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Beyond Worst-Case Budget-Feasible Mechanism Design

Authors Aviad Rubinstein, Junyao Zhao

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  • Theory of computation → Computational pricing and auctions
Keywords
  • Procurement auctions
  • Mechanism design
  • Beyond worst-case analysis

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Abstract

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.

Cite As Get BibTex

Aviad Rubinstein and Junyao Zhao. Beyond Worst-Case Budget-Feasible Mechanism Design. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 93:1-93:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ITCS.2023.93

Author Details

Aviad Rubinstein
  • Computer Science Department, Stanford University, CA, USA
Junyao Zhao
  • Computer Science Department, Stanford University, CA, USA

Funding

  • Rubinstein, Aviad: Supported by NSF CCF-1954927, and a David and Lucile Packard Fellowship.
  • Zhao, Junyao: Supported by NSF CCF-1954927.

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