Characterizations of the Random Order Values by Harsanyi Payoff Vectors

Jean Derks, Gerard Laan () and Valery Vasil’ev ()
Authors registered in the RePEc Author Service: Valery Alexandrovich Vasil'ev ()

Mathematical Methods of Operations Research, 2006, vol. 64, issue 1, 155-163

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. Copyright Springer-Verlag 2006

Keywords: TU-games; Harsanyi set; Weber set; Selectope; Monotonic sharing systems; C71 (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s00186-006-0063-7

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