Conferences at Department of Economics, University of Toronto, Canadian Economic Theory Conference 2014

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Multi-stage unmediated communication in a sender-receiver model

Gregory Pavlov*, Yi Chen, Maria Goltsman, Johannes Horner

Last modified: 2014-04-05

Abstract


We study multi-stage unmediated communication in the framework of Crawford and Sobel (Crawford, V. and J. Sobel (1982) Strategic information transmission, Econometrica 50, 1431–1451). The sender, who has private information about the state of the world, and the receiver, who has to take an action, engage in a (possibly arbitrarily long) face-to-face cheap talk. We focus on the case when the degree of conflict between the sender and the receiver is intermediate, because for the case of low conflict an optimal unmediated communication protocol, which involves two stages of communication, is already known (Goltsman, M., J. Hörner, G. Pavlov, and F. Squintani (2009) Mediation, arbitration and negotiation, Journal of Economic Theory 144, 1397-1420).

For the case of intermediate bias, we construct a new class of equilibria with multi-stage communication that result in higher ex ante payoffs of the players than the equilibria that are known in the literature (Krishna, V. and J. Morgan (2004) The art of conversation: eliciting information from informed parties through multi-stage communication, Journal of Economic Theory 117, 147-179). The information is revealed gradually in equilibrium, and at every stage there is a positive chance that the communication ends. Such sequential screening is possible because every sender’s strategy corresponds to a lottery over the actions taken by the receiver, and the sender’s preferences over the lotteries depend on the state of the world. We show that the greater the number of communication stages in equilibrium, the higher are the players' payoffs that can be achieved in equilibria of this class. We also characterize the structure of equilibria and the payoffs in the limiting case as the number of communication stages increases without bound. The constructed equilibria perform strictly worse than the optimal mediated communication mechanism, and the informative equilibria cease to exist for sufficiently high degrees of conflict while the informative mediated communication is still possible.