On the solution of cooperative games

Cooperative games are real-valued lattice functions quantifying the TU (transferable utility) worth of cooperation within a (finite) player set. A fundamental issue is how to share this worth amongst the players, i.e., the solution problem. Although cooperative games were originally conceived exclusively in terms of coalitional games, associating a worth to each coalition, later more complex games were added, crucially involving the lattice of partitions of players. In fact, the worth-sharing approach traditionally used for coalitional games (which simply yields a TU share for each player), becomes combinatorially ambiguous when applied to more complex games. This paper provides a novel and most general idea: a wort-sharing criterion is a mapping associating to any game a game of the same type, i.e., taking values on the same lattice elements, and with Möbius inversion living only on atoms. 1. Department of Computer Science, University of Bologna, Mura Anteo Zamboni 7, 40126 Bologna, Italy. [email protected]. 2. I thank Itzhak Gilboa, Ehud Lehrer, Giorgio Nicoletti and Stefano Vannucci for fruitful conversations. The usual disclaimer applies