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  • A new allocation method for simple barganing problems: the Shapley rule

     Carreras Escobar, Francisco; Owen, Guillermo
    Date of publication: 2014
    Book chapter

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  • Power, cooperation indices and coalition structures

     Amer Ramon, Rafael; Carreras Escobar, Francisco
    Date of publication: 2013
    Book chapter

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    The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publication "Power, voting and voting power" (edited by Manfred J.Holler.) Thirty years later this essential topic has been taken up again and many of the authors from its predecessor participate here again in discussing the state-of-the-art, demonstrating the achievements of three decades of intensive research, and pointing the way to key issues for future work.

    The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publication

  • Pure bargaining problems and the Shapley rule

     Carreras Escobar, Francisco; Owen, Guillermo
    Date of publication: 2013
    Book chapter

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    The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publication "Power, voting and voting power" (edited by Manfred J.Holler.) Thirty years later this essential topic has been taken up again and many of the authors from its predecessor participate here again in discussing the state-of-the-art, demonstrating the achievements of three decades of intensive research, and pointing the way to key issues for future work.

    The developments over a thirty-year time span in the study of power, especially voting power, are traced in this book, which provides an up-to-date overview of applications of n-person game theory to the study of power in multimember bodies. Other theories that shed light on power distribution (e.g. aggregation theory) are treated as well. the book revisits the themes discussed in the well-known 1982 publication

  • Axiomatic characterizations of the proportional partitional Shapley value

     Costa, Julián; Alonso, José-María; Carreras Escobar, Francisco; García Jurado, Ignacio
    Spain-Italy-Netherlands Meeting on Game Theory
    Presentation's date: 2013-07-09
    Presentation of work at congresses

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  • Cooperation tendencies in games with a coalition structure

     Puente Del Campo, Mª Albina; Carreras Escobar, Francisco
    Congreso Nacional de Estadística e Investigación Operativa y Jornadas de Estadística Pública
    Presentation's date: 2013-09-11
    Presentation of work at congresses

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  • Cooperation tendencies and evaluation of games

     Carreras Escobar, Francisco; Puente Del Campo, Mª Albina
    International Conference on Enterprise International Systems
    Presentation's date: 2013-07-04
    Presentation of work at congresses

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    Multinomial probabilistic values were first introduced by one of us in reliability and later on by the other, independently, as power indices. Here we study them on cooperative games from several viewpoints, and especially as a powerful generalization of binomial semivalues. We establish a dimensional comparison between multinomial values and binomial semivalues and provide two characterizations within the class of probabilistic values: one for each multinomial value and another for the whole family. An example illustrates their use in practice as power indices.

    Multinomial probabilistic values were first introduced by one of us in reliability and later on by the other, independently, as power indices. Here we study them on cooperative games from several viewpoints, and especially as a powerful generalization of binomial semivalues. We establish a dimensional comparison between multinomial values and binomial semivalues and provide two characterizations within the class of probabilistic values: one for each multinomial value and another for the whole family. An example illustrates their use in practice as power indices.

  • TEORIA DE JUEGOS: FUNDAMENTOS MATEMÁTICOS Y APLICACIONES

     Amer Ramon, Rafael; Carreras Escobar, Francisco; Freixas Bosch, Josep; Giménez Pradales, José Miguel; Llongueras Arola, Maria Dolors; Magaña Nieto, Antonio; Molinero Albareda, Xavier; Pons Vallès, Montserrat; Puente Del Campo, Mª Albina; Sales Ingles, Vicente
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  • A new allocation method for simple bargaining problems: the Shapley rule

     Carreras Escobar, Francisco
    International Conference on Operations Research
    Presentation's date: 2012-09-06
    Presentation of work at congresses

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  • A model for players' tendencies when playing a cooperative game

     Puente Del Campo, Mª Albina; Carreras Escobar, Francisco
    European Conference on Operational Research
    Presentation's date: 2012-07-09
    Presentation of work at congresses

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    We present the theory for multibinary probabilistic values on cooperative games. As they are defined by tendency profiles, new tools are provided to encompass situations due to the influence of players' personality when playing a given game. When the profile is positive, the multilinear extension is a potential function and gives a computational tool. We also adapt to these values some properties, concerning null and nonnull players, balanced contributions, dominance and monotonicity, and regularity arises as a convenient condition. The subject falls within the topic of restricted cooperation.

