We consider a sender-receiver game with an outside option for the sender. After the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject. We study situations in which the sender’s approval is crucial to the receiver. We show that a partitional, (perfect Bayesian Nash) equilibrium exists if the sender has only two types or if the receiver’s preferences over decisions do not depend on the type of the sender as long as the latter participates. The result does not extend: we construct a counter-example (with three types for the sender and type-dependent affine utility functions) in which there is no mixed equilibrium. In the three type case, we provide a full characterization of (possibly mediated) equilibria.
- C: Mathematical and Quantitative Methods
- C7: Game Theory and Bargaining Theory
- C72: Noncooperative Games
- C78: Bargaining Theory • Matching Theory
Jérôme Renault et Françoise Forges, « Strategic information transmission with sender's approval », International Journal of Game Theory, vol. 50, juin 2021, p. 475–502.
International Journal of Game Theory, vol. 50, juin 2021, p. 475–502