Center Publications

In this paper, we consider production economies with possibly unequal production skills and with the possibility of technological innovations, in which resource allocations are determined via bargaining among individuals. We define the Nash (resp. the Kalai-Smorodinsky) bargaining solution as the (bargaining) allocation rule whose utility outcomes just result in the Nash (resp. the Kalai-Smorodinsky) bargaining outcomes. Two new axioms regarding compensation for low skill agents are introduced as...

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