No abstract

We develop a tool akin to the revelation principle for mechanism design with limited commitment. We identify a canonical class of mechanisms rich enough to replicate the payoffs of any equilibrium in a mechanism-selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. We show how this insight can be used to transform the designer's problem into a constrained optimization one: To the usual truthtelling and participation constraints, one must add the designer's sequential rationality constraint.

We study games of incomplete information as both the information structure and the extensive form vary. An analyst may know the payoff‐relevant data but not the players' private information, nor the extensive form that governs their play. Alternatively, a designer may be able to build a mechanism from these ingredients. We characterize all outcomes that can arise in an equilibrium of some extensive form with some information structure. We show how to specialize our main concept to capture the additional restrictions implied by extensive‐form refinements.

We develop a tool akin to the revelation principle for dynamic mechanism‐selection games in which the designer can only commit to short‐term mechanisms. We identify a canonical class of mechanisms rich enough to replicate the outcomes of any equilibrium in a mechanism‐selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. Our result simplifies the search for the designer‐optimal outcome by reducing the agent's behavior to a series of participation, truth telling, and Bayes' plausibility constraints the mechanisms must satisfy.

I study a single-agent sequential search problem as in Weitzman [13].Contrary to Weitzman, conditional on stopping, the agent may take any uninspected box without first inspecting its contents. This introduces a new trade-off. By taking a box without inspection, the agent saves on its inspection costs. However, by inspecting it, he may discover that its contents are lower than he anticipated. I identify sufficient conditions on the parameters of the environment under which I characterize the optimal policy. Both the order in which boxes are inspected and the stopping rule may differ from that in Weitzman's model. Moreover, I provide additional results that partially characterize the optimal policy when these conditions fail.