Andrés Jiménez Losada - Academia.edu (original) (raw)

Papers by Andrés Jiménez Losada

Fuzzy Sets and Systems, 2019

This paper deals with cooperative games over fuzzy coalitions. In these situations there is a con... more This paper deals with cooperative games over fuzzy coalitions. In these situations there is a continuous set of fuzzy coalitions instead of a finite set of them (as in the classical case), the unit square in an n-dimensional space. There exist in the literature two different extensions of the known Shapley value for crisp games to games with fuzzy coalitions: the crisp Shapley value and the diagonal value. The first value only uses a finite information in the set of fuzzy coalitions, the vertices of the square. While the second one uses a neighbourhood of the diagonal of the square. We propose a new extension of the Shapley value improving the crisp Shapley value for games with fuzzy coalitions. This new version uses the faces of the square, namely an infinity quantity of information. We analyze several properties of the new value, we endow it with an axiomatization and we study the behavior when it is applied to known fuzziness of crisp games.

Symmetry

A cooperative game represents a situation in which a set of agents form coalitions in order to ac... more A cooperative game represents a situation in which a set of agents form coalitions in order to achieve a common good. To allocate the benefits of the result of this cooperation there exist several values such as the Shapley value or the Banzhaf value. Sometimes it is considered that not all communications between players are feasible and a graph is introduced to represent them. Myerson (1977) introduced a Shapley-type value for these situations. Another model for cooperative games is the Owen model, Owen (1977), in which players that have similar interests form a priori unions that bargain as a block in order to get a fair payoff. The model of cooperation introduced in this paper combines these two models following Casajus (2007). The situation consists of a communication graph where a two-step value is defined. In the first step a negotiation among the connected components is made and in the second one players inside each connected component bargain. This model can be extended to f...

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Lecture Notes in Computer Science, 2016

Fuzzy Sets and Systems, 2014

ABSTRACT A cooperative game consists of a set of players and a characteristic function which dete... more ABSTRACT A cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. It is often assumed that the players are free to participate in any coalition, but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions. Those relationships must be taken into account if we want to distribute the profits fairly. In this respect, several models have been proposed in literature. In all of them dependency relationships are considered to be complete, in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all. Nevertheless, in some situations it is possible to consider another option: that a player has a degree of freedom to cooperate within a coalition. A model for those situations is presented.

Top, 2002

In the classical model of games with transferable utility one assumes that each subgroup of playe... more In the classical model of games with transferable utility one assumes that each subgroup of players can form and cooperate to obtain its value. However, we can think that in some situations this assumption is not realistic, that is, not all coalitions are feasible. This suggests that it is necessary to raise the whole question of generalizing the concept of transferable utility game, and therefore to introduce new solution concepts. In this paper we define games on matroids and extend the τ-value as a compromise value for these games.

Top, 2000

The Shapley-Shubik power index in a voting situation depends on the number of orderings in which ... more The Shapley-Shubik power index in a voting situation depends on the number of orderings in which each player is pivotal. The Banzhaf power index depends on the number of ways in which each voter can e¤ect a swing. We introduce a combinatorial method based in generating functions for computing these power indices e¢ciently and we study the time complexity of the algorithms. We also analyze the meet of two weighted voting games. Finally, we compute the voting power in the Council of Ministers of the European Union with the generating functions algorithms and we present its implementation in the system Mathematica. Mathematics Subject Classi…cation 2000: 91A12.

Mathematical Methods of Operations Research (ZOR), 2003

Games on antimatroids are cooperative games restricted by a combinatorial structure which general... more Games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economic and politic. Therefore, the study of the rectricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Shapley value on antimatroids by conditions on the cooperative game v and the structure determined by the antimatroid. This axiomatization generalizes the axiomatizations of both the conjunctive and disjunctive permission value for games with a permission structure. We also provide an axiomatization of the Shapley value restricted to the smaller class of poset antimatroids.

Mathematical Methods of Operations Research (ZOR), 2002

According to the work of Faigle [3] a static Shapley value for games on matroids has been introdu... more According to the work of Faigle [3] a static Shapley value for games on matroids has been introduced in Bilbao, Driessen, Jiménez-Losada and Lebrón [1]. In this paper we present a dynamic Shapley value by using a dynamic model which is based on a recursive sequence of static models. In this new model for games on matroids, our main result is that there exists a unique value satisfying analogous axioms to the classical Shapley value. Moreover, we obtain a recursive formula to calculate this dynamic Shapley value. Finally, we prove that its components are probabilistic values.

Mathematical Methods of Operations Research (ZOR), 2001

In the classical model of cooperative games, it is considered that each coalition of players can ... more In the classical model of cooperative games, it is considered that each coalition of players can form and cooperate to obtain its worth. However, we can think that in some situations this assumption is not real, that is, all the coalitions are not feasible. This suggests that it is necessary to rise the whole question of generalizing the concept of cooperative game, and therefore to introduce appropriate solution concepts. We propose a model for games on a matroid, based in several important properties of this combinatorial structure and we introduce the probabilistic Shapley value for games on matroids.

