# A little game theory history

06 Oct 2006
I've been working through the book, *Evolutionary Game Theory*, by Jörgen Weibull, and it has a really concise two-page history of game theory (as applied in an evolutionary context) in a foreword by Ken Binmore.

At first it was thought that the problem could be tackled by refining the Nash equilibrium concept. Despite Nash's remarks in his thesis about a possible evolutionary interpretation of the idea of a Nash equilibrium, attention at that time was focused almost entirely on its interpretation as the only viable outcome of careful reasoning by ideally rational players. Various bells and whistles were therefore appended to the definition of rationality. These allowed some Nash equilibria to be discarded as inadequately rational according to whatever new definition of rationality was being proposed. However, different game theorists proposed so many different rationality definitions that the available set of refinements of Nash equilibrium became embarrassingly large. Eventually, almost any Nash equilibrium could be justified in terms on somone or other's refinement. As a consequence a new period of disillusionment with game theory seemed inevitable by the late 1980s.

Fortunately the 1980s saw a new development. Maynard Smith's bookEvolution and the Theory of Gamesdirected game theorists' attention away from their increasingly elaborate definitions of rationality. After all, insects can hardly be said to think at all, and so rationality cannot be so crucial if game theory somehow manages to predict their behavior under appropriate conditions. Simultaneously the advent of experimental economics brought home the fact that human subjects are no great shakes at thinking either. When they find their way to an equilibrium of a game, they typically do so using trial-and-error methods.

As the appearance of this book indicates, the 1990s have therefore seen a turning away from attempts to model people as hyperrational players. The new approch to the equilibrium selection problem emphasizes the almost tautological assertion that the equilibrium selected will be a function of the equilibriating process by means of which it is achieved. The process may be slow, as in biological evolution. It may be fast, as in social evolution, when the mechanism for the transmission of superior strategies from one head to another is imitation. It may be almost instantaneous, as when the price adjusts to equate supply and demand in the Chicago wheat market. However, we have learned that all these different processes have features in common that make it worthwhile considering evolutionary processes in the abstract (Binmore 1997:ix-x).

Binmore goes on to discuss some of the ways that the equilbriating process may influence the outcome of a system, which is a major theme of the entire book as well. An important point is that fast-acting equilbriating factors may quickly swamp the importance of slow-acting ones, leading to population as a whole to miss optimum outcomes.

I'm reading through the Weibull book at the moment, which is extremely math-dense (*extremely* meaning more than three mathematical expressions per page). In one of the more interesting sections, Weibull considers circumstances under which the process of adapting toward an evolutionarily stable strategy will fit Fisher's Fundamental Theorem, and those circumstances when it may not in general do so (notably, the latter include the Prisoner's Dilemma-like games).

#### References:

Binmore K. 1997. Foreword. pp. ix-xi in Weibull, J, *Evolutionary Game Theory*. MIT Press, Cambridge, MA.