Quality of Information, Survival, and Incentives

Abstract

This dissertation is devoted to questions on long run survival, the optimal elicitation of private information, and the optimal order of gathering information. In Chapter 2, I consider an infinite horizon risk sharing game in which players have heterogeneous priors about future endowments, and analyze asymptotic behavior of efficient allocation depending on whether the players have commitment power and whether the players are Bayesian or ambiguity averse (Gilboa and Schmeidler (1989)). As in Blume and Easley (2006), I show that if the players are expected utility maximizing Bayesian learners and have commitment power, only survivors are those with the least incorrect beliefs. All other players starve in the long run. In other cases, no player vanishes. When the players are Bayesian and have no commitment power, no player starves in a Pareto efficient subgame perfect equilibrium. When the players are ambiguity averse and have commitment power, they can agree on a stationary allocation, which means that no player vanishes. When the players are ambiguity averse and have no commitment power, for sufficiently large discount factors, a stationary Pareto efficient allocation with commitment is a subgame perfect equilibrium. In Chapter 3, I consider a principal-agent problem in which a principal elicits an agent’s information when the quality of information provided by the agent depends on the agent’s type. We investigate the impact of the agent’s type dependent outside option on the optimal contract. Under restrictive assumptions on the type dependent outside option and the agent’s vii information structure, I show that the principal admits bad types and good types, but reject intermediate types. By further restricting our attention to a smaller class of decision problems, I show the existence of an optimal contract and construct how to design an optimal contract. Finally, I provide an example in which the principal optimally hires bad types to reduce the expected payment to good types. In the example, the principal actually loses if the agent draws a bad type. In Chapter 4, co-authored with Professor Tilman B¨orgers, we study the optimal order of experimentation, considering a class of dynamic decision problems in which two experiments are available and a decision maker incurs costs of experimentation. Given the class of two binary experiments, there is no non-trivial comparison of sequential experiments. The reason why the decision maker runs a less informative experiment first in some circumstances is because the less informative experiment triggers the second experiment less frequently than the more informative experiment does. This idea allows us to come up with another class of two experiments, for which there exists non-trivial comparison of experiments. Given the second class of experiment, informativeness of static decision problems implies informativeness of dynamic decision problems. That is, it is optimal for the decision maker to run a more informative experiment first in every decision problem under study.