Alexey I. Kushnir

On the Equivalence of Bayesian and Dominant Strategy Implementation

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann, Kemperman, Reeds, and Shepp (1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations.

On the Equivalence of Bayesian and Dominant Strategy Implementation in a General Class of Social Choice Problems

We consider a standard social choice environment with linear utilities and independent, one-dimensional, private values. We provide a short and constructive proof that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents. We demonstrate the usefulness and applicability of our approach with several examples. Finally, we show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when utilities are non-linear or when values are interdependent, multi-dimensional, or correlated.

On the equivalence of bayesian and dominant strategy implementation: the case of non-linear utilities

We extend the equivalence between Bayesian and dominant strategy implementation established by Gershkov et al. (Econometrica, 2013) to environments with non-linear utilities satisfying the average single-crossing property and the convex-valued assumption. The new equivalence result produces novel implications to the literature on the principal-agent problem with allocative externalities, environmental mechanism design, and public good provision.

On the Equivalence between Bayesian and Dominant Strategy Implementation: The Case of Correlated Types

We consider general social choice environments with private values and correlated types. Each agents matrix of conditional probabilities satisfies the full rank condition. We show that for any Bayesian incentive compatible mechanism there exists a dominant strategy incentive compatible mechanism that delivers the same interim expected utilities to all agents and generates at least the same social surplus. In addition, if there is a social alternative that is inferior to the other alternatives for all agents the dominant strategy incentive compatible mechanism matches exactly the social surplus. These results extend to environments with interdependent values satisfying the single crossing condition.

On Linear Transformations of Intersections

For any linear transformation and two convex closed sets, we provide necessary and sufficient conditions for when the transformation of the intersection of the sets coincides with the intersection of their images. We also identify analogous conditions for non-convex sets, general transformations, and multiple sets. We demonstrate the usefulness of our results via an application to the economics literature of mechanism design.

Reduced form implementation for environments with value interdependencies

We provide a unified and simple treatment of reduced-form implementation for general social choice problems and extend it to environments with value interdependencies. We employ the geometric approach developed by Goeree and Kushnir (2016) to characterize the set of feasible interim agent values (agent utilities excluding transfers) by deriving the analytical expression of its support function. As an application, we use the reduced-form implementation to analyze second-best mechanisms in environments with value interdependencies.