Envy driven dynamics in single peaked, single crossing cheap talk games
Résumé
We study pure perfect Bayesian equilibria (PBE) in Sender-Receiver
games with finitely many types for the Sender. Such equilibria are characterized by
incentive compatible (IC) partitions of the Sender's types, in which an optimal action
for the Receiver is associated with every cell of the partition and types do not envy
each other. In the case of ordered types, real valued actions and single-peaked,
single-crossing utility functions, we construct sequences of partitions by making
recursive use of the possible envy of some Sender's types. When initialized at the fully
separating partition, every sequence converges to a unique IC partition. The
achieved partition survives many selection criteria for cheap talk games.