Abstract
For each cooperative n-person game v and each hε{1, 2 . . . . . n}, let νh be the average worth of coalitions of size h and νih the average worth of coalitions of size h which do not contain player iε N. The paper introduces the notion of a proportional average worth game (or PAW-game), i.e., the zero-normalized game v for which there exist numbers chεℝ such that νh- νhi=ch (νn-1-v n-1i) for all hε{2, 3 . . . . , n-1}, and iε N. The notion of average worth is used to prove a formula for the Shapley value of a PAW-game. It is shown that the Shapley value, the value representing the center of the imputation set, the egalitarian nonseparable contribution value and the egalitarian non-average contribution value of a PAW-game are collinear. The class of PAW-games contains strictly the class of k-coalitional games possessing the collinearity property discussed by Driessen and Funaki (1991). Finally, it is illustrated that the unanimity games and the landlord games are PAW-games.
Original language | English |
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Pages (from-to) | 97-105 |
Number of pages | 9 |
Journal | OR Spectrum |
Volume | 18 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1996 |
Externally published | Yes |
Keywords
- Cooperative game
- Egalitarian division rules
- PAW-game
- Shapley value
- k-Coalitional game
ASJC Scopus subject areas
- Management Science and Operations Research