Antonio Magaña

Uniqueness and Growth of Solutions in Two-Temperature Generalized Thermoelastic Theories

In this work we study modifications of the non-classical models of thermoelasticity, the one proposed Green and Lindsay and the one stated by Lord and Shulman, to two-temperature setting. We prove uniqueness results for the solutions of the systems of equations that model both theories for isotropic material. We also provide growth estimates for the solutions.

The multilinear extension and the modified Banzhaf-Coleman index

Abstract Owen suggests a modification of the Banzhaf-Coleman index for games where a coalition structure is given. We provide a procedure to obtain this new index by using the multilinear extension of the original game and we apply it to real-world examples.

Extension of values to games withmultiple alternatives

Games with multiple alternatives enlarge the domain of social situations modelled by the classical cooperative game theory. In this paper, we prove that any linear value defined for traditional cooperative games admits a natural extension to games with multiple alternatives. A method to compute the extended values is also provided. As specific examples, we present an application of the Shapley value and the Banzhaf-Coleman index to two voting situations taken from the real world.

Accessibility in oriented networks

The aim of this work consists of allocating a value that allows us to emphasize the importance of each player in a cooperative game when the cooperation possibilities are limited according to the links of an oriented network. The proposed concept of accessibility tries to conjugate the marginal contributions of each node as a game player with the cooperation geometry imposed by the digraph that models the network. We study general properties of this concept and particularly with respect to oriented paths. Concrete applications are proposed.

On the spatial behavior of solutions for porous elastic solids with quasi-static microvoids

The spatial behavior of solutions for the dynamic problem of elasticity with voids is well known. It has been analyzed making use of the usual techniques for hyperbolic differential equations. Here we consider a related but different problem, the problem determined by the dynamic deformations of porous elasticity with porous dissipation when the motion of the microvoids is supposed to be quasi-static. We think that this kind of dynamical problem deserves some consideration. However, little attention has been paid to it in the literature. On the one hand, the problem has interest from a mechanical point of view, because this is the system that one must study when the microvoids deformations are small enough as to assume that their acceleration is nearly zero. On the other hand, the problem has also interest from its mathematical structure, because the coupling of a parabolic equation with a hyperbolic one arises in the system.

On the Convenience to Form Coalitions or Partnerships in Simple Games

A partnership in a cooperative game is a coalition that possesses an internal structure and, simultaneously, behaves as an individual member. Forming partnerships leads to a modification of the original game which differs from the quotient game that arises when one or more coalitions are actually formed.In this paper, the Shapley value is used to discuss the convenience to form either coalitions or partnerships. To this end, the difference between the additive Shapley value of the partnership in the partnership game and the Shapley alliance value of the coalition, and also between the corresponding value of the internal and external players, are analysed. Simple games are especially considered.

Accessibility measures to nodes of directed graphs using solutions for generalized cooperative games

The aim of this paper consists of constructing accessibility measures to the nodes of directed graphs using methods of Game Theory. Since digraphs without a predefined game are considered, the main part of the paper is devoted to establish conditions on cooperative games so that they can be used to measure accessibility. Games that satisfy desirable properties are called test games. Each ranking on the nodes is then obtained according to a pair formed by a test game and a solution defined on cooperative games whose utilities are given on ordered coalitions. The solutions proposed here are extensions of the wide family of semivalues to games in generalized characteristic function form.

The Shapley–Shubik index for simple games with multiple alternatives

Abstract When analyzing mathematically decision mechanisms ruled by voting it is sometimes convenient to include abstention as a possible alternative for the voters. In classical simple games, abstention, if considered, is formally equivalent to voting against the proposal. Simple games with alternatives are useful to study voting systems where abstention does not favour any of the options. In this work, we axiomatically characterize the Shapley–Shubik index for simple games with alternatives and apply it to an example taken from real life.

The accessibility of an access structure

In secret sharing, different access structures have different difficulty degrees for acceding to the secret. We give a numerical measure of how easy or how difficult is to recover the secret, depending only on the structure itself and not on the particular scheme used for realizing it. We derive some consequences.

Alliances, partnerships and the Banzhaf semivalue

Abstract The coordination of strategies in a cooperative game, when some players decide to act together, is the basis of the partnership notion. Nevertheless, in some situations, it may be more convenient to form an effective coalition or alliance. In this work, we consider the Banzhaf semivalue and use it to discuss the convenience to form either partnerships or alliances, especially in simple games. Throughout the paper, some mathematical properties of the Banzhaf semivalue, in relation with the partnership formation, are derived.