Non-Clairvoyant Dynamic Mechanism Design with Budget Constraints and Beyond
38 Pages Posted: 10 Jun 2019 Last revised: 12 Jul 2019
Date Written: May 6, 2019
We design a non-clairvoyant dynamic mechanism under budget and ex-post individual rationality constraints that is dynamic incentive-compatible and achieves non-trivial revenue performance, even without any knowledge about the future. In particular, our dynamic mechanism obtains a constant approximation to the optimal dynamic mechanism having access to all information in advance. To the best of our knowledge, this is the first dynamic mechanism that achieves a constant approximation and strictly respects dynamic incentive-compatibility and budget constraints without relying on any forecasts of the future.
Our dynamic mechanism is enabled by a general design framework for dynamic mechanisms under complex environments, coined Lossless History Compression (LHC) mechanisms. LHC mechanisms compress the history into a state carrying the least historical information without losing any generality in terms of either revenue or welfare. In particular, the characterization works for i) almost arbitrary constraints on the outcomes, ii) private type distributions that are publicly correlated, and iii) any objective function defined on the historical reports, allocations, and the cumulative payments. We further prove that a non-clairvoyant dynamic mechanism is dynamic incentive-compatible if and only if it is equivalent to a stage-wise incentive compatible and state-utility independent mechanism, in which the latter means that the buyer's expected utility at each stage is independent of the state.
Keywords: dynamic mechanism design, general constraints, public correlation, repeated auctions, budget, non-clairvoyance, bank account mechanisms
JEL Classification: D44, C73, D82
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