The key issue in selecting between equilibria in signalling games is determining how receivers will interpret deviations from the path of play. We develop a foundation for these off-path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises from non-equilibrium learning by  long-lived senders and receivers. In our model, non-equilibrium signals are sent by young senders as experiments to learn about receivers' behavior , and different types of senders have different incentives for these various experiments. Using the Gittins index (Gittins, 1979), we characterize which sender types use each signal more often, leading to a constraint we call the "compatibility criterion" on the receiver's off-path beliefs and to the concept of a " type-compatible equilibrium. " We compare type-compatible equilibria to signalling-game refinements such as the Intuitive Criterion (Cho and Kreps, 1987) and divine equilibrium (Banks and Sobel, 1987) .
Equilibrium outcomes in signalling games can be very sensitive to the specification of how receivers interpret and thus respond to deviations from the path of play. We develop a micro-foundation for these off-path beliefs, and an associated equilibrium refinement, in a model where equilibrium arises through non-equilibrium learning by populations of patient and long-lived senders and receivers. In our model, young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals as experiments to learn about receivers' behavior . Differences in the payoff functions of the types of senders generate different incentives for these experiments. Using the Gittins index (Gittins, 1979), we characterize which sender types use each signal more often, leading to a constraint on the receiver's off-path beliefs based on " type-compatibility " and hence a learning-based equilibrium selection .
R
The key issue in selecting between equilibria in signalling games is determining how receivers will interpret
Equilibrium outcomes in signalling games can be very sensitive to the specification of how receivers interpret and thus respond to
R
foundation
micro-foundation
R
from
through
A
populations of patient and
R
non-equilibrium signals are sent by young senders
young senders are uncertain about the prevailing distribution of play, so they rationally send out-of-equilibrium signals
R
, and different
. Differences in the payoff functions of the
R
have
generate
D
various
D
we call the "compatibility criterion"
R
and to the concept of a
based on
R
type-compatible equilibrium.
type-compatibility
R
We compare type-compatible equilibria to signalling-game refinements such as the Intuitive Criterion (Cho and Kreps, 1987) and divine equilibrium (Banks and Sobel, 1987)
and hence a learning-based equilibrium selection