GAMES AND ECONOMIC BEHAVIOR 1, 213-221 (1989) Bounded versus Unbounded Rationality: The Tyranny of the Weak* ITZHAK GILBOA-~ Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University AND Dov SAMET~ Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management. Northwestern University, Evanston, Illinois 60208, and Recanati School of Business, Tel-Aviv University, Tel-Aviv 69978. Israel We examine the case of a two-person repeated game played by a boundedly rational player versus an unboundedly rational opponent. The former is restricted to strategies which are implementable by connected finite automata. It is shown that the “rational” player has a dominant strategy, and that in some cases the “weaker“ (boundedly rational) player may exploit this fact to “blackmail” him. It is also shown that for a repeated zero-sum game, the rational player has a strategy which drives the automaton player’s limit payoff down to his security (maxmin) level, even if he may choose any finite automaton. 0 19X9 Academic Press. Inc. I. INTRODUCTION The concept of bounded rationality (or “limited rationality”), originally introduced by Simon (1972, 1978), and also discussed in Radner (1986), was recently formalized for the case of repeated games using the model of a finite automaton. (See Aumann (1981), Rubinstein (1986), Neyman (1985), Kalai and Stanford (1985, 1988), and others.) * We thank Ehud Kalai, Ehud Lehrer, and an anonymous referee for comments and references. t Partial support from the National Science Foundation (Grant IRI-8814672) is gratefully acknowledged. $ Partial support from the National Science Foundation (Grant SES-8720342) is gratefully acknowledged. 213 0899-8256189 $3.00 Copyright 0 19X9 by Academic Press. Inc. All right\ of reproduction in any form reserved.