***CANCELED*** Dynamic Bayesian Persuasion with bounded recall

We study the setting of dynamic Bayesian Persuasion games in which the states follow an irreducible Markov chain. We assume that the sender has a commitment power, and maximizes his utility by choosing the optimal signalling strategy, conditional on the receiver playing a best response. Since the states follow a Markov chain, a best response of the receiver may depend not only on the current signal, but also the past signals. We are interested in studying the effects on the optimal expected utility of the sender, when the receiver has a bounded recall. We show that if the sender observes the past actions of the receiver, he is able to punish the receiver to obtain the maximum payoff that is possible, conditional on that the receiver obtains at least his individually rational payoff, irrespective of the receiver's recall. However, when the sender is not able to punish the receiver, there are games in which the sender is able to achieve a strictly higher payoff when the receiver has bounded recall.  

Joint work with Ehud Lehrer.