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Weighted weak semivalues

Author

Listed:
  • E. Calvo

    () (Departamento de AnÂlisis EconÕmico, Universidad de Valencia, Campus dels Tarongers, Avinguda dels Tarongers s/n, Edificio Departamental Oriental, 46022 Valencia, Spain Departamento de Economi´a Aplicada 1, Universidad del Pai´s Vasco/Euskal Herriko Unibertsitatea, Lehendakari Aguirre 83, 48015 Bilbao, Spain)

  • Juan Carlos Santos

    () (Departamento de AnÂlisis EconÕmico, Universidad de Valencia, Campus dels Tarongers, Avinguda dels Tarongers s/n, Edificio Departamental Oriental, 46022 Valencia, Spain Departamento de Economi´a Aplicada 1, Universidad del Pai´s Vasco/Euskal Herriko Unibertsitatea, Lehendakari Aguirre 83, 48015 Bilbao, Spain)

Abstract

We introduce two new value solutions: weak semivalues and weighted weak semivalues. They are subfamilies of probabilistic values, and they appear by adding the axioms of balanced contributions and weighted balanced contributions respectively. We show that the effect of the introduction of these axioms is the appearance of consistency in the beliefs of players about the game.

Suggested Citation

  • E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 1-9.
  • Handle: RePEc:spr:jogath:v:29:y:2000:i:1:p:1-9 Note: Received: March 1998/revised version: October 1998
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    References listed on IDEAS

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    1. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    2. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 417-435.
    3. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
    4. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 417-435.
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    Citations

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    Cited by:

    1. Albizuri Irigoyen, Miren Iosune & Laruelle, Annick, 2011. "An axiomatization of success," IKERLANAK 2011-49, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Balanced per capita contributions and level structure of cooperation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, pages 167-176.
    3. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    5. Maurice Koster & Sascha Kurz & Ines Lindner & Stefan Napel, 2017. "The prediction value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 433-460, February.
    6. Annick Laruelle & Federico Valenciano, 2008. "Potential, value, and coalition formation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, pages 73-89.
    7. Pritchard, Geoffrey & Reyhani, Reyhaneh & Wilson, Mark C., 2013. "Power measures derived from the sequential query process," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 174-180.
    8. Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. M. Albizuri & Annick Laruelle, 2013. "An axiomatization of success," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 145-155, June.

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