Root Dominance 

PDF April 2023 

SSRN  

Abstract: 

Root dominance is an intermediate dominance relation between weak and strict dominances. In addition to weak dominance, root dominance requires strict dominance on all profiles where an opponent plays a best response to the dominating strategy. The iterated elimination of root dominated strategies (IERDS) outcome refines the iterated elimination of strictly dominated strategies (IESDS) outcome, and IERDS is an order independent procedure in finite games, contrary to the iterated elimination of weakly dominated strategies (IEWDS). In addition, IERDS does not face the inconsistency that we call mutability. That is, IERDS does not alter the dominance relation between two strategies like IEWDS does. Finally, we introduce a rationality concept which corresponds to root undominated strategies. This rationality concept is induced by perturbations of the game such that a player believes that the strategies he considers might be observable by his opponent. We discuss the links between our concept and other concepts established in various literatures such as the conjectural variations theory.

Top Dominance   

Abstract: 

To deal with issues of inconsistency faced by iterated elimination of weakly or strictly dominated strategies (IEWDS or IESDS), we propose a new elimination procedure. Our procedure, named iterated elimination of top dominated strategies (IETDS), is based on the new notion of top dominance. It is more consistent than IESDS in a certain sense. Top dominance is more stringent than weak dominance (and may be more stringent than strict dominance in infinite games): it requires weak dominance and strict payoff domination of the strategy on a specific profiles set. Furthermore, it requires that the dominating strategy to be not weakly dominated. Contrary to IESDS, IETDS can reduce the set of Nash equilibria (whilst never eliminating strict Nash equilibria) without the problems of order dependence and spurious Nash equilibria encountered by IEWDS and IESDS.