ABSTRACT
Shapley (Shapley, L.S. (1953). A value for n-person games. In Contributions to the Theory of Games, volume II, H.W. Kuhn and A.W. Tucker (Eds.), 307-317) formulates his proposal of a value for cooperative games with transferable utility in characteristic function form, that is, for games where the resources every group of players has available to distribute among its members only depend on the members of the group. However, the worth of a coalition of agents often depends on the organization of the rest of the players. The existence of externalities is one of the key ingredients in most interesting economic, social, or political environments. Thrall and Lucas (Thrall, R.M., and Lucas, W.F. (1963). n-Person games in partition function form. Naval Research Logistics 10(1), 281-298) provide the first formal description of settings with externalities by introducing the games in partition function form. This chapter presents the extensions of the Shapley value to this larger set of games. The different approaches that lead to the Shapley value in characteristic function form games (axiomatic, marginalistic, potential, dividends, non-cooperative) provide alternative routes for addressing the question of the most suitable extension of the Shapley value for the set of games in partition function form.
