@book{0b4566a711c340e49c763308f3b36e41,

title = "Consistency and potentials in cooperative TU-games: Sobolev's reduced game revived",

abstract = "It was a quarter of a century ago that Sobolev proved the reduced game (otherwise called consistency) property for the much-discussed Shapley value of cooperative TU-games. The purpose of this paper is to extend Sobolev's result in two ways. On the one hand the unified approach applies to the enlarged class consisting of game-theoretic solutions that possess a so-called potential representation; on the other Sobolev's reduced game is strongly adapted in order to establish the consistency property for solutions that admit a potential. Actually, Sobolev's explicit description of the reduced game is now replaced by a similar, but implicit definition of the modified reduced game; the characteristic function of which is implicitly determined by a bijective mapping on the universal game space (induced by the solution in question). The resulting consistency property solves an outstanding open problem for a wide class of game-theoretic solutions. As usual, the consistency together with some kind of standardness for two-person games fully characterize the solution. A detailed exposition of the developed theory is given in the event of dealing with so-called semivalues of cooperative TU-games and the Shapley and Banzhaf values in particular.",

keywords = "MSC-91D12, IR-65748, EWI-3381, MSC-91D40",

author = "Theo Driessen",

note = "Imported from MEMORANDA",

year = "2000",

language = "Undefined",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1561",

}