Information Sciences, 2014

ABSTRACT A cooperative game consists of a set of players and a characteristic function which dete... more ABSTRACT A cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. A permission structure over the set of players describes a hierarchical organization where there are players who need permission from certain other players before they are allowed to cooperate with others. Various assumptions can be made about how a permission structure affects the cooperation possibilities. In the conjunctive approach it is assumed that each player needs permission from all his superiors. This paper deals with fuzzy permission structures in the conjunctive approach. In this model, players could depend partially on other players, that is, they may have certain degree of autonomy. First, we define a value for games with fuzzy permission structure that only takes into account the direct relations among players and provide a characterization for this value. Finally, we study a value for games with fuzzy permission structure which takes account of the indirect relations among players.

Fuzzy Sets and Systems, 2013

In 1977, Myerson considered cooperative games with communication structure. A communication struc... more In 1977, Myerson considered cooperative games with communication structure. A communication structure is an undirected graph describing the bilateral relationships among the players. He introduced the concept of allocation rule for a game as a function obtaining an outcome for each communication structure among the players of the game. The Myerson value is a specific allocation rule extending the Shapley value of the game. More recently, the authors studied games with fuzzy communication structures using fuzzy graph-theoretic ideas. Now we propose a general framework in order to define fuzzy Myerson values. Players in a coalition need to measure their profit using their real individual and communication capacities at every moment because these attributes are fuzzy when the game is proposed. So, they look for forming connected coalitions working at the same level. The different ways to obtain these partitions by levels determine different Myerson values for the game. Several interesting examples of these ways are studied in the paper, following known models in games with fuzzy coalitions: the proportional model and the Choquet model.

Fuzzy Sets and Systems, 2013

In 2013, Jiménez-Losada et al. introduced several extensions of the Myerson value for games with ... more In 2013, Jiménez-Losada et al. introduced several extensions of the Myerson value for games with fuzzy communication structure. In a fuzzy communication structure the membership of the players and the relations among them are leveled. Now we study a Banzhaf value for these situations. The Myerson model is followed to define the fuzzy graph Banzhaf value taking as base point the Choquet integral. We propose an axiomatization for this value introducing leveled amalgamation of players. An algorithm to calculate this value is provided and its complexity is studied. Finally we show an applied example computing by this fuzzy value the power of the groups in the European Parliament.

European Journal of Operational Research, 2009

This paper deals with cooperative games in which only certain coalitions are allowed to form. The... more This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed.

Discrete Mathematics, 2004

and it is a condition of accessing publications that users recognise and abide by the legal requi... more and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research-You may not further distribute the material or use it for any profit-making activity or commercial gain-You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Fuzzy Sets and Systems, 2019

This paper deals with cooperative games over fuzzy coalitions. In these situations there is a con... more This paper deals with cooperative games over fuzzy coalitions. In these situations there is a continuous set of fuzzy coalitions instead of a finite set of them (as in the classical case), the unit square in an n-dimensional space. There exist in the literature two different extensions of the known Shapley value for crisp games to games with fuzzy coalitions: the crisp Shapley value and the diagonal value. The first value only uses a finite information in the set of fuzzy coalitions, the vertices of the square. While the second one uses a neighbourhood of the diagonal of the square. We propose a new extension of the Shapley value improving the crisp Shapley value for games with fuzzy coalitions. This new version uses the faces of the square, namely an infinity quantity of information. We analyze several properties of the new value, we endow it with an axiomatization and we study the behavior when it is applied to known fuzziness of crisp games.

Symmetry

A cooperative game represents a situation in which a set of agents form coalitions in order to ac... more A cooperative game represents a situation in which a set of agents form coalitions in order to achieve a common good. To allocate the benefits of the result of this cooperation there exist several values such as the Shapley value or the Banzhaf value. Sometimes it is considered that not all communications between players are feasible and a graph is introduced to represent them. Myerson (1977) introduced a Shapley-type value for these situations. Another model for cooperative games is the Owen model, Owen (1977), in which players that have similar interests form a priori unions that bargain as a block in order to get a fair payoff. The model of cooperation introduced in this paper combines these two models following Casajus (2007). The situation consists of a communication graph where a two-step value is defined. In the first step a negotiation among the connected components is made and in the second one players inside each connected component bargain. This model can be extended to f...

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Studies in Fuzziness and Soft Computing, 2017

Lecture Notes in Computer Science, 2016

Fuzzy Sets and Systems, 2014

ABSTRACT A cooperative game consists of a set of players and a characteristic function which dete... more ABSTRACT A cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. It is often assumed that the players are free to participate in any coalition, but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions. Those relationships must be taken into account if we want to distribute the profits fairly. In this respect, several models have been proposed in literature. In all of them dependency relationships are considered to be complete, in the sense that either a player is allowed to fully cooperate within a coalition or they cannot cooperate at all. Nevertheless, in some situations it is possible to consider another option: that a player has a degree of freedom to cooperate within a coalition. A model for those situations is presented.

Top, 2002

In the classical model of games with transferable utility one assumes that each subgroup of playe... more In the classical model of games with transferable utility one assumes that each subgroup of players can form and cooperate to obtain its value. However, we can think that in some situations this assumption is not realistic, that is, not all coalitions are feasible. This suggests that it is necessary to raise the whole question of generalizing the concept of transferable utility game, and therefore to introduce new solution concepts. In this paper we define games on matroids and extend the τ-value as a compromise value for these games.

