Abstract
A Harsanyi payoff vector (see Vasil’ev in Optimizacija Vyp 21:30–35, 1978) of a cooperative game with transferable utilities is obtained by some distribution of the Harsanyi dividends of all coalitions among its members. Examples of Harsanyi payoff vectors are the marginal contribution vectors. The random order values (see Weber in The Shapley value, essays in honor of L.S. Shapley, Cambridge University Press, Cambridge, 1988) being the convex combinations of the marginal contribution vectors, are therefore elements of the Harsanyi set, which refers to the set of all Harsanyi payoff vectors.
The aim of this paper is to provide two characterizations of the set of all sharing systems of the dividends whose associated Harsanyi payoff vectors are random order values. The first characterization yields the extreme points of this set of sharing systems and is based on a combinatorial result recently published (Vasil’ev in Discretnyi Analiz i Issledovaniye Operatsyi 10:17–55, 2003) the second characterization says that a Harsanyi payoff vector is a random order value iff the sharing system is strong monotonic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Derks J (2005) A new proof for Weber’s characterization of the random order values. Math Soc Sci 49:327–334
Derks J, Peters H (2002) A note on a consistency property for permutations. Discrete Math 250:241–244
Derks J, Haller H, Peters H (2000) The selectope for cooperative games. Int J Game Theory 29:23–38
Dragan I (1994) Multiweighted Shapley values and random order values. In: Proceedings of the 10th conference on applied mathematics, U.C. Oklahoma, pp 33–47
Hammer PL, Peled UN, Sorensen S (1977) Pseudo-boolean functions and game theory. I. Core elements and Shapley value. Cahiers Centre Etudes Rech Oper 19:159–176
Harsanyi JC (1959) A bargaining model for cooperative n-person games. In: Tucker AW, Luce RD (eds) Contributions to the theory of games vol IV. Princeton University Press, Princeton, pp 325–355
Harsanyi JC (1963) A simplified bargaining model for the n-person game. Int Econ Rev 4:194–220
Shapley LS (1953) A value for n-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games, vol II. Princeton University Press, Princeton, pp 307–317
Vasil’ev VA (1978) Support function of the core of a convex game. Optimizacija Vyp 21:30–35 (in Russian)
Vasil’ev VA (1980) On the H-payoff vectors for cooperative games. Optimizacija Vyp 24:18–32 (in Russian)
Vasil’ev VA (1981) On a class of imputations in cooperative games. Soviet Math Dokl 23:53–57
Vasil’ev VA (1988) Characterization of the cores and generalized NM-solutions for some classes of cooperative games. Proc Inst Math Novosibirsk Nauk 10:63–89 (in Russian)
Vasil’ev VA (2003) Extreme points of the Weber polyhedron. Discretnyi Analiz i Issledovaniye Operatsyi Ser.1 10:17–55 (in Russian)
Vasil’ev VA, Laan, G van der (2002) The Harsanyi set for cooperative TU-games. Siberian Adv Math 12:97–125
Weber RJ (1988) Probabilistic values for games. In: Roth AE (eds) The Shapley value, Essays in honor of L.S. Shapley. Cambridge University Press, Cambridge, pp 101–119
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partly done whilst Valeri Vasil’ev was visiting the Department of Econometrics at the Free University, Amsterdam. Financial support from the Netherlands Organisation for Scientific Research (NWO) in the framework of the Russian-Dutch programme for scientific cooperation, is gratefully acknowledged. The third author would also like to acknowledge partial financial support from the Russian Fund of Basic Research (grants 98-01-00664 and 00-15-98884) and the Russian Humanitarian Scientific Fund (grant 02-02-00189a).
Rights and permissions
About this article
Cite this article
Derks, J., van der Laan, G. & Vasil’ev, V. Characterizations of the Random Order Values by Harsanyi Payoff Vectors. Math Meth Oper Res 64, 155–163 (2006). https://doi.org/10.1007/s00186-006-0063-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00186-006-0063-7