On The Extensive Form Of N-Person Cooperative Games

This paper is concerned with improving our conceptual understanding of the extensive form of N-person cooperative games. The extensive form of N-person cooperative game is such that the game is played repeatedly for very much number of times, such that in the long run, the chances of being favoured and not being favoured are equally likely. Using the same examples as used by [3], it was observed that the Nucleolus method turned out to be better with standard error of 0.1334 and 0.2887 and coefficient of variation of 7.7% and 9.38% than the Shapley value method with standard error of 0.1498 and 0.3442 and coefficient of variation of 8.65% and 11.19% respectively. We also observe that in all, the standard error and coefficients of variation using both methods are lower in the extensive form of Nperson cooperative games than in the normal form of N-person cooperative games.Keywords: Extensive form game, Normal form game, characteristic function, Coalition, Imputation, Player, Payoff, Strategy and Cor

On The Solution Of N-Person Cooperative Games

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 CoreGlobal Journal of Mathematical Sciences Vol. 7 (1) 2008: pp. 49-5