A New Procedure to Calculate the Owen Value

José Miguel Giménez, María Albina Puente

2017

Abstract

In this paper we focus on games with a coalition structure. Particularly, we deal with the Owen value, the coalitional value of the Shapley value, and we provide a computational procedure to calculate this coalitional value in terms of the multilinear extension of the original game.

References

  1. Albizuri, M. J. (2002). Axiomatizations of Owen value without efficiency. Discussion Paper 25. Department of Applied Economics IV, Basque Country University.
  2. Alonso, J. M., Carreras, F., and Fiestras, M. G. (2005). The multilinear extension and the symmetric coalition Banzhaf value. Theory and Decision, 59:111-126.
  3. Alonso, J. M. and Fiestras, M. G. (2002). Modification of the Banzhaf value for games with a coalition structure. Annals of Operations Research, 109:213-227.
  4. Amer, R. and Carreras, F. (1995). Cooperation indices and coalition value. TOP, 3:117-135.
  5. Amer, R. and Carreras, F. (2001). Power, cooperation indices and coalition structures. Power Indices and Coalition Formation, pages 153-173.
  6. Amer, R., Carreras, F., and Giménez, J. M. (2002). The modified Banzhaf value for games with a coalition structure. Mathematical Social Sciences, 43:45-54.
  7. Aumann, R. and Drèze, J. (1974). Cooperative games with coalition structures. nternational Journal of Game Theory, 3:217-237.
  8. Banzhaf, J. (1965). Weigthed voting doesn't work: A mathematical analysis. Rutgers Law Review, 19:317-343.
  9. Carreras, F. (2004). a-decisiveness in simple games. Theory and Decision, 56:77-91.
  10. Carreras, F. and Giménez, J. (2011). Power and potential maps induced by any semivalue: Some algrebraic properties and computation by multilinear extension. European Journal of Operational Research, 211:148- 159.
  11. Carreras, F. and Maga n˜a, A. (1994). The multilinear extension and the modified Banzhaf-Coleman index.Mathematical Social Sciences, 28:215-222.
  12. Carreras, F. and Maga n˜a, A. (1997). The multilinear extension of the quotient game. Games and Economic Behavior, 18:22-31.
  13. Carreras, F. and Puente, M. (2011). Symmetric coalitional binomial semivalues. Group Decision and Negotiation, 21:637-662.
  14. Carreras, F. and Puente, M. (2015). Coalitional multinomial probabilistic values. European Journal of Operational Research, 245:236-246.
  15. Dragan, I. (1997). Some recursive definitions of the Shapley value and other linear values of cooperative tu games. Working paper 328. University of Texas at Arlington.
  16. Dubey, P. (1975). On the uniqueness of the Shapley value. International Journal of Game Theory, 4:131-139.
  17. Feltkamp, V. (1995). Alternative axiomatic characterizations of the Shapley and Banzhaf values. International Journal of Game Theory, 24:179-186.
  18. Hamiache, G. (1999). A new axiomatization of the owen value for games with coalition structures. Mathematical Social Sciences, 37:281-305.
  19. Hamiache, G. (2001). The Owen value friendship. International Journal of Game Theory, 29:517-532.
  20. Hart, S. and Kurz, M. (1983). Endogeneous formation of coalitions. Econometrica, 51:1047-1064.
  21. Owen, G. (1972). Multilinear extensions of games. Management Science, 18:64-79.
  22. Owen, G. (1975). Multilinear extensions and the Banzhaf value. Naval Research Logistics Quarterly, 22:741- 750.
  23. Owen, G. (1977). Values of games with a priori unions. Mathematical Economics and Game Theory, R. Henn and O. Moeschlin, eds.:76-88.
  24. Owen, G. (1982). Modification of the Banzhaf-Coleman index for games with a priori unions. Power, Voting and Voting Power, M.J. Holler, ed:232-238.
  25. Owen, G. (1995). Game Theory. Academic Press Inc.
  26. Owen, G. and Winter, E. (1992). Multilinear extensions and the coalitional value. Games and Economic Behavior, 4:582-587.
  27. Peleg, B. (1989). Introduction to the theory of cooperative games. Chapter 8: The Shapley value. RM 88, Center for Research in Mathematical Economics and Game Theory, the Hebrew University, Israel.
  28. Puente, M. A. (2000). Aportaciones a la representabilidad de juegos simples y al cálculo de soluciones de esta clase de juegos. Ph.D. Thesis. Technical University of Catalonia, Spain.
  29. Roth, A. (1988). The Shapley Value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press, Cambridge.
  30. Shapley, L. and Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48:787-792.
  31. Shapley, L. S. (1953). A value for n-person games. Contributions to the Theory of Games II (H.W. Kuhn and A.W. Tucker, eds).
  32. Vázquez, M. (1998). Contribuciones a la teoría del valor en juegos con utilidad transferible. Ph.D. Thesis. University of Santiago de Compostela, Spain.
  33. Vázquez, M., Nouweland, A. v. d., and García Jurado, I. (1997). Owen's coalitional value and aircraft landing fees. Mathematical Social Sciences, 4:132-144.
  34. Winter, E. (1992). The consistency and potential for values with coalition structure. Games and Economic Behavior, 4:132-144.
Download


Paper Citation


in Harvard Style

Giménez J. and Puente M. (2017). A New Procedure to Calculate the Owen Value . In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES, ISBN 978-989-758-218-9, pages 228-233. DOI: 10.5220/0006113702280233


in Bibtex Style

@conference{icores17,
author={José Miguel Giménez and María Albina Puente},
title={A New Procedure to Calculate the Owen Value},
booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},
year={2017},
pages={228-233},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006113702280233},
isbn={978-989-758-218-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,
TI - A New Procedure to Calculate the Owen Value
SN - 978-989-758-218-9
AU - Giménez J.
AU - Puente M.
PY - 2017
SP - 228
EP - 233
DO - 10.5220/0006113702280233