= Equilibrium preservation under iterated weak dominance
Starting from the full finite <bimatrix game>, sequentially remove actions weakly dominated by current <mixed strategies>, with a strict improvement somewhere. At least one <Nash equilibrium> survives on the final action sets. Take an <Nash equilibrium> of the reduced game and restore actions in reverse. A restored action is no better against the fixed surviving opponent strategy than its dominating mixture of already available actions, so it introduces no profitable deviation. Any self-weight in a dominating mixture can be removed and renormalized because strict improvement forces that weight below one. Using dominance tested only against an arbitrary initially restricted opponent set does not guarantee an <Nash equilibrium> of the original full game.
Back to article page
