U-transfer schemes and dynamical systems in n-person TU-games

Abstract

In this paper we define a non-continuous discrete dynamical system re-lated to a transfer scheme designed originally to approximate imputations in the core of balanced games. We show that the dynamical system may have either periodic point of period 1 (fixed points) or periodic points with period greater than one, but not both. Moreover, the fixed points of the dynamical system characterize the core of a balanced game. On the other side, periodic points of period greater than one are associated with certain class of cycles of pre-imputations that can appear in non-balanced games (maximal U-cycles). For monotonic non-balanced 3-person games we de-scribe completely the set of periodic points and their associated (forward) stable sets.