Incentives in Cooperation and Communication

This dissertation consists of three self-contained papers in which we analyze cooperation and strategic information transmission in situations of asymmetric information where communication is subject to incentive constraints. Chapter 1 proposes a new solution concept for cooperative games with incomplete information. Chapter 2 compares this solution and other cooperative solutions in various classes of games (two-player games, games with transferable utility, games with verifiable information). Chapter 3 proposes a new approach to Bayesian persuasion by characterizing the ex-ante optimal communication equilibrium for the sender in the class of sender-receiver games. Myerson [Cooperative games with incomplete information. Int. J. Game Theory, 13, 1984, pp. 69- 96] has made significant progress towards a general concept of value for cooperative games with asymmetric information. His cooperative solution, called the M-value (short for Myerson value), generalizes the Shapley non-transferable utility (NTU) value to games with incomplete information. In Chapter 1, we show that Myerson’s theory exhibits some “difficulties” for recognizing certain informational externalities. To do this, we construct a three-player cooperative game in which the M-value does not capture some “negative” externality generated by the adverse selection. We then introduce a new solution concept, which we call the H-value. Our theory generalizes the Harsanyi NTU value to cooperative games with incomplete information. When we explicitly compute the H-value in our game, it turns out that it prescribes a more intuitive outcome taking into account the informational externalities not captured by the M-value. In Chapter 2 we explore the relationship between the following value like solution concepts for cooperative games with incomplete information: the M-value, the H-value and A. Kalai and E. Kalai’s [Cooperation in strategic games revisited. Q. J. Econ., 128, (2013), 917-966] cooperative-competitive (or “coco”) value. We consider a model in which utility transfers in the form of sidepayments are allowed. In our model, however, state-contingent contracts are required to be incentive compatible, thus utility might not be not fully transferable (as it would be in the complete information case). Restricting attention to games with orthogonal coalitions, which do not involve strategic externalities, we show that the M-value and the H-value coincide. Allowing for arbitrary informational and strategic externalities, we show that the ex-ante evaluation of the M-value equals the coco value in two-player games with verifiable information. In Chapter 3 we provide an analytical framework for studying Bayesian persuasion problems. We consider a model of strategic information transmission in which a sender chooses a communication system for signaling his information to an uninformed receiver, who then takes an action that affects the welfare of both individuals. Our main concern in this chapter is the question, what kinds of communication systems are the best ones for the informed party? By a use of a general form of the revelation principle, we can restrict attention to communication equilibria (mediated communication protocols). Using a geometric approach based on Duality Theory, we are able to characterize the optimal communication equilibrium from the concavification of a (modified) non-revealing payoff function as in Aumann and Maschler [Repeated Games with Incomplete Information. (1995). Cambridge, MIT Press. ].