Juan Tejada

Centrality and power in social networks: a game theoretic approach

Abstract A new family of centrality measures, based on game theoretical concepts, is proposed for social networks. To reflect the interests that motivate the interactions among individuals in a network, a cooperative game in characteristic function form is considered. From the graph and the game, the graph-restricted game is obtained. Shapley value in a game is considered as actor’s power. The difference between actor’s power in the new game and his/her power in the original one is proposed as a centrality measure. Conditions are given to reach some desirable properties. Finally, a decomposition is proposed.

Polynomial calculation of the Shapley value based on sampling

In this paper we develop a polynomial method based on sampling theory that can be used to estimate the Shapley value (or any semivalue) for cooperative games. Besides analyzing the complexity problem, we examine some desirable statistical properties of the proposed approach and provide some computational results.

A general model for deriving preference structures from data

In this paper we comment upon the integrated model for valued preferences introduced by Fodor, Ovchinnikov and Roubens. In particular, while on one hand we revise basic assumptions and point out their intuitive meaning, on the other hand we propose an alternative mathematical justification of such a model which allows not only a better understanding of the obtained results, but also a functional characterization of the whole family of solutions.

Some problems on the definition of fuzzy preference relations

In this paper we deal with decision-making problems over an unfuzzy set of alternatives. On one hand, we propose the problem of finding a max-min transitive relation as near as possible to a given initial preference relation, under the least-squares criterion and such that it does not introduce deep qualitative changes. On the other hand, we define a linear extension of the initial preference relation between alternatives to a preference relation between lotteries.

The equalizer and the lexicographical solutions for cooperative fuzzy games: characterization and properties

In this paper we analyze the lexicographical solution for fuzzy TU games, we study its properties and obtain a characterization. The lexicographical solution was introduced by Sakawa and Nishizaki (Fuzzy Sets and Systems 61 (1994) 265 -275) as a solution for crisp TU games, and then extended as a value for fuzzy TU games. We approach the problem by means of the close relationship that exists between the lexicographical solution for crisp TU games and the least square nucleolus, a crisp value defined by Ruiz et al. (Internat. J. Game Theory 25 (1996) 113-134). Previously, and also based on this relationship, we axiomatically characterize the equalizer solution for fuzzy TU games. Both values, the equalizer and the lexicographical solutions, are based on the consideration of a measure of dissatisfaction of players rather than coalitions.

A necessary and sufficient condition for the existence of Orlovsky's choice set

Abstract In a previous paper [2], the authors proved that a property of ‘acyclity’ in fuzzy preference relations was a necessary and sufficient condition for the existence of unfuzzy nondominated alternatives when such a set of alternatives is finite. In this paper, a general property of ‘foundation’ is proved to be a necessary and sufficient condition, without requiring finiteness on the set of alternatives. Both concepts are based on classical results in crisp binary relations.

Structural properties of continuum systems

Abstract This paper deals with monotonic systems where the performance levels of the system and its components range from perfect functioning to complete failure, allowing any intermediate state in the unit interval. In particular, general bounds are found for the reliability of such systems. Moreover, it is shown how these continuum systems can be approached by finite multistate systems.

A polynomial rule for the problem of sharing delay costs in PERT networks

In this paper we define the weighted serial cost sharing rule for the cost allocation problem. We apply this new rule to the problem of sharing delay costs in a PERT network. This rule belongs to the Core and is the Weighted Shapley Value for a particular game. Furthermore, we present a characterization of this rule and a polynomial algorithm for its calculation.

A project game for PERT networks

An important topic in PERT networks is how to allocate the total expedition (or delay) for situations in which the project is not executed as planned. In order to do that we define a TU project game that satisfies some desirable properties from the management project and game theory point of view.

A rule for slack allocation proportional to the duration in a PERT network

In this paper, we define a new rule for the resolution of the slack allocation problem in a PERT network. This problem exists of allocating existing extra time in some paths among the activities belonging to those paths. The allocation rule that we propose assigns extra time to the activities proportionally to their durations in such a way that no path duration exceeds the completion time of the whole project. This time allocation enables us to make a schedule for the PERT project under study. We give two characterizations of the rule and we compare it with others that have been previously defined in the literature.