Discussion Papers 2019

CIRJE-F-1124	"Mechanism Design with General Ex-Ante Investments"
Author Name	Matsushima, Hitoshi and Shunya Noda
Date	September 2019
Full Paper	PDF file
Remarks

Abstract
We investigate the general mechanism design problems in which agents take ex-ante hidden actions (or investments) that influence state distribution. We show that the variety of action choices drastically shrinks the set of mechanisms that induce targeted actions in the sense that there is a one-to-one tradeoff between the dimensionality of action space and that of payment rules with which the targeted action profile is taken in an equilibrium. This result comprehends the observations made by previous works. When agents can take unilateral deviations to change the state distribution in various directions, we have equivalence properties with respect to ex-post payoffs, payments, and revenues. In particular, the pure-VCG mechanism, the simplest form of the canonical VCG mechanism, becomes the only mechanism that induces an efficient action profile. Contrarily, the popular pivot mechanism generically fails to induce efficient actions, even when the action space is one-dimensional.

Abstract

We investigate the general mechanism design problems in which agents take ex-ante hidden actions (or investments) that influence state distribution. We show that the variety of action choices drastically shrinks the set of mechanisms that induce targeted actions in the sense that there is a one-to-one tradeoff between the dimensionality of action space and that of payment rules with which the targeted action profile is taken in an equilibrium. This result comprehends the observations made by previous works. When agents can take unilateral deviations to change the state distribution in various directions, we have equivalence properties with respect to ex-post payoffs, payments, and revenues. In particular, the pure-VCG mechanism, the simplest form of the canonical VCG mechanism, becomes the only mechanism that induces an efficient action profile. Contrarily, the popular pivot mechanism generically fails to induce efficient actions, even when the action space is one-dimensional.