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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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    Citations

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    Cited by:

    1. 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.
      • Albizuri Irigoyen, Miren Iosune & Laruelle, Annick, 2011. "An axiomatization of success," IKERLANAK 6256, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. Casajus, André, 2021. "Weakly balanced contributions and the weighted Shapley values," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    3. Annick Laruelle & Federico Valenciano, 2001. "Shapley-Shubik and Banzhaf Indices Revisited," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 89-104, February.
    4. 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, vol. 19(1), pages 167-176, July.
    5. Casajus, André, 2019. "Relaxations of symmetry and the weighted Shapley values," Economics Letters, Elsevier, vol. 176(C), pages 75-78.
    6. 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.
    7. 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, vol. 16(1), pages 73-89, July.
    8. Li, Wenzhong & Xu, Genjiu & van den Brink, René, 2024. "Sign properties and axiomatizations of the weighted division values," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    9. 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.
    10. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.
    11. 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.
    12. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    13. Estela Sánchez-Rodríguez & Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Iago Núñez Lugilde, 2024. "Coalition-weighted Shapley values," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 547-577, June.
    14. Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    15. Emilio Calvo, 2021. "Redistribution of tax resources: a cooperative game theory approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(4), pages 633-686, December.

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