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Random marginal and random removal values

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  • Emilio Calvo

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Abstract

We propose two variations of the non-cooperative bargaining model for games in coalitional form, introduced by Hart and Mas-Colell (1996a). These strategic games implement, in the limit, two new NTU-values: The random marginal and the random removal values. The main characteristic of these proposals is that they always select a unique payoff allocation in NTU-games. The random marginal value coincides with the Consistent NTU-value (Maschler and Owen, 1989) for hyperplane games, and with the Shapley value for TU games (Shapley, 1953). The random removal coincides with the solidarity value (Novak and Radzik, 1994) in TU-games. In large games it is showed that, in the special class of market games, the random marginal coincides with the Shapley NTU-value (Shapley,1969), and that the random removal coincides with the equal split solution.
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Suggested Citation

  • Emilio Calvo, 2008. "Random marginal and random removal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 533-563, December.
  • Handle: RePEc:spr:jogath:v:37:y:2008:i:4:p:533-563
    DOI: 10.1007/s00182-008-0132-7
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Hart, Oliver & Moore, John, 1990. "Property Rights and the Nature of the Firm," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1119-1158, December.
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    4. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038.
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    9. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    10. Anbarci, Nejat & Bigelow, John P., 1994. "The area monotonic solution to the cooperative bargaining problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 133-142, October.
    11. Emilio Calvo & Iñaki Garci´a & José M. Zarzuelo, 2001. "Replication invariance on NTU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 473-486.
    12. Hart, Sergiu, 2002. "Values of perfectly competitive economies," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 57, pages 2169-2184 Elsevier.
    13. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    14. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    15. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    16. Calvo, Emilio & Santos, Juan Carlos, 1997. "Potentials in cooperative TU-games," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 175-190, October.
    17. Shapley, Lloyd S & Shubik, Martin, 1969. "Pure Competition, Coalitional Power, and Fair Division," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 337-362, October.
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    Cited by:

    1. Radzik, Tadeusz & Driessen, Theo, 2013. "On a family of values for TU-games generalizing the Shapley value," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 105-111.
    2. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
    3. Bourheneddine Ben Dhaou & Abderrahmane Ziad, 2015. "The Free Solidarity Value," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 201508, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    4. Calvo, Emilio & Gutiérrez-López, Esther, 2014. "Axiomatic characterizations of the weighted solidarity values," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 6-11.
    5. Karl Ortmann, 2013. "A cooperative value in a multiplicative model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 561-583, September.
    6. Tadeusz Radzik & Theo Driessen, 2016. "Modeling values for TU-games using generalized versions of consistency, standardness and the null player property," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 179-205, April.
    7. Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 195-202.
    8. Emilio Calvo & Esther Gutiérrez-López, 2017. "Asymmetric players in the Solidarity and Shapley values," Discussion Papers in Economic Behaviour 0217, University of Valencia, ERI-CES.
    9. Kawamori, Tomohiko & Miyakawa, Toshiji, 2016. "Nash bargaining solution under externalities," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 1-7.

    More about this item

    Keywords

    Shapley value; Solidarity value; NTU-games; Large market games; C71;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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