Approximated Cycles in TU-Games

Abstract

Non-balanced TU-games, which are games with empty core, can also be characterized by the existence of certain type of cycles of pre-imputations. A particular sub-class of these cycles is that of maximal U-cycles. They show up in connection with the application of a transfer scheme to games with empty core, although this transfer scheme was originally designed however, to reach a point in the core of a balanced TU-game. While the appearance of one of such cycles is enough to detect the non-balancedness of the game, it is still an open question if every non- balanced game has a maximal U-cycle. The aim of this note is to show, however, that there are always, in non-balanced games, approximated maximal U-cycles sharing with the true maximal U-cycles all their good properties.