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Job
Market Paper :
" Endogeneous Learning with
Bounded Memory "
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I analyze the effects of memory
limitations on the endogenous learning behavior of an agent. An infinitely
lived agent chooses each period between alternatives A and B whose types
are unknown to him. The agent can experiment with each alternative
and receive payoffs that are partially informative about the type
of that alternative. He has a
finite number of memory states as
in Wilson (2004) and a strategy
specifies how to choose an alternative
at each memory state together with
which memory state to go to depending on the
payoff received from that alternative: he can condition his behavior only
on the memory state he is currently in. I am interested in the optimal
memory rules.
I find that the inclination
to choose the currently better alternative does not constrain the extent
of learning about the types. However,
the agent faces a tradeoff between
more precise information on one alternative versus
the other. The optimal beliefs are evenly spaced and linear in the
log-likelihood space for the beliefs on alternatives; thus a
potentially two dimensional problem reduces to a single dimension. The
memory states reflect the magnitude of
the superiority of one alternative
over the other. Optimally, the agent moves one memory
state to the right both after good payoffs from A and also bad payoffs
from B, and to the left after opposite payoffs. Starting at any memory
state, the probability of moving in response to a signal about A is a
constant multiple of the respective probability after a signal about B.
The agent is almost always at two extreme memory states where he is most
confident of the superiority of one alternative over the other.
For the special case with one unknown and one safe alternative, a very
patient agent will try the unknown option at least
occasionally after any history; this
is counter to what theory predicts
with unbounded memory, but in agreement with experimental findings. Also,
an agent will concentrate most of his strategic
weight on the safe alternative, at
a range of priors where unbounded
memory would dictate otherwise; this is in accord with further
findings from the experimental literature.
If A is much more informative than
B, there is no learning on B, and B is treated as if it were a safe
alternative. In the extreme case when ex-ante expectations are
sufficiently separated, there can be no useful learning and the agent
optimally chooses the ex-ante best alternative in every
period.
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