  • On two allocation methods: proportional rule vs. Shapley rule

     Carreras Escobar, Francisco; Owen Salazar, Guillermo
    Congrès Annuel de la Société Française de Recherche Opérationnelle et d'Aide à la Décision
    Presentation's date: 2012-04-11
    Presentation of work at congresses

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  • El valor coalicional proporcional de Shapley para juegos con comunicación restringida

     Alonso Meijide, José María; Carreras Escobar, Francisco; Costa Bouzas, Julián; García Jurado, Ignacio
    Congreso Nacional de Estadística e Investigación Operativa y Jornadas de Estadística Pública
    Presentation's date: 2012-04-20
    Presentation of work at congresses

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  • Symmetric coalitional binomial semivalues

     Carreras Escobar, Francisco; Puente Del Campo, Mª Albina
    Group decision and negotiation
    Date of publication: 2011-03-01
    Journal article

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    We introduce here a family of mixed coalitional values. They extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the Shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched

    We introduce here a family of mixed coalitional values. They extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the Shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched

  • The proportional coalitional Shapley value

     Alonso-Meijide, José María; Carreras Escobar, Francisco
    Expert systems with applications
    Date of publication: 2011-06
    Journal article

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    We propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by any union coincides with the Shapley value of the union in the quotient game; and (2) the players of the union share this amount proportionally to their Shapley value in the original game (i.e., without unions). We provide axiomatic characterizations of this value close to those existing in the literature for the Owen value and include applications to coalition formation in bankruptcy and voting problems.

  • Power and potential maps induced by any semivalue: some algebraic properties and computation by multilinear extensions

     Carreras Escobar, Francisco; Giménez Pradales, José Miguel
    European journal of operational research
    Date of publication: 2011-05-16
    Journal article

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    The notions of total power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of cooperative games on any given player set where the semivalue is defined. Several properties of these linear mappings are stated and the role of unanimity games as eigenvectors is described. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game. As a consequence, we derive a method to compute for any semivalue by means of multilinear extensions, in the original game and also in all its subgames, (a) the total power, (b) the potential, and (c) the allocation to each player given by the semivalue.

  • A note on decisive symmetric games

     Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente Del Campo, Mª Albina
    Decision support systems
    Date of publication: 2011
    Journal article

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    Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the “decisiveness index” of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricted to decisive symmetric games and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negative, in p when p=1/2 takes the decisiveness to quickly approach, respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.

  • Pure bargaining problems and the Shapley rule

     Carreras Escobar, Francisco; Owen Salazar, Guillermo
    Homo oeconomicus
    Date of publication: 2011
    Journal article

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  • A procedure to compute allocations by semivalues on cooperative games through modified multilinear extensions

     Giménez Pradales, José Miguel; Carreras Escobar, Francisco
    IADIS Multi Conference on Computer Science and Information Systems
    Presentation's date: 2011-07-25
    Presentation of work at congresses

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  • A new value for cooperative games with a coalition structure

     Carreras Escobar, Francisco; Alonso-Meijide, José María
    Congrès Annuel de la Société Française de Recherche Opérationnelle et d'Aide à la Décision
    Presentation's date: 2011-03-04
    Presentation of work at congresses

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  • The proportional coalitional Shapley value for cooperative games with a coalition structure

     Carreras Escobar, Francisco; Alonso-Meijide, José María
    Spanish-Italian-Netherlands Meeting on Game Theory
    Presentation's date: 2011-07-19
    Presentation of work at congresses

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  • Shapley rule, core and monotonicity

     Carreras Escobar, Francisco; Owen, Guillermo
    Congreso Galego de Estatística e Investigación de Opéracions
    Presentation's date: 2011-11-03
    Presentation of work at congresses

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  • Multilinear extensions and semivalues related through potential maps

     Carreras Escobar, Francisco; Giménez Pradales, José Miguel
    Congreso Galego de Estatística e Investigación de Operacións
    Presentation's date: 2011-11-04
    Presentation of work at congresses

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  • Multibinary probabilistic values

