Egalitarism of the prenucleolus for cooperative games
The prenucleolus is a well-known solution concept for cooperative games in characteristic function form which is always contained in the prekernel. In fact, the prenucleolus concept is based on the idea of excess. The current paper examines the set of efficient payoff vectors in an n person game which attain their maximal excesses at the (n {minus} 2)-person coalitions. It is established that, under a certain condition on the worth of (n {minus} 2)-person coalitions in the n-person game, the intersection of the relevant set with the prekernel is either empty or a singleton. A description of that single point is provided in terms of the egalitarian division of the remaining total worth, given that each player is already paid a special kind of an average of the player`s contributions with respect to (n {minus} 2)-person coalitions. The latter division rule is called the egalitarian non-average contribution (ENAC)-method. The main purpose of the paper is to present conditions on the game to guarantee that the ENAC-method agrees with the prenucleolus concept. The main sufficient condition expresses that the maximal excesses at the ENAC solution in the n-person game are determined by the (n {minus} 2)-person coalitions. A reformulation of the main sufficient condition in terms of the data of the game itself is added. Finally three types of conditions which are stronger than the main sufficient condition, are listed.
- OSTI ID:
- 35964
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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