On The Solution Of N-Person Cooperative Games

Abstract

In this paper, two existing optimal allocation to N-person cooperative games are reviewed for comparison-The Shapley Value introduced by Shapley (1953) and the Nucleolus introduced by Schmeidler (1969). Given the nonempty Core of an N-person cooperative game, both optimal allocation procedures consider that one point of the Core is more efficient than the other points of the Core while the approaches to choosing the efficient allocation differ. Whereas Shapley employed the marginal contribution of the players into the game to achieve his aim, Schmeidler employed the extent of dissatisfaction to achieve his own aim. To choose the “best” of the optimal allocations, the Standard error and Coefficient of Variation of solutions were used to discriminate between the two procedures. When the two approaches were applied to the same sets of data, the Shapley value method produced smaller standard errors and coefficients of variation than the Nucleolus method. The Shapley value approach was therefore chosen as the better one for allocation (the value of the game) to an N-person cooperative game. Keywords : Characteristic Function; Coalition; Constant Sum Game; Imputation; Player ; Payoff; Strategy; The Core Global Journal of Mathematical Sciences Vol. 7 (1) 2008: pp. 49-52