Refinements of Nash Equilibrium: A critique

Rational play of Noncooperative Games is investigated under the assumptions that a particular form of Best Reply Principle holds, each player has at least one rational strategy and all strategies are either rational or irrational. These assumptions are shown to imply that (a) some weakly dominated strategies are rational (b) recursive reasoning can be misleading (c) only a Strict Nash Equilibrium can be a solution. A Supplementary Best Reply Principle is formulated. It sheds further light on which games have solutions and on rational play in games without them. The relationship between these results and those of other authors is discussed.