Dynamic Sender-Receiver Games

TL;DR

This paper characterizes the equilibrium payoffs in dynamic sender-receiver games with Markovian states, showing that as players become very patient, the payoffs depend only on the invariant measure of the state process and satisfy certain rationality and incentive conditions.

Contribution

It provides a simple characterization of the limit set of equilibrium payoffs in dynamic sender-receiver games with Markov states, highlighting the role of the invariant measure.

Findings

Limit set of equilibrium payoffs depends only on the invariant measure.

Equilibrium payoffs satisfy individual rationality for the receiver.

Incentive compatibility conditions for the sender are characterized.

Abstract

We consider a dynamic version of sender-receiver games, where the sequence of states follows an irreducible Markov chain observed by the sender. Under mild assumptions, we provide a simple characterization of the limit set of equilibrium payoffs, as players become very patient. Under these assumptions, the limit set depends on the Markov chain only through its invariant measure. The (limit) equilibrium payoffs are the feasible payoffs that satisfy an individual rationality condition for the receiver, and an incentive compatibility condition for the sender.