Top, 2000

The Shapley-Shubik power index in a voting situation depends on the number of orderings in which ... more The Shapley-Shubik power index in a voting situation depends on the number of orderings in which each player is pivotal. The Banzhaf power index depends on the number of ways in which each voter can e¤ect a swing. We introduce a combinatorial method based in generating functions for computing these power indices e¢ciently and we study the time complexity of the algorithms. We also analyze the meet of two weighted voting games. Finally, we compute the voting power in the Council of Ministers of the European Union with the generating functions algorithms and we present its implementation in the system Mathematica. Mathematics Subject Classi…cation 2000: 91A12.

Mathematical Methods of Operations Research (ZOR), 2003

Games on antimatroids are cooperative games restricted by a combinatorial structure which general... more Games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economic and politic. Therefore, the study of the rectricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Shapley value on antimatroids by conditions on the cooperative game v and the structure determined by the antimatroid. This axiomatization generalizes the axiomatizations of both the conjunctive and disjunctive permission value for games with a permission structure. We also provide an axiomatization of the Shapley value restricted to the smaller class of poset antimatroids.

Mathematical Methods of Operations Research (ZOR), 2002

According to the work of Faigle [3] a static Shapley value for games on matroids has been introdu... more According to the work of Faigle [3] a static Shapley value for games on matroids has been introduced in Bilbao, Driessen, Jiménez-Losada and Lebrón [1]. In this paper we present a dynamic Shapley value by using a dynamic model which is based on a recursive sequence of static models. In this new model for games on matroids, our main result is that there exists a unique value satisfying analogous axioms to the classical Shapley value. Moreover, we obtain a recursive formula to calculate this dynamic Shapley value. Finally, we prove that its components are probabilistic values.

Mathematical Methods of Operations Research (ZOR), 2001

In the classical model of cooperative games, it is considered that each coalition of players can ... more In the classical model of cooperative games, it is considered that each coalition of players can form and cooperate to obtain its worth. However, we can think that in some situations this assumption is not real, that is, all the coalitions are not feasible. This suggests that it is necessary to rise the whole question of generalizing the concept of cooperative game, and therefore to introduce appropriate solution concepts. We propose a model for games on a matroid, based in several important properties of this combinatorial structure and we introduce the probabilistic Shapley value for games on matroids.

Information Sciences, 2014

ABSTRACT A cooperative game consists of a set of players and a characteristic function which dete... more ABSTRACT A cooperative game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. A permission structure over the set of players describes a hierarchical organization where there are players who need permission from certain other players before they are allowed to cooperate with others. Various assumptions can be made about how a permission structure affects the cooperation possibilities. In the conjunctive approach it is assumed that each player needs permission from all his superiors. This paper deals with fuzzy permission structures in the conjunctive approach. In this model, players could depend partially on other players, that is, they may have certain degree of autonomy. First, we define a value for games with fuzzy permission structure that only takes into account the direct relations among players and provide a characterization for this value. Finally, we study a value for games with fuzzy permission structure which takes account of the indirect relations among players.

Fuzzy Sets and Systems, 2013

In 1977, Myerson considered cooperative games with communication structure. A communication struc... more In 1977, Myerson considered cooperative games with communication structure. A communication structure is an undirected graph describing the bilateral relationships among the players. He introduced the concept of allocation rule for a game as a function obtaining an outcome for each communication structure among the players of the game. The Myerson value is a specific allocation rule extending the Shapley value of the game. More recently, the authors studied games with fuzzy communication structures using fuzzy graph-theoretic ideas. Now we propose a general framework in order to define fuzzy Myerson values. Players in a coalition need to measure their profit using their real individual and communication capacities at every moment because these attributes are fuzzy when the game is proposed. So, they look for forming connected coalitions working at the same level. The different ways to obtain these partitions by levels determine different Myerson values for the game. Several interesting examples of these ways are studied in the paper, following known models in games with fuzzy coalitions: the proportional model and the Choquet model.

Fuzzy Sets and Systems, 2013

In 2013, Jiménez-Losada et al. introduced several extensions of the Myerson value for games with ... more In 2013, Jiménez-Losada et al. introduced several extensions of the Myerson value for games with fuzzy communication structure. In a fuzzy communication structure the membership of the players and the relations among them are leveled. Now we study a Banzhaf value for these situations. The Myerson model is followed to define the fuzzy graph Banzhaf value taking as base point the Choquet integral. We propose an axiomatization for this value introducing leveled amalgamation of players. An algorithm to calculate this value is provided and its complexity is studied. Finally we show an applied example computing by this fuzzy value the power of the groups in the European Parliament.

European Journal of Operational Research, 2009

This paper deals with cooperative games in which only certain coalitions are allowed to form. The... more This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed.

Discrete Mathematics, 2004

and it is a condition of accessing publications that users recognise and abide by the legal requi... more and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research-You may not further distribute the material or use it for any profit-making activity or commercial gain-You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.