We analyze a Sender–Receiver game in which the Sender can choose between a costless cheap-talk message and a costly verifiable message. In a discrete setting we state conditions under which the Receiver always learns the true state while the Sender uses different message types in different states. On the contrary we show that such a fully revealing equilibrium does not exist if the state and action space are continuous.
Schopohl, S. (2019). Full revelation under optional verification. Economics Letters, 176(1), 14-16. https://doi.org/10.1016/j.econlet.2018.12.021 (Original work published 2019)