Strategic information transmission with sender's approval

Françoise Forges (1, 2) , Jérôme Renault (3, 4)

1 LEDa - Laboratoire d'Economie de Dauphine
2 Université Paris Dauphine-PSL
3 TSE-R - Toulouse School of Economics
4 UT Capitole - Université Toulouse Capitole

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.

Mots clés: Approval, Cheap talk, Sender–receiver game, Participation constraints

Domaines: Economies et finances; Optimisation et contrôle [math.OC]; Sciences de l'information et de la communication

Françoise Forges, Jérôme Renault. Strategic information transmission with sender's approval. International Journal of Game Theory, In press, 50 (2), ⟨10.1007/s00182-021-00757-1⟩. ⟨hal-02440627⟩