Probabilistic Verification in Mechanism Design

We introduce a model of probabilistic verification in a mechanism design setting. The principal verifies the agent's claims with statistical tests. The agent's probability of passing each test depends on his type. In our framework, the revelation principle holds. We characterize whether each type has an associated test that best screens out all the other types. In that case, the testing technology can be represented in a tractable reduced form. In a quasilinear environment, we solve for the revenue-maximizing mechanism by introducing a new expression for the virtual value that encodes the effect of testing

Linking Mechanisms: Limits and Robustness

Quota mechanisms are commonly used to elicit private information when agents face multiple decisions and monetary transfers are infeasible. As the number of decisions grows large, quotas asymptotically implement the same set of social choice functions as do separate mechanisms with transfers. We analyze the robustness of quota mechanisms. To set the correct quota, the designer must have precise knowledge of the environment. We show that, without transfers, only trivial social choice rules can be implemented in a prior-independent way. We obtain a tight bound on the decision error that results when the quota does not match the true type distribution. Finally, we show that in a multi-agent setting, quotas are robust to agents' beliefs about each other. Crucially, quotas make the distribution of reports common knowledge

Comment on Jackson and Sonnenschein (2007) "Overcoming Incentive Constraints by Linking Decisions"

We correct a bound in the definition of approximate truthfulness used in the body of the paper of Jackson and Sonnenschein (2007). The proof of their main theorem uses a different permutation-based definition, implicitly claiming that the permutation-version implies the bound-based version. We show that this claim holds only if the bound is loosened. The new bound is still strong enough to guarantee that the fraction of lies vanishes as the number of problems grows, so the theorem is correct as stated once the bound is loosened

Mechanisms without transfers for fully biased agents

A principal must decide between two options. Which one she prefers depends on the private information of two agents. One agent always prefers the first option; the other always prefers the second. Transfers are infeasible. One application of this setting is the efficient division of a fixed budget between two competing departments. We first characterize all implementable mechanisms under arbitrary correlation. Second, we study when there exists a mechanism that yields the principal a higher payoff than she could receive by choosing the ex-ante optimal decision without consulting the agents. In the budget example, such a profitable mechanism exists if and only if the information of one department is also relevant for the expected returns of the other department. We generalize this insight to derive necessary and sufficient conditions for the existence of a profitable mechanism in the n-agent allocation problem with independent types