Bayesian persuasion in unlinked games

Originating from Kamenica and Gentzkow (Am Econ Rev 101(6):2590–2615, 2011), we analyze multi-receiver Bayesian persuasion games with heterogeneous beliefs without strategic interactions among receivers, which we call unlinked. We show that given the receivers’ best-responses, the sender’s rationalizable strategies are obtained from a single linear programming problem.

Group-Managed Real Options

We study a standard real-option problem in which sequential decisions are made through voting by a group of members with heterogeneous beliefs. We show that, when facing both investment and abandonment timing decisions, the group behavior cannot be replicated by that of a representative “median” member. As a result, members’ disagreement generates inertia—the group delays investment relative to a single-agent case—and underinvestment—the group rejects projects that are supported by a majority of members, acting in autarky. These coordination frictions hold in groups of any size, for general voting protocols, and are exacerbated by belief polarization.

Utilitarian Aggregation with Heterogeneous Beliefs

The utilitarian aggregation rule requires social utility and beliefs to be a convex combination of individual utilities and beliefs, respectively. Since, in the case of belief heterogeneity, the standard Pareto condition is incompatible with such a separate aggregation, a new condition, called the belief-proof Pareto condition, is proposed to alleviate occurrences of spurious agreement by restricting unanimity to beliefs that can be considered reasonable by society. Then, we show, in the Anscombe-Aumann and the Savage framework, that the belief-proof Pareto condition is equivalent to separate aggregation of individual beliefs and tastes. (JEL D11, D71, D83)

Adverse Selection, Heterogeneous Beliefs, and Evolutionary Learning

We relax the common assumption of homogeneous beliefs in principal-agent relationships with adverse selection. Principals are competitors in the product market and write contracts also on the base of an expected aggregate. The model is a version of a cobweb model. In an evolutionary learning set-up, which is imitative, principals can have different beliefs about the distribution of agents’ types in the population. The resulting nonlinear dynamic system is studied. Convergence to a uniform belief depends on the relative size of the bias in beliefs.