Reduced game property of the Egalitarian Non-k-Averaged Contribution (EN k AC-) value and the Shapley value

The Egalitarian Non- k -Averaged Contribution (EN ^k AC-) value for TU-game represents the equal division of the surplus of the total profits, given that each player is already allocated his individual contribution specified by worths of coalitions of size k . This paper deals with the axiomatic characterization of the EN ^k AC-value on the class of cooperative games with a fixed player set as well as a variable player set. The latter axiomatization involves a consistency axiom in terms of the reduced games. The EN ^k AC-value is the unique value on the class of cooperative games with a variable player set which possesses the relative invariance under strategic equivalence, the equal treatment property and the reduced game property for two types of reduced games. We also propose a new reduced game in terms of which the Shapley value is axiomatized.