Mechanism design with general ex-ante investments (published in “Journal of Mathematical Economics”, by Hitoshi Matsushima, Shunya Noda)
Hitoshi Matsushima, Shunya Noda
We investigate mechanism design problems wherein agents take hidden actions that affect the state distribution. As agents’ action space expands, the set of mechanisms that yields a targeted action profile reduces. When agents can choose from various actions to change the state distribution in full-dimensional directions, the payment rule that induces a targeted action profile along with a given allocation rule becomes unique up to a constant. We subsequently utilize this characterization result to examine efficient mechanism design and demonstrate that the pure-VCG mechanism, the most basic form of the canonical VCG mechanism, is the only mechanism that produces an efficient action profile when agents can choose from various actions. Contrarily, the widely used pivot mechanism frequently fails to induce an efficient action profile as long as an agent’s action impacts the private types of other agents, even if the agent’s action space is one-dimensional.
*Published in “Journal of Mathematical Economics”