Lessons from Evolutionary Game Theory

Journal of Economic Literature Vol. XXXVI (September 1998), pp. 1347–1374 Mailath: Do PeopleJournal of Economic Play Literature, Nash Vol. Equilibrium? XXXVI (September 1998) Do People Play Nash Equilibrium? Lessons From Evolutionary Game Theory GEORGE J. MAILATH1 1. Introduction such justification, the use of game theory in applications is problematic. The T THE SAME TIME that noncoopera- appropriate use of game theory requires tive game theory has become a stan- A understanding when its assumptions dard tool in economics, it has also come make sense and when they do not. under increasingly critical scrutiny from In some ways, the challenge of pro- theorists and experimentalists. Noncoop- viding a compelling justification is not a erative game theory, like neoclassical new one. A major complaint other so- economics, is built on two heroic as- cial scientists (and some economists) sumptions: Maximization—every eco- have about economic methodology is nomic agent is a rational decision maker the central role of the maximization hy- with a clear understanding of the world; pothesis. A common informal argument and consistency—the agent’s under- is that any agent not optimizing—in standing, in particular, expectations, of particular, any firm not maximizing other agents’ behavior, is correct (i.e., profits—will be driven out by market the overall pattern of individual optimiz- forces. This is an evolutionary argu- ing behavior forms a Nash equilibrium). ment, and as is well known, Charles These assumptions are no less controver- Darwin was led to the idea of natural sial in the context of noncooperative selection from reading Thomas game theory than they are in neoclassical Malthus.2 But does such a justification economics. work? Is Nash equilibrium (or some re- A major challenge facing noncooperative game theorists today is that of 2 “In October 1838, that is, fifteen months after providing a compelling justification for I had begun my systematic enquiry, I happened to these two assumptions. As I will argue read for amusement ‘Malthus on Population,’ and here, many of the traditional justifica- being well prepared to appreciate the struggle for existence which everywhere goes on from long- tions are not compelling. But without continued observation of the habits of animals and plants, it at once struck me that under these cir- 1 University of Pennsylvania. Acknowledgments: cumstances favorable variations would tend to be I thank Robert Aumann, Steven Matthews, preserved, and unfavorable ones to be destroyed. Loretta Mester, John Pencavel, three referees, The results of this would be the formation of new and especially Larry Samuelson for their com- species. Here, then I had at last got a theory by ments. Email: [email protected]. which to work;” Charles Darwin (1887, p. 83). 1347 1348 Journal of Economic Literature, Vol. XXXVI (September 1998) lated concept) a good predictor of be- of players, these players are interacting, havior? and the behavior is naive (in two senses: While the parallel between noncoop- players do not believe—understand— erative game theory and neoclassical that their own behavior potentially af- economics is close, it is not perfect. fects future play of their opponents, Certainly, the question of whether and players typically do not take into agents maximize is essentially the same account the possibility that their oppo- in both. Moreover, the consistency as- nents are similarly engaged in adjusting sumption also appears in neoclassical their own behavior). It is important to economics as the assumption that prices note that successful behavior becomes clear markets. However, a fundamental more prevalent not just because market distinction between neoclassical eco- forces select against unsuccessful be- nomics and noncooperative game theory havior, but also because agents imitate is that, while the many equilibria of a successful behavior. competitive economy almost always Since evolutionary game theory stud- share many of the same properties ies populations playing games, it is also (such as efficiency or its lack),3 the useful for studying social norms and many equilibria of games often have conventions. Indeed, many of the moti- dramatically different properties. While vating ideas are the same.4 The evolu- neoclassical economics does not address tion of conventions and social norms is the question of equilibrium selection, an instance of players learning to play game theory must. an equilibrium. A convention can be Much of the work in evolutionary thought of as a symmetric equilibrium game theory is motivated by two basic of a coordination game. Examples in- questions: clude a population of consumers who 1. Do agents play Nash equilib- must decide which type of good to pur- rium? chase (in a world of competing stan- 2. Given that agents play Nash equi- dards); a population of workers who librium, which equilibrium do they must decide how much effort to exert; a play? population of traders at a fair (market) Evolutionary game theory formalizes who must decide how aggressively to and generalizes the evolutionary argu- bargain; and a population of drivers ran- ment given above by assuming that domly meeting at intersections who more successful behavior tends to be must decide who gives way to whom. more prevalent. The canonical model Evolutionary game theory has pro- has a population of players interacting vided a qualified affirmative answer to over time, with their behavior adjusting the first question: In a range of settings, over time in response to the payoffs agents do (eventually) play Nash. There (utilities, profits) that various choices is thus support for equilibrium analysis have historically received. These play- in environments where evolutionary ar- ers could be workers, consumers, firms, guments make sense. Equilibrium is etc. The focus of study is the dynamic best viewed as the steady state of a behavior of the system. The crucial as- community whose members are myopi- sumptions are that there is a population cally groping toward maximizing behavior. This is in marked contrast to the 3 Or perhaps economists have chosen to study only those properties that are shared by all equi- 4 See, for example, Jon Elster (1989), Brian libria. For example, different competitive equilib- Skyrms (1996), Robert Sugden (1989), and H. ria have different income distributions. Peyton Young (1996). Mailath: Do People Play Nash Equilibrium? 1349 earlier view (which, as I said, lacks in Section 5. As much as possible, I satisfactory foundation), according to have used simple examples. Very few which game theory and equilibrium theorems are stated (and then only in- analysis are the study of the interaction formally). Recent surveys of evolution- of (ultra-) rational agents with a large ary game theory include Eric van amount of (common) knowledge.5 Damme (1987, ch. 9), Michihiro Kan- The question of which equilibrium is dori (1997), Mailath (1992), and Jörgen played has received a lot of attention, Weibull (1995). most explicitly in the refinements literature. The two most influential ideas in 2. The Question that literature are backward and for- Economics and game theory typically ward induction. Backward induction assume that agents are “rational” in the and its extensions—subgame perfection sense of pursuing their own welfare, as and sequentiality—capture notions of they see it. This hypothesis is tautologi- credibility and sequential rationality. cal without further structure, and it is Forward induction captures the idea usually further assumed that agents un- that a player’s choice of current action derstand the world as well as (if not can be informative about his future better than) the researcher studying the play. The concerns about adequate world inhabited by these agents. This foundations extend to these refinement often requires an implausible degree of ideas. While evolutionary game theory computational and conceptual ability on does discriminate between equilibria, the part of the agents. For example, backward induction receives little sup- while chess is strategically trivial,6 it is port from evolutionary game theory. computationally impossible to solve (at Forward induction receives more sup- least in the foreseeable future). port. One new important principle for Computational limitations, however, selecting an equilibrium, based on sto- are in many ways less important than chastic stability, does emerge from conceptual limitations of agents. The evolutionary game theory, and this prin- typical agent is not like Gary Kasparov, ciple discriminates between strict equi- the world champion chess player who libria (something backward and forward knows the rules of chess, but also knows induction cannot do). that he doesn’t know the winning strat- The next section outlines the major egy. In most situations, people do not justifications for Nash equilibrium, and know they are playing a game. Rather, the difficulties with them. In that sec- people have some (perhaps imprecise) tion, I identify learning as the best notion of the environment they are in, available justification for Nash equilib- their possible opponents, the actions rium. Section 3 introduces evolutionary they and their opponents have available, game theory from a learning perspec- and the possible payoff implications of tive. The idea that Nash equilibrium different actions. These people use heu- can be usefully thought of as an evolu- ristics and rules of thumb (generated tionary stable state is described in Sec-

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