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Abstract
We investigate games whose Nash equilibria are mixed and are
unstable under fictitious play-like learning processes. We show
that when players learn using weighted stochastic fictitious play
and so place greater weight on more recent experience that the
time average of play converges even in these "unstable" games,
even while mixed strategies and beliefs continue to cycle. This
time average is related to the best response cycle first
identified by Shapley (1964). For many games, the time average is
close enough to Nash equilibrium to create the appearance of
convergence to equilibrium. We show that our theoretical results
help to explain data from recent experimental studies of price
dispersion.
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