Rationality vs Evolution

F.A. Hayek was one of the pioneers of the evolutionary approach to economics.  Rereading Hayek's The Constitution of Liberty on the difference between Gallican and Anglican concepts of liberty- the former based on Cartesian rationality and the latter on an evolutionary theory of moral intuitions and institutions(see Vernon Smith on this here)- reminds me of the history of game theory. We need look no further than John Nash’s PhD dissertation- 27 pages of typescript, double-spaced! (see the Nobel seminar here)

On page 21, Nash introduces the evolutionary approach to game theory, what he calls the “mass action interpretation of equilibrium points.” The approach, as it has been elaborated, goes something like this: boundedly rational players are drawn from a large population to engage in a social interaction. Occasionally, they experiment with a new strategy, but usually they deliberately revise their strategy according to a learning rule. For example, they may (i) play a best response to the empirical distribution of play, i.e. what others did in the past (e.g. Young 1998); (ii) choose a strategy at random when their own payoffs fall below some aspiration level (Young 2004, Marden et al. 2007); or (iii) imitate a player earning higher payoffs (Schlag 1998).

But it was not economists that developed evolutionary game theory, but theoretical biologists such as Fisher, Maynard Smith and Price, who were inspired by early game-theoretic work by mathematicians and economists. Hayek is perceptive: “for in social evolution, the decisive factor is not the selection of the physical and inheritable properties of the individuals but the selection by imitation of successful institutions and habits” [p. 59]. In fact, Karl Schlag (1998) shows that an imitation-based dynamic such as (iii) approximates the replicator dynamic used to model evolution via natural selection. So the analytical tools developed by biologists could be adopted (and extended) to study the evolution of social behavior and cultural traits, but as Hayek notes the interpretation and terminology need to be distinct.

Evolutionary game theory is, however, still a heterodox approach in economics. Economics went another way. On page 23 of his dissertation, Nash moves to a second interpretation, asking “what would be a “rational” prediction of the behavior to be expected of rationally playing the game in question.” In this approach, there is no learning about the other players’ strategies, instead players reason their way into (Nash) equilibrium- a set of mutual best responses, or a collection of strategies (one for each player) from which no player would have an incentive to deviate. The rational- dubbed the ‘classical’- approach to game theory often places a massive cognitive burden upon the agents, requires common knowledge of the strategic environment, and mutually correct expectations of players’ strategies. Perhaps it is a testament to the psychological appeal of rationality that this was seen as the natural way to proceed in economics. When publishing his seminal work, Nash was forced to cut his evolutionary interpretation by an editor; it remains to this day buried in his dissertation.

Comments

[Dan in EuroLand]

Do think think that evolutionary arguments will become more common or will there just be additional refinements to rationality in game theory? I know Binomre, Gintis and Bowles have all argued for a evolutionary approach. I thought Bowles's recent micro book was quite good. But, if I remember correctly, peoplelike Fudenberg and Levine have argued that evolutionary approaches remove too much rationality to be really effective as models of human learning. What is your take?

[Jean-Paul Carvalho]

I agree with both sides, in the sense that in many contexts I advocate a middle path. You can use approaches from cultural evolutionary theory, evolutionary game theory or the theory of learning in games to model the evolution of preferences and beliefs even while agents rationally play a stage game. Preferences/beliefs and play coevolve- the first process is evolutionary, the second is based upon rational calculation and attendant paraphernalia.