Welfare-maximizing Guaranteed Dashboard Mechanisms

Abstract

Bidding dashboards are used in online marketplaces to aid a bidder in computing good bidding strategies, particularly when the auction used by the marketplace is constrained to have the winners-pay-bid payment format. A dashboard predicts the outcome a bidder can expect to get at each possible bid. To convince a bidder to best respond to the information published in a dashboard, a dashboard mechanism should ensure either (a) that best responding maximizes the bidder's utility (a weaker requirement) or (b) that the mechanism implements the outcome published in the dashboard (a stronger requirement that subsumes (a)). Recent work by Hartline et al. EC'19 formalized the notion of dashboard mechanisms and designed winners-pay-bid mechanisms that guaranteed epsilon-optimal utility (an epsilon-approximate version of (a)), but not (b). I.e., the mechanism could end up implementing arbitrarily different outcomes from what was promised. While this guarantee is sufficient from a purely technical perspective, it is far from enough in the real world: it is hard to convince bidders to best respond to information which could be arbitrarily inaccurate, regardless of the theoretical promise of near-optimality. In this paper we study guaranteed dashboard mechanisms, namely, ones that are guaranteed to implement what they publish, and obtain good welfare.

We study this question in a repeated auction setting for general single-dimensional valuations and give tight characterizations of the loss in welfare as a function of natural parameters upper bounding the difference in valuation profile across the rounds. In particular, we give three different characterizations, bounding the loss in welfare in terms of the 0 norm, 1 norm and infinite norm of difference in valuation profile across rounds. All the characterizations generalize at least up to matroid feasibility constraints, and the infinite norm characterization extends to general downward-closed feasibility constraints. We bring to bear different techniques for each of these characterizations, including connections to differential privacy and online convex optimizations.

Keywords: Dynamic mechanism design; Online advertising; Welfare maximization;