TY - JOUR

T1 - Characterizations of the random order values by Harsanyi payoff vectors

AU - Derks, J.

AU - Laan, G. van der

AU - Vasilev, V.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

U2 - 10.1007/s00186-006-0063-7

DO - 10.1007/s00186-006-0063-7

M3 - Article

SN - 1432-2994

VL - 64

SP - 155

EP - 163

JO - Mathematical Methods of Operations Research

JF - Mathematical Methods of Operations Research

ER -