When does society eventually learn the truth, or underlying state, via sequential observational learning? This paper develops the interplay of preferences satisfying single-crossing differences (SCD) and a new informational condition, directionally un- bounded beliefs (DUB). SCD preferences and DUB information are a jointly minimal pair of sufficient conditions for learning. When there are more than two states, DUB is weaker than unbounded beliefs, which characterizes learning for all preferences (Smith and Sorensen, 2000). Unlike unbounded beliefs, DUB is compatible with the monotone likelihood ratio property, and satisfied, for example, by normal information.
Rank Uncertainty in Organizations, with Marina Halac and Elliot Lipnowski (American Economic Review, 2021)
A principal incentivizes a team of agents to work by privately offering them bonuses contingent on team success. We study the principal’s optimal incentive scheme that implements work as a unique equilibrium. This scheme leverages rank uncertainty to address strategic uncertainty. Each agent is informed only of a ranking distribution and his own bonus, the latter making work dominant provided that higher-rank agents work. If agents are symmetric, their bonuses are identical. Thus, discrimination is strictly suboptimal, in sharp contrast with the case of public contracts (Winter, 2004). We characterize how agents’ ranking and compensation vary with asymmetric effort costs.
A key feature of communication with evidence is skepticism: to the extent possible, a receiver will attribute any incomplete disclosure to the sender concealing unfavorable evidence. The degree of skepticism depends on how much evidence the sender is expected to possess. I characterize when a change in the prior distribution of evidence induces more skepticism, i.e. induces any receiver to take an equilibrium action that is less favorable to the sender following every message. I formalize an increase in the sender’s (ex-ante) amount of evidence and show that this is equivalent to inducing more skepticism. My analysis provides a method to solve general verifiable disclosure games, including an expression for equilibrium actions. I apply my results to a dynamic disclosure problem in which the sender obtains and discloses evidence over time. I identify the necessary and sufficient condition on the evidence structure such that the receiver can benefit from early disclosures. If this condition does not hold then informative early disclosures would induce more skepticism in the receiver violating incentive compatibility.
We characterize when choices among lotteries over arbitrary allocations are monotonic in an expected-utility agent’s type. Our necessary and sufficient condition is on the von Neumann-Morgenstern utility function; we identify an order over lotteries that generates the choice monotonicity when the condition holds. We discuss applications to cheap-talk games, costly signaling games, and collective choice problems. Our characterization requires some new results on monotone comparative statics and aggregating single-crossing functions, a by-product of which is a characterization of the monotone likelihood ratio property.
We study a principal who hires an agent to acquire costly information that will influence the decision of a third party. While the realized piece of information is observable and contractible, the experimental process is not. Assuming a general family of information cost functions (inclusive of Shannon’s mutual information), we show that the first best is achievable when the agent has limited liability or when he is risk averse, in contrast to standard moral hazard models. However, when the agent is both risk averse and has limited liability, efficiency losses arise generically. Specifically, we show that the principal obtains his first best outcome if and only if he intends to implement a ”symmetric” experiment, i.e. one in which the cost of generating each piece of evidence is the same. On the other hand, ”asymmetric” experiments that are uninformative with high probability but occasionally produce conclusive evidence will bear large agency costs.
Works in Progress:
Delegation with a Reputational Bias
Humility In Experts
Humility In Experts