  In settings where full incentive-compatibility is not available, such as
core-constraint combinatorial auctions and budget-balanced combinatorial
exchanges, we may wish to design mechanisms that are as incentive-compatible as
possible. This paper offers a new characterization of approximate
incentive-compatibility by casting the pricing problem as a meta-game between
the center and the participating agents. Through a suitable set of
simplifications, we describe the equilibrium of this game as a variational
problem. We use this to characterize the space of optimal prices, enabling
closed-form solutions in restricted cases, and numerically-determined prices in
the general case. We offer theory motivating this approach, and numerical
experiments showing its application.
