About U-cycles in TU-games

Abstract

Recently we prove that the existence of certain type of cycles of preimputations characterizes TU-games with empty core. A particular sub-class of these cycles has also appeared in connection with the application of a transfer scheme, developed in [5]. This transfer scheme was designed to reach a point in the core of a TU-game provided this set is non-empty. It is still an open question if these cycles also characterize games with empty core. It is also unknown if the transfer scheme always converges, in some sense, to those cycles provided the core of the game is empty. Here we present some results addressing to these two issues.