Abstract
We study online multi-unit auctions in which each agent’s private type consists of the agent’s arrival and departure times, valuation function and budget. Similarly to secretary settings, the different attributes of the agents’ types are determined by an adversary, but the arrival process is random. We establish a general framework for devising truthful random sampling mechanisms for online multi-unit settings with budgeted agents. We demonstrate the applicability of our framework by applying it to different objective functions (revenue and liquid welfare), and a range of assumptions about the agents’ valuations (additive or general) and the items’ nature (divisible or indivisible). Our main result is the design of mechanisms for additive bidders with budget constraints that extract a constant fraction of the optimal revenue, for divisible and indivisible items (under a standard large market assumption). We also show a mechanism that extracts a constant fraction of the optimal liquid welfare for general valuations over divisible items.
This work was partially supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 337122.
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Notes
- 1.
This impossibility holds even if budgets are public.
- 2.
Based on personal communication with the authors, this is essentially what is assumed for the correctness of Mechanism \(RM_k\) in Sect. 6 in [19].
- 3.
A description of the tie-breaking rule for this case appears in the full version.
- 4.
While VCG is defined and analyzed for offline settings, it is shown in [19] that it can also be applied in online settings by invoking it at the time where last agent arrives, serving only the agents that haven’t departed yet. While this method does not give any revenue guarantees, it is only used to extract truthful information from agents in the sampling set.
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Eden, A., Feldman, M., Vardi, A. (2017). Online Random Sampling for Budgeted Settings. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_3
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