On the Nonmonotonicity of the Bargaining Set, the Kernel and the Nucleolus of Game

Source abstract

A solution concept for n-person games is called monotonic if the players, after committing themselves to payoff vectors that solve (in the sense of this concept) the game, can still assure that every individual’s payment grows with the total amount paid. The bargaining set $\mathcal{M}_1^{(i)}$, the kernel, and the nucleolus are shown to be nonmonotonic.