Before revision:  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.
After revision:  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 based on " type-compatible equilibrium.