February 27, 2020 –
Strategic information transmission with receiver's type-dependent decision sets.
We consider a sender-receiver game, in which the sender has finitely many types and the receiver makes decisions in a bounded real interval. We assume that utility functions are concave, single-peaked and supermodular. After the cheap talk phase, the receiver makes a decision, which must fulfill a constraint (e.g., a participation constraint) that depends on the sender's type. Hence a necessary equilibrium condition is that the receiver maximizes his expected utility subject to the constraints of all positive probability types. This necessary condition may not hold at the receiver's prior belief, so that a non-revealing equilibrium may fail to exist. We propose a constructive algorithm that always achieves a partitional perfect Bayesian equilibrium