     Puente Del Campo, Mª Albina; Carreras Escobar, Francisco
    Spanish-Italian-Netherlands Meeting on Game Theory
    Presentation's date: 2011-07-19
    Presentation of work at congresses

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  • The Shapley rule for simple bargaining problems with a coalition structure

     Carreras Escobar, Francisco; Owen, Guillermo
    International Conference on Operations Research
    Presentation's date: 2011-09-01
    Presentation of work at congresses

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  • One parameter per player: a class of balanced probabilistic values

     Carreras Escobar, Francisco; Puente Del Campo, Mª Albina
    Date: 2011-05
    Report

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  • Decisiveness of decisive symmetric games

     Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente Del Campo, Mª Albina
    Date: 2011-04-08
    Report

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    Symmetric coalitional binomial semivalues  Open access

     Carreras Escobar, Francisco; Puente Del Campo, Mª Albina
    Date: 2011-02-02
    Report

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    We introduce here a family of mixed coalitional values. they extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotidient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.

    Reseach supported by Grant SGR 2009-01029 of the Catalonia Government (Generalitat de Catalunya) and Frants MTM 2006-06064 and MTM 2009-08037 of the Science and Innovation Spanish Ministry and the European Regional Development Fund.

  • Solidarity and consistency in simple bargaining problems

     Carreras Escobar, Francisco; Owen, Guillermo
    European Conference on Mathematics for Industry
    Presentation's date: 2010-07-29
    Presentation of work at congresses

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  • Shapley rule for simple bargaining problems with a coalition structure

     Carreras Escobar, Francisco; Owen, Guillermo
    Congreso Nacional de Estadística e Investigación Operativa y Jornadas de Estadística Pública
    Presentation's date: 2010-09-15
    Presentation of work at congresses

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  • On the generalized decisiveness of decisive symmetric games

     Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente Del Campo, Mª Albina
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2010-09-17
    Presentation of work at congresses

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  • The proportional coalitional Shapley value

     Carreras Escobar, Francisco
    European Conference on Operational Research
    Presentation's date: 2010-07-13
    Presentation of work at congresses

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  • A value for games with a coalition structure

     Carreras Escobar, Francisco; Alonso Meijide, José María
    International Conference on Operations Research
    Presentation's date: 2010-09-02
    Presentation of work at congresses

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  • TEORÍA DE JUEGOS Y SISTEMAS DE DECISIÓN COLECTIVA CON APLICACIONES TECNOLÓGICAS, ECONÓMICAS, POLÍTICAS Y SOCIOLÓGICAS

     Freixas Bosch, Josep; Amer Ramon, Rafael; Carreras Escobar, Francisco; Giménez Pradales, José Miguel; Llongueras Arola, Maria Dolors; Molinero Albareda, Xavier; Pons Vallès, Montserrat; Puente Del Campo, Mª Albina; Sales Ingles, Vicente; Magaña Nieto, Antonio
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  • Semivalues: power, potential and multilinear extensions

     Carreras Escobar, Francisco; Giménez Pradales, José Miguel
    Date: 2010-12-20
    Report

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  • Protectionism and blocking power indices

     Carreras Escobar, Francisco
    TOP
    Date of publication: 2009-07
    Journal article

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  • Partnership formation and binomial semivalues

     Carreras Escobar, Francisco; Llongueras Arola, Maria Dolors; Puente Del Campo, Mª Albina
    European journal of operational research
    Date of publication: 2009-01
    Journal article

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  • Access to the full text
    Notas sobre los rappels y los descuentos uniformes  Open access

     Magaña Nieto, Antonio; Carreras Escobar, Francisco; Rajadell Carreras, Manuel
    Intangible capital
    Date of publication: 2009
    Journal article

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    Consideramos los descuentos comerciales por compras basados en rappels. Si se plantea un descuento de tipo uniforme aparece una paradoja no deseada: el “truco del comprador”. Para eludirla se proponen dos variantes que respetan el principio básico de “a mayor pedido, mayor descuento”. La primera es la de los descuentos continuos. La segunda, la de los descuentos graduales.

