Two axiomatizations of the kernel of TU games: bilateral and converse reduced game properties

We provide two axiomatic characterizations of the kernel of TU games by means of both bilateral consistency and converse consistency with respect to two types of 2-person reduced games. According to the first type, the worth of any single player in the 2-person reduced game is derived from the difference of player’s positive (instead of maximum) surpluses. According to the second type, the worth of any single player in the 2-person reduced game either coincides with the 2-person max reduced game or refers to the constrained equal loss rule applied to an appropriate 2-person bankruptcy problem, the claims of which are given by the player’s positive surpluses. 2000 Mathematics Subject Classifications : 91A12