WE ARE MOST GRATEFUL to Glazer and Rosenthal for the attention they have paid to our work (Abreu and Matsushima (1992a, b, c)). In the process of criticizing our mechanism, they have provided an elegant exposition of it which usefully supplements our own efforts. The criticisms themselves we feel are misplaced, and based on a close reading but narrow interpretation of our results. Glazer and Rosenthal seek to show that in our mechanisms .. . the iterative removal of strictly dominated strategies is (or indeed ought to be) controversial. In terms of conventional decision theory the iterative logic is impeccable. When iterative deletion leads to a unique profile, that profile is the unique rationalizable profile, the unique Nash equilibrium, and so on. Of course, the logic of iterative dominance entails common knowledge of rationality. The theoretical coherence of this assumption has been questioned in the context of backward programming in extensive form games (see Luce and Raiffa (1957, pp. 80-81), Rosenthal (1981), Basu (1988), Reny (1992a, 1992b), Bonanno (1991), Binmore (1987a, 1987b), and Gul (1989) among others). These paradoxes of common knowledge of rationality have been highlighted in stylized examples such as the finitely repeated prisoners' dilemma and Rosenthal's centipede which in fact has been a seminal inspiration for this recent literature.2 But our mechanisms are simultaneous. There is no opportunity to demonstrate irrationality, strategic or otherwise, and therefore no scope to rationalize iteratively dominated behavior. From a decision theory perspective, the Glazer and Rosenthal critique might therefore be viewed as an elaborate revival of the (indefensible) claim that players in a one-short prisoners' dilemma will choose not to confess because they are both better off doing so than by both playing their dominant strategies. Within the standard game theory paradigm there is really nothing more to be said. Before turning to issues of bounded rationality, we note that the Glazer and Rosenthal critique is essentially premised on the existence of a countervailing focal point. But what is a focal point? The notion is notoriously vague, and we are aware of no widely accepted definition.3 This is not to deny that in very simple and particular games, certain behavior may be focal. Frequently, focalness is identified with a Pareto dominating equilibrium, and this is the point of view Glazer and Rosenthal seem to adopt.4 This is implicit in their acknowledgement that ... . when the social choice function does satisfy Pareto optimality, our objection loses much of its immediate