  • 2009 SGR 1029-Grup de recerca de teoria de jocs (L-00411)

     Freixas Bosch, Josep; Carreras Escobar, Francisco; Giménez Pradales, José Miguel; Llongueras Arola, Maria Dolors; Puente Del Campo, Mª Albina; Amer Ramon, Rafael; Magaña Nieto, Antonio; Sales Ingles, Vicente; Pons Vallès, Montserrat
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  • A new coalitional value

     Carreras Escobar, Francisco; Alonso Meijide, José María
    Date: 2009-10
    Report

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    We propose a modification of the Shapley value for monotonic games with a coalition structure. The resulting coalitional value is a twofold extension of the Shapley value in the following sense: (1) the amount obtained by any union coincides with the Shapley value of the union in the quotient game; and (2) the players of the union share this amount proportionally to their Shapley value in the original game (i.e., without unions). We provide axiomatic characterizations of this value close to those existing in the literature for the Owen value and include applications to coalition formation in bankruptcy and voting problems.

  • A proportional extension of the Shapley value for monotone games with a coalition structure

     Alonso Meijide, José María; Carreras Escobar, Francisco
    Date: 2009-03-06
    Report

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  • Grup de Recerca en Teoría de Jocs

     Amer Ramon, Rafael; Freixas Bosch, Josep; Giménez Pradales, José Miguel; Llongueras Arola, Maria Dolors; Magaña Nieto, Antonio; Pons Vallès, Montserrat; Puente Del Campo, Mª Albina; Sales Ingles, Vicente; Carreras Escobar, Francisco
    Participation in a competitive project

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  • Pure bargaining problems and the Shapley rule

     Carreras Escobar, Francisco; Owen Salazar, Guillermo
    Date: 2009-03
    Report

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  • Access to the full text
    Semivalues: power, potential and multilinear extensions  Open access

     Carreras Escobar, Francisco; Giménez Pradales, José Miguel
    Date: 2009-04
    Report

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    The notions of power and potential, both defined for any semivalue, give rise to two endomorphisms of the vector space of all cooperative games on a given player set. Several properties of these linear mappings are stated and their action on unanimity games is emphasized. We also relate in both cases the multilinear extension of the image game to the multilinear extension of the original game.

  • Game theory and cryptography

     Magaña Nieto, Antonio; Amer Ramon, Rafael; Carreras Escobar, Francisco; Giménez Pradales, José Miguel
    Annual Conference of the Operational Research Society
    Presentation's date: 2009-09-09
    Presentation of work at congresses

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  • Juegos cooperativos y conflictos de intereses. Teoría y práctica. MTM 2006-06064

     Carreras Escobar, Francisco
    Jornadas de Seguimiento de Proyectos I+D MTM 2006
    Presentation's date: 2009-03-31
    Presentation of work at congresses

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  • El valor coalicional proporcional de Shapley

     Carreras Escobar, Francisco; Alonso Meijide, José María
    Congreso Galego de Estadística e Investigación de Operacións
    Presentation's date: 2009-11-12
    Presentation of work at congresses

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  • A note on quasi-additive games

     Carreras Escobar, Francisco
    Congreso Nacional de Estadística e Investigación Operativa
    Presentation's date: 2009-02-11
    Presentation of work at congresses

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  • Simple bargaining problems and sharing rules

     Carreras Escobar, Francisco
    Annual Conference of the Operational Research Society
    Presentation's date: 2009-09-08
    Presentation of work at congresses

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  • Simple bargaining problems and Shapley rule

     Carreras Escobar, Francisco
    European Conference on Operational Research
    Presentation's date: 2009-07-07
    Presentation of work at congresses

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  • A note about decisive symmetric games

     Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente Del Campo, Mª Albina
    International workshop:new topics on Game Theory
    Presentation's date: 2009-04
    Presentation of work at congresses

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    S'estudien diverses funcions relacionades amb la presa de decisions en jocs simples. L'anàlisi es restringeix a jocs de decisió simètrics i la seva composició i es dóna per suposat que tots els jugadors comparteixen els mateixos objectius pels quals ells competeixen.

  • On pure bargaining problems

     Carreras Escobar, Francisco
    Congreso Galego de Estadística e Investigación de Operacións
    Presentation's date: 2009-11-12
    Presentation of work at congresses

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