Budget-Constrained Incentive Compatibility for Stationary Mechanisms

Abstract

Motivated by online advertising applications, we study incentive properties of stationary mechanisms that satisfy budget constraints in expectation at a stationary equilibrium. We consider a general repeated auction setting where a seller sells identical items to buyers with budget constraints and the buyers' value distributions can be arbitrarily correlated. We introduce the novel notion of budget-constrained incentive compatibility (BCIC) under which each buyer chooses an optimal bidding strategy among stationary budget-feasible bidding strategies. Armed with the notion of BCIC, we characterize Bayesian optimal mechanisms that satisfy the budget constraints in expectation with respect to the profit, utility and welfare objectives in the restricted setting where the buyers' value distributions are independent. Furthermore, in the general setting where the buyers' value distributions are correlated, we provide the first systematic study on the incentive properties of different budget management mechanisms, including those studied in the literature and, to the best of our knowledge, used in the industry. We explore the following mechanisms and show some popular mechanisms are not incentive compatible even when restricting attention to stationary budget-feasible deviations: throttling, thresholding, bid shading, reserve pricing and two versions of multiplicative boosting.