Consider an arbitrary two-player game with action spaces and payoff functions that are twice…

Consider an arbitrary two-player game with action spaces  and payoff functions that are twice continuously differentiable and concave in own action. Say that the game is locally solvable by iterated strict dominance at a* if there is a rectangle N containing a* such that when players are restricted to choosing actions in N, the successive elimination of strictly dominated strategies vields the unique point a*. Relate the conditions for local solvability by iterated strict dominance of the simultaneous-move process to those for local stability of the alternating-move Cournot adjustment process. (The answer is in Gabay and Moulin 1980)