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A consistent value for games with n players and r alternatives

Author

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  • Edward M. Bolger

    (Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056, USA)

Abstract

In Bolger [1993], an efficient value was obtained for a class of games called games with n players and r alternatives. In these games, each of the n players must choose one and only one of the r alternatives. This value can be used to determine a player's "a priori" value in such a game. In this paper, we show that the value has a consistency property similar to the "consistency" for TU games in Hart/Mas-Colell [1989] and we present a set of axioms (including consistency) which characterizes this value.

Suggested Citation

  • Edward M. Bolger, 2000. "A consistent value for games with n players and r alternatives," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 93-99.
    • Handle: RePEc:spr:jogath:v:29:y:2000:i:1:p:93-99
    Note: Received: April 1994/final version: June 1999
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    Citations

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    Cited by:

    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence with an ordered set of possible actions," Theory and Decision, Springer, vol. 69(4), pages 635-656, October.
    2. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    3. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley–Shubik power index for dichotomous multi-type games," Theory and Decision, Springer, vol. 81(3), pages 413-426, September.
    4. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    5. René Brink & Agnieszka Rusinowska & Frank Steffen, 2013. "Measuring power and satisfaction in societies with opinion leaders: an axiomatization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 671-683, September.
    6. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "A model of influence with a continuum of actions," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 576-587.
    7. Sébastien Courtin & Zéphirin Nganmeni & Bertrand Tchantcho, 2016. "The Shapley-Shubik power index for dichotomous multi-type games," Post-Print halshs-01545769, HAL.
    8. Josep Freixas, 2005. "Banzhaf Measures for Games with Several Levels of Approval in the Input and Output," Annals of Operations Research, Springer, vol. 137(1), pages 45-66, July.
    9. Sascha Kurz, 2014. "Measuring Voting Power in Convex Policy Spaces," Economies, MDPI, vol. 2(1), pages 1-33, March.
    10. Maria Ekes, 2013. "Application of Generalized Owen Value for Voting Games in Partition Function Form," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 32, pages 43-53.
    11. René van den Brink & Agnieszka Rusinowska & Frank Steffen, 2009. "Measuring Power and Satisfaction in Societies with Opinion Leaders: Dictator and Opinion Leader Properties," Tinbergen Institute Discussion Papers 09-052/1, Tinbergen Institute.
    12. Michel Grabisch & Agnieszka Rusinowska, 2009. "A model of influence with a continuum of actions," Post-Print halshs-00464460, HAL.
    13. Bilbao, J.M. & Jiménez, N. & López, J.J., 2010. "The selectope for bicooperative games," European Journal of Operational Research, Elsevier, vol. 204(3), pages 522-532, August.
    14. Josep Freixas & Roberto Lucchetti, 2016. "Power in voting rules with abstention: an axiomatization of a two components power index," Annals of Operations Research, Springer, vol. 244(2), pages 455-474, September.
    15. Freixas, Josep & Zwicker, William S., 2009. "Anonymous yes-no voting with abstention and multiple levels of approval," Games and Economic Behavior, Elsevier, vol. 67(2), pages 428-444, November.
    16. Sébastien Courtin & Zephirin Nganmeni & Bertrand Tchantcho, 2015. "Dichotomous multi-type games: Shapley-Shubik and Banzhaf-Coleman power indices," THEMA Working Papers 2015-05, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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