Review of Economic Studies (1998) 65, 761–771 0034-65279800340761$02.00  1998 The Review of Economic Studies Limited The Selection of Preferences Through Imitation ROBIN P. CUBITT and ROBERT SUGDEN University of East Anglia First version received November 1996; final version accepted December 1997 (Eds.) The paper presents a model in which a population of agents repeatedly play games against nature; the rules of behaviour followed are revised over time through a process of imitation. For binary decisions, imitation selects rules consistent with a preference relation of the kind proposed by SSB utility theory and regret theory. In general, this preference relation need not satisfy either independence or transitivity; we state conditions on imitation necessary for it to do so. For decisions over three or more options, the long-run tendency is for options that are maximally preferred in terms of SSB preferences to be chosen. If no maximally preferred option exists, the process of imitation may not converge. I. INTRODUCTION In game-theoretic analysis, it is standard practice to start with games in which, for each player and for each combination of strategies, there is an index of von Neumann–Morgen- stern utility. 1 However, it might seem more natural to begin with a ‘‘game form’’, in which outcomes are simply descriptions of the world. What grounds do we have for assigning von Neumann–Morgenstern utility indices to outcomes? The traditional answer is that game theory assumes players to be rational, and that if a person is rational, her preferences must satisfy certain axioms which imply the expected utility representation. But, in much recent work in game theory, the assumption that players are fully rational in this sense has been dropped. In this literature, it is now common to treat the process by which equilibria are reached (if at all), not as one of instantaneous reasoning by ideally rational players, but as an evolutionary path through time. The evolutionary process is understood either as one in which imperfectly rational agents learn by trial and error, or as a process analogous with natural selection, for which no rationality assumptions of any kind need be made. Nevertheless, the games themselves are still usually described in terms of von Neumann–Morgenstern utilities. 2 The question of what justification there is for assuming the existence of von Neu- mann–Morgenstern utility indices is crucial in this context. If the traditional justification 1. Here, and elsewhere, we include games against nature in the domain of game theory. We use the term ‘‘von Neumann–Morgenstern utility’’ to refer to any index of utility which is cardinal (i.e. unique to affine transformations) and which allows behaviour to be representated as expected utility maximizing. 2. For example, the 1992 Symposium on Evolutionary Game Theory in the Journal of Economic Theory contains ten papers. Each of them either takes the existence of von Neumann–Morgenstern utility for granted, or presents a biological model of natural selection which is then given an informal economic interpretation. Introducing the symposium, Mailath (1992) follows the standard practice of describing games in terms of von Neumann–Morgenstern utility, but characterizes evolutionary game theory as assuming ‘‘unsophisticated’’ play- ers who do not take account of one another’s reasoning. In a more recent survey of evolutionary game theory, Banerjee and Weibull (1996) take the existence of a payoff function as primitive, even though they countenance the possibility that payoffs are not simple measures of reproductive fitness. 761