Monotonicity, Revenue Equivalence and Budgets

TL;DR

This paper characterizes mechanisms with private budgets in auction settings, showing how to prevent over-reporting and establishing a revenue equivalence theorem for bidders with financial constraints.

Contribution

It provides a complete characterization of incentive-compatible mechanisms with private budgets and extends revenue equivalence results to financially constrained bidders.

Findings

Reporting larger budgets can be made suboptimal with small modifications.

Mechanisms with publicly-known budgets have simple characterizations.

Revenue equivalence holds for bidders with private financial constraints.

Abstract

We study multidimensional mechanism design in a common scenario where players have private information about their willingness to pay and their ability to pay. We provide a complete characterization of dominant-strategy incentive-compatible direct mechanisms where over-reporting the budget is not possible. In several settings, reporting larger budgets can be made suboptimal with a small randomized modification to the payments. We then derive a closely related partial characterization for the general case where players can arbitrarily misreport their private budgets. Immediate applications of these results include simple characterizations for mechanisms with publicly-known budgets and for mechanisms without monetary transfers. The celebrated revenue equivalence theorem states that the seller"s revenue for a broad class of standard auction formats and settings will be the same in equilibrium. Our main application is a revenue equivalence theorem for financially constrained bidders.