Strategic claim games corresponding to an NTU-game

Abstract This paper introduces a way to construct a game Λ ( V ) in strategic form to a standard NTU-game V . In the strategic claim game Λ ( V ) the players are allowed to make claims on the coalition they want to participate in, and ontthe payoff they want to attain. Conversely, to construct an NTU-game to each game in strategic form the paper follows R. J. Aumann (1961, in Contributions to the Theory of Games (A. W. Tucker and R. D. Luce, Eds.), Vol. IV, pp. 287–324. Princeton, NJ: Princeton Univ. Press), but instead of correlation only coordination of the players' actions is allowed. Applying this procedure to the claim game Λ ( V ), an NTU-game V is associated with an NTU-game V . It is found that V is the superadditive hull of V . Further, it is shown that if V is superadditive, strong core elements of V exactly correspond to the payoff vectors of strong Nash equilibria for Λ ( V ). Finally, some applications of the Aumann procedure are discussed.