We study adverse selection problems in which the agent's type is multidimensional
and there are contractible ex-post signals of some components of the agent's type.
We analyze the extent to which the principal can use the ex-post signals to mitigate
the effects of the asymmetric information concerning these components of the agent's
type, and we characterize when the principal can completely eliminate such effects.
Throughout, we focus on a motivating example involving a firm employing an informed
worker on a project, where the worker has superior information both about the difficulty
of the project and the project's potential value to the firm.
We show how to use fictitious types and redefine the agent's utility function to transform
a screening problem in which the agent's utility is a nonlinear function of their type into an
equivalent problem in which the agent's utility is an affine function of their expanded type.
We present complementary results concerning mechanism incentive compatibility when the
agent's type space is non-convex. Combining these results enables analysis of screening
problems that do not satisfy commonly imposed, but restrictive, assumptions such as the
increasing differences condition, as we illustrate with examples.
Robust Cooperation with First-Order Information (joint with Drew Fudenberg and Alexander Wolitzky)
We study the repeated prisoner's dilemma in a large population with random matching and
overlapping generations. Our goal is to study the extent to which cooperation can be supported
by equilibria where players use simple strategies and have very limited information about their
opponents. To this end, we assume players have access to only first-order information about
their current partners, meaning that a player's record tracks information about her past actions
only, and not her partners' past actions (or her partners' partners' actions). Cooperation in strict
equilibrium is impossible if payoffs are submodular, or if players can erase their records. If payoffs
are sufficiently supermodular, then cooperation can be sustained by a tolerant version of grim
trigger strategies, where a player retains good standing until her record reflects a certain number
of defections. Players close to the threshold may cooperate even with defectors; this "unconditional
cooperation" is crucial for sustaining maximal cooperation. If players can forge records of fake past
interactions and successfully coordinate with their current partners, this tolerant version of grim
trigger is the unique family of strategies that sustains cooperation in equilibrium.