weakly dominated strategies, much less to perform iterated eliminations. Given the
close link between dominance and backward induction arguments, it is no surprise
that evolutionary models also provide very little motivation for backward induction.
In terms of sorting between Nash equilibria, the lesson of evolutionary game theory
is that we should be less anxious to apply dominance or backward induction based
refinements than the refinements literature would suggest.
This finding dovetails nicely with the recent experimental literature, which
provides ample reason to believe that backward induction should not be taken for
granted (Davis and Holt, 1993, chapter 5; Roth, 1995). But in the experiments, the
game literally is as transparent as that shown in Figure 5. Then why do we suppose
that responders require learning or trial-and-error or experience to know what to
do? We must remember that while the game itself is transparent, the context in
which it is played, including the absence of any chance of repeated play or breach
of anonymity between the players, is quite foreign. What do players do when faced
with an unprecedented context? One possibility is that they strip away the context
and analyze the game. Another is that they search their experience for the closest
analogies they can find, using the game’s context as a clue in searching for a similar
situation and choosing behavior they have found to be effective in the latter. It may
then take considerable experience to hit upon appropriate analogies, producing a
dynamic process that, for reasons described above, need not produce the backward
induction solution. The role of analogies in reasoning is pursued further in Jehiel
(2000) and Samuelson (2001).
What Do We Take Away?
Will evolutionary game theory have an impact on the way people practice game
theory, or will it fade away, leaving economists to carry on as they have before? The
latter will surely be its fate if it does nothing other than ease our consciences a bit
when doing what we’ve been doing all along, namely examining Nash equilibria.
But I believe that evolutionary game theory has the potential to do more.
Evolutionary game theory will have done much if we simply take seriously the
caution that dominance and backward induction arguments are not as compelling
as they may first appear. It is common in models of bargaining, contracting and
exchange to assume that an agent can be pushed to the brink of indifference and
still be relied upon to agree to the deal. Though these arguments appear in a
variety of guises, they are all variations on the assertion that the subgame perfect
equilibrium will appear in the ultimatum game. The more we learn from evolutionary
games, the less certain can we be that we have good reason for doing so.
For evolutionary game theory to realize its potential, however, it must go
beyond warnings about what we should not do to provide results concerning what
we should do. Here, evolutionary game theory runs the risk that plagued the
equilibrium refinements literature: so many equilibrium concepts and so little basis