The Weak Core of Simple Games with Ordinal Preferences : Implementation in Nash Equilibrium

In a simple game, coalitions belonging to a given class are supposed to be "absolutely powerful" while others have no power. We attempt to make this distinction operational. Toward this end, we propose two axioms, Exclusion and Strong Non-Discrimination. Strong Non-Discrimination describes circumstances under which certain coalitions, the losing coalitions, can have no influence over social choice. Exclusion requires that there are situations in which certain coalitions, the winning coalitions, can exercise their power, We show that the weak core correspondence is the minimal correspondence satisfying Maskin Monotonicity and Strong Non-Discrimination. We also show that the weak core is the unique correspondence satisfying Nash implementability, Strong Non-Discrimination and Exclusion