Learning in Games

Rakesh V. Vohra
Northwestern University

The notion of an equilibrium in a game attracts criticism in much the 
same way that corpses attract flies.  The objections are three:
 1) The Presumption of Unreasonable Rationality
 2) Identifying them is Computationally Burdensome
 3) There are too many.
In response, game theorists have attempted to provide a justification
in terms of `learning'.  Fudenberg and Levine, write, for example:
`..... equilibrium arises as the long-run outcome of a process in
which less than fully rational players grope for optimality over
time.'  To which one could add Keynes' remark: `like a peregrination
through the catacombs with a guttering candle.'

I'll survey some of the findings of the literature, highlighting the 
main difficulty: in games, the act of learning changes the thing 
being learned.