Motivated by large-market applications such as crowdsourcing, we revisit the problem of budget-feasible mechanism design under a "small-bidder assumption". Anari, Goel, and Nikzad (2018) gave a mechanism that has optimal competitive ratio 1-1/e on worst-case instances. However, we observe that on many realistic instances, their mechanism is significantly outperformed by a simpler open clock auction by Ensthaler and Giebe (2014), although the open clock auction only achieves competitive ratio 1/2 in the worst case. Is there a mechanism that gets the best of both worlds, i.e., a mechanism that is worst-case optimal and performs favorably on realistic instances? To answer this question, we initiate the study of beyond worst-case budget-feasible mechanism design. Our first main result is the design and the analysis of a natural mechanism that gives an affirmative answer to our question above: - We prove that on every instance, our mechanism performs at least as good as all uniform mechanisms, including Anari, Goel, and Nikzad’s and Ensthaler and Giebe’s mechanisms. - Moreover, we empirically evaluate our mechanism on various realistic instances and observe that it beats the worst-case 1-1/e competitive ratio by a large margin and compares favorably to both mechanisms mentioned above. Our second main result is more interesting in theory: We show that in the semi-adversarial model of budget-smoothed analysis, where the adversary designs a single worst-case market for a distribution of budgets, our mechanism is optimal among all (including non-uniform) mechanisms; furthermore our mechanism guarantees a strictly better-than-(1-1/e) expected competitive ratio for any non-trivial budget distribution regardless of the market. (In contrast, given any bounded range of budgets, we can construct a single market where Anari, Goel, and Nikzad’s mechanism achieves only 1-1/e competitive ratio for every budget in this range.) We complement the positive result with a characterization of the worst-case markets for any given budget distribution and prove a fairly robust hardness result that holds against any budget distribution and any mechanism.
@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2023.93, author = {Rubinstein, Aviad and Zhao, Junyao}, title = {{Beyond Worst-Case Budget-Feasible Mechanism Design}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {93:1--93:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.93}, URN = {urn:nbn:de:0030-drops-175969}, doi = {10.4230/LIPIcs.ITCS.2023.93}, annote = {Keywords: Procurement auctions, Mechanism design, Beyond worst-case analysis} }
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