Robert W. Rosenthal

Robert Rosenthal died on February 27, 2002, of a sudden heart attack. He was just 57, in the prime of his professional life. He is missed and loved by the many friends, colleagues and students who knew him. His incisive, constructive views helped develop many new ideas, and even inspired directions of research that do not explicitly bear his name. The fact that he never took received wisdom for granted was profoundly nurturing, and he applied this ability not just to the research of others but also to his own work. In examining his distinguished list of publications, one is struck by a constant sense of unease with economic theory, and game theory in particular, which led him to visit and revisit many of the outstanding problems in the area—particularly those dealing with the question of rational behavior—in different, eclectic ways. Bob Rosenthal made fundamental contributions to the way in which we think about game theory, some better known than others. To take an example of a littleknown contribution, Theorem 3 in [9] is a formal statement of what is now widely known as the Revelation Principle. Roger Myerson refers to this theorem in his own first paper on this subject [5], indicating Bob’s priority for this result. (Of course, the Revelation Principle has been independently ‘‘discovered’’ more than once, and Bob himself, seeing the result formally re-stated some years after his own rendition of it, reportedly remarked, ‘‘Why on earth would anybody want to write that down?’’) What follows is a (necessarily) selective account of some of Bob’s contributions to economic theory. In [10] Bob introduced a now-classical framework: random matching. To our understanding, this is the first explicit and rigorous analysis of games played across ‘‘a sequence of varying opponents’’. The paper reads as a reaction to the theory of repeated games, observing correctly that many problems involve not repeated play, but changing partners. One immediate and basic implication of this structure is (or should be) that histories are imperfectly observed. Bob assumed that only the most recent action taken by a freshly matched partner is observable. With this assumption in hand, one may describe a (Markov) strategy by a rule that maps one’s immediate past actions, and that of the opponent, to an action to be taken today. Together, these strategies induce a Markov process on societal actions as a whole. Bob considered the steady states of such processes, against which each individual Markov strategy forms a best response. [He recognized that out-of-steady-state individual best responses are no longer Markov, thus raising the very difficult question of convergence in this framework.] Random matching is, of course, widely used today. Indeed, Bob applied the idea himself in joint work with Henry Landau [12]. This beautiful paper (one of the few ARTICLE IN PRESS