Potential bases for some linear values of cooperative TU games

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35961

Dragan, I ^[1]

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1. Univ. of Texas, Arlington, TX (United States)

For the Shapley value, S. Hart and A. Mas-Colell (1988, 1989), have introduced the potentials of the value and extended it to the weighted Shapley value. In a paper by Dragan, Potters and Tijs (1989) a basis of the space of TU games with a fixed set of players has been found, such that the coordinates of each game are the potentials of the game and its subgame. In the present paper, we show first that the same approach used for the Shapley value works also for the weighted Shapley value. Then, we use the potential functions introduced recently by Dragan and Driessen (1994) for some fair division rules: the Center of the imputation set (CIS-value), the Egalitarian non-separable contribution (ENSC-value) and the Egalitarian non-average contribution (ENAC-value). We show that the approach used for finding {open_quotes}potential bases{close_quotes} for weighted Shapley values works also for these egalitarian division rules. In each case, we found a potential basis, the values of the basic vectors have been computed and based upon these values a basis for the null space has been determined.

• OSTI ID: 35961
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
LINEAR PROGRAMMING
MATRICES
NUMERICAL SOLUTION
PARAMETRIC ANALYSIS