Luisa Monroy

Multicriteria goal games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponents deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.

Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game

In this paper we study cooperative games with fuzzy payoffs. The main advantage of the approach presented is the incorporation into the analysis of the problem of ambiguity inherent in many real-world collective decision situations. We propose extensions of core concepts which maintain the fuzzy nature of allocations, and lead to a more satisfactory study of the problem within the fuzzy context. Finally, we illustrate the extended core concepts and the approach to obtain the corresponding allocations through the analysis of assignment games with uncertain profits.

An equitable solution for multicriteria bargaining games

In this paper we study bargaining models where the agents consider several criteria to evaluate the results of the negotiation process. We propose a new solution concept for multicriteria bargaining games based on the distance to a utopian minimum level vector. This solution is a particular case of the class of the generalized leximin solutions and can be characterized as the solution of a finite sequence of minimax programming problems.

Generalized Maximin Solutions in Multicriteria Bargaining

In this paper we address bargaining games where the agents have to take into account different criteria to value the decisions. We propose the class of generalized maximin solutions, as the natural extension for these games of the maximin solutions in conventional bargaining. In order to refine this solution concept, we define a multicriteria lexicographic partial ordering and present the class of generalized leximin solutions as those that are nondominated with respect to this relation. We establish some properties of these solutions and characterize them as solutions of multicriteria problems.

The Shapley-Shubik index for multi-criteria simple games

In this paper we address multi-criteria simple games which constitute an extension of the basic framework of voting systems and related social-choice situations. For these games, we propose the extended Shapley-Shubik index as the natural generalization of the Shapley-Shubik index in conventional simple games, and establish an axiomatic characterization of this power index.

A general model for voting systems with multiple alternatives

In this paper, the extension of simple games to the vector case is proposed. Games with multiple qualitative criteria and multi-criteria simple games are introduced as a natural tool for modelling voting systems and related social-choice situations. After formally defining these games, the special class of monotonic multi-criteria simple games is characterized. We show that these games enable the formulation and analysis of several collective decision models proposed in the literature. Furthermore, our model can be applied to group-decision problems which cannot be analyzed in the existing frameworks.

Multi-Criteria Simple Games

In this paper multi-criteria simple games are introduced. These games constitute an extension of the basic framework of voting systems and related social-choice situations and are a natural tool for modelling these kinds of problems. After introducing and formally defining these games, the special class of monotonic multi-criteria games is characterized. In addition, we analyze core solution concepts for multi-criteria simple games*.

Utopian Efficient Strategies in Multicriteria Matrix Games

In this paper we present a new solution concept for multiple objective problems which generalizes the balance points introduced by Galperin (1992). We apply this solution concept, called utopian efficiency, for solving multiple criteria matrix games. For these games it is shown how to get the whole set of utopian efficient strategies by means of multiobjective linear programs. Finally, we derive a decision criterion which is based on no ”a priori” information for choosing a strategy out of the proposed set.

Banzhaf index for multiple voting systems. An application to the European Union

Multi-criteria simple games constitute an extension of the basic framework of voting systems and collective decision-making. The study of power index plays an important role in the theory of multi-criteria simple games. Thus, in this paper, we propose the extended Banzhaf index for these games, as the natural generalization of this index in conventional simple games. This approach allows us to compare various criteria simultaneously. An axiomatic characterization of this power index is established. The Banzhaf index is computed by taking into account the minimal winning coalitions of each class. Since this index depends on the number of ways in which each player can effect a swing, one of the main difficulties for finding this index is that it involves a large number of computations. We propose a combinatorial procedure, based on generating functions, to obtain the Banzhaf index more efficiently for weighted multi-criteria simple games. As an application, the distribution of voting power in the European Union is calculated.

Two-person non-zero-sum gamesas multicriteria goal games

In this paper, we propose a new way to analyze bimatrix games. This new approach consists of considering the game as a bicriteria matrix game. The solution concepts behind this game are based on getting the probability to achieve some prespecified goals. We consider as a part of the solution, not only the payoff values, but also the probability to get them. In addition, to avoid the choice of only one goal, two different approaches are used. Firstly, sensitivity analysis of the solution set is carried out on the range of goals, secondly a partition of the goal space in a finite number of regions is presented. Some examples are included to illustrate the results in the paper.