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An average lexicographic value for cooperative games

Author

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  • Tijs, Stef
  • Borm, Peter
  • Lohmann, Edwin
  • Quant, Marieke

Abstract

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.

Suggested Citation

  • Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
  • Handle: RePEc:eee:ejores:v:213:y:2011:i:1:p:210-220
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Richard Startz & Kwok Ping Tsang, 2014. "On the Present Value Model in a Cross Section of Stocks," Working Papers e07-47, Virginia Polytechnic Institute and State University, Department of Economics.
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Weighted component fairness for forest games," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 144-151.
    3. repec:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2435-1 is not listed on IDEAS
    4. repec:eee:gamebe:v:108:y:2018:i:c:p:541-557 is not listed on IDEAS
    5. Grabisch, Michel & Sudhölter, Peter, 2018. "On a class of vertices of the core," Games and Economic Behavior, Elsevier, vol. 108(C), pages 541-557.
    6. Xiaojin Sun & Kwok Ping Tsang, 2013. "Housing Markets, Regulations and Monetary Policy," Working Papers e07-45, Virginia Polytechnic Institute and State University, Department of Economics.
    7. 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.
    8. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    9. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    10. Chen, Haoxun, 2017. "Undominated nonnegative excesses and core extensions of transferable utility games," European Journal of Operational Research, Elsevier, vol. 261(1), pages 222-233.
    11. Eric Bahel, 2016. "On the core and bargaining set of a veto game," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 543-566, August.
    12. Li, Deng-Feng, 2012. "A fast approach to compute fuzzy values of matrix games with payoffs of triangular fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 223(2), pages 421-429.
    13. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
    14. Lohmann, E.R.M.A., 2012. "Joint decision making and cooperative solutions," Other publications TiSEM 500d8ee1-4f93-4e78-940b-9, Tilburg University, School of Economics and Management.

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