Non-empty core-type solutions over balanced coalitions in TU-games

J. C. CESCO

International Game Theory Review

WORLD SCIENTIFIC PUBLISHING

Año: 2012

0219-1989

In this paper we introduce two related core-type solutions for games with transferableutility (TU-games) the B-core and the M-core. The elements of the solutions are pairs(x, B), where x, as usual, is a vector representing a distribution of utility and B is abalanced family of coalitions, in the case of the B-core, and a minimal balanced one,in the case of the M-core, describing a plausible organization of the players to achievethe vector x. Both solutions extend the notion of classical core but, unlike it, they arealways nonempty for any TU-game. For the M-core, which also exhibits a certain kind ofminimality property, we provide a nice axiomatic characterization in terms of the four axioms nonemptiness (NE), individual rationality (IR), superadditivity (SUPA) and aweak reduced game property (WRGP) (with appropriate modifications to adapt themto the new framework) used to characterize the classical core. However, an additionalaxiom, the axiom of equal opportunity is required. It roughly states that if (x, B) belongs to the M-core then, any other admissible element of the form (x, B
24 ) should belong tothe solution too.