BoundedRationality_TheAdaptiveToolbox.pdf

78 Peter Hammerstein
Biologist: Well, the ant is able to go straight back home. It solves this task very
well, but like a golf ball that ends up a little to the left or right of the hole, the
ant does not always hit its target exactly by merely relying on the procedure
I outlined a few minutes ago. Instead, the ant deals with the imperfection of
its basic navigation mechanism by using a second mechanism, which corrects
the error of the first. It uses landmarks as soon as it is close to its target.
I am not worried that the ant could do slightly better; in our theory,
optimality is also an idealization. What really worries me is that one cannot
design a model for the evolution of desert navigation systems, calculate the
optima, and predict Cataglyphis in the end. The space of all potential navigation
systems would be so immense that it seems impossible to ever delineate
the optimization problem. A similar problem would arise in the study
of the evolution of learning procedures.
Mind you, some biologists may have a different opinion and think that
by knowing the properties of the primordial soup we can predict the elephant,
solving a few optimization problems along the way. However, those
who really participate in the mathematical modeling of evolutionary biology
often feel like detectives trying to reconstruct a crime instead of predicting
it. Perhaps the most frequent job of an evolutionary theorist is to
reconstruct the selective forces that are likely to have shaped a trait under
investigation. The reconstruction often involves construction of an optimization
model or a game.
Economist: This sounds like curve fitting, except that you fit optimization mod
els instead of simple curves to your data.
Biologist: I think you are right. Let me add that model fitting is what physicists
have done throughout the history of their discipline. One has to do a lot of
model fitting before new general principles are discovered.
Economist: One thing occurs like an indisputable law of nature in your picture
of evolution: the principle of fitness maximization. Perhaps it blindfolds
you in the same way that we have been blindfolded by assuming full
rationality?
Biologist {reflectively)'. A blindfold? I would be as skeptical as you are if biologists
had not succeeded in explaining so many traits of organisms by searching
for optimality and the Nash equilibrium. But fitness maximization is far
from being a law or first principle of evolutionary theory. We can write
down models that idealize the evolutionary process in different ways. And
in these models, optimality or Nash equilibria will occur if one characterizes
equilibrium states with certain stability properties. Of course, this is
only true if the appropriate assumptions are made.