Von Neumann–Morgenstern stable sets, discounting, and Nash bargaining

We establish a link between von Neumann–Morgenstern stable set and the Nash solution in a general nn-player utility set. The stable set-solution is defined with respect to a dominance relation: payoff vector u   dominates vv if one player prefers u even with one period delay. We show that a stable set exists and, if the utility set has a smooth surface, any stable set converges to the Nash bargaining solution when the length of the period goes to zero.