Renault, Jérôme and Forges, Françoise (2021) Strategic information transmission with sender’sapproval. TSE Working Paper, n. 21-1216, Toulouse.

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Abstract

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.