The Nash solution and relevant expansions (Q811423)

We propose a new axiom, Relevant Balanced Expansion Monotonicity (RBEM), to replace Nash's original Independent of Irrelevant Alternatives (IIA) axiom. Intuitively, RBEM states the circumstances under which the Nash solution of one game would dominate the solution of another game; take a symmetric game, and then take another game which does not necessarily contain the symmetric game; on the latter game's Pareto frontier, find the points which dominate the solution of the symmetric game; if the slope of such a point is equal to the slope at the solution of the symmetric game, then the solution of that game should dominate the solution of the symmetric game. Using the RBEM axiom and the other three original axioms suggested by Nash, we provide a characterization of the Nash solution.