Abstract
This paper presents a characterization of the non-emptiness of the intersection between the imputation set and the Weber set. Tools from non-cooperative zero-sum finite games are used. We assign a matrix game to any cooperative game and the sign of the value of this matrix game is used for the characterization mentioned above. The cases of two or three players are discussed. Moreover, bounds and some particular cases for this value are studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.J.M. Derks, A short proof of the inclusion of the core in the Weber set, International Journal of Game Theory 21(1992)149–150.
Th. Driessen, Cooperative Games, Solutions and Applications, Kluwer Academic, 1988.
J.A.M. Potters and S.H. Tijs, The nucleolus of a matrix game and other nucleoli, Mathematics of Operations Research 17(1992)164–174.
C. Rafels and S.H. Tijs, On the cores of cooperative games and the stability of the Weber set, International Journal of Game Theory 26(1997)491–499.
L.S. Shapley, Cores of convex games, International Journal of Game Theory 1(1971)11–26.
P. Sudhoelter, The modified nucleolus: Properties and Axiomatizations, International Journal of Game Theory 26(1997)147–182.
N.N. Vorob'ev, Game Theory, Springer, 1977.
R.J. Weber, Probabilistic values for games, Cowles Foundation Discussion Paper No. 471R, Yale University, New Haven, CT, 1978.
R.J. Weber, Probabilistic values for games, in: The Shapley Value, ed. A.E. Roth, Cambridge University Press, 1988, pp. 101–117.
Rights and permissions
About this article
Cite this article
Javier Martinez-de-Albeniz, F., Rafels, C. On the intersection between the imputation setand the Weber set. Annals of Operations Research 84, 111–120 (1998). https://doi.org/10.1023/A:1018928618125
Issue Date:
DOI: https://doi.org/10.1023/A:1018928618125