The bounded core for games with restricted cooperation

A game with restricted (incomplete) cooperation is a triple (N, v, Ω), where N represents a finite set of players, Ω ⊂ 2^N is a set of feasible coalitions such that N ∈ Ω, and v: Ω → R denotes a characteristic function. Unlike the classical TU games, the core of a game with restricted cooperation can be unbounded. Recently Grabisch and Sudhölter [9] proposed a new solution concept–the bounded core–that associates a game (N, v,Ω) with the union of all bounded faces of the core. The bounded core can be empty even if the core is nonempty. This paper gives two axiomatizations of the bounded core. The first axiomatization characterizes the bounded core for the class G ^r of all games with restricted cooperation, whereas the second one for the subclass G bc ^r ⊂ G ^r of the games with nonempty bounded cores.