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On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives

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Web and Internet Economics (WINE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10660))

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Abstract

We study a class of procurement auctions with a budget constraint, where an auctioneer is interested in buying resources from a set of agents. The auctioneer would like to select a subset of the resources so as to maximize his valuation function, without exceeding his budget. As the resources are owned by strategic agents, our overall goal is to design mechanisms that are truthful, budget-feasible, and obtain a good approximation to the optimal value. Previous results on budget-feasible mechanisms have considered mostly monotone valuation functions. In this work, we mainly focus on symmetric submodular valuations, a prominent class of non-monotone submodular functions that includes cut functions. We begin with a purely algorithmic result, obtaining a \(\frac{2e}{e-1}\)-approximation for maximizing symmetric submodular functions under a budget constraint. We then proceed to propose truthful, budget feasible mechanisms (both deterministic and randomized), paying particular attention on the Budgeted Max Cut problem. Our results significantly improve the known approximation ratios for these objectives, while establishing polynomial running time for cases where only exponential mechanisms were known. At the heart of our approach lies an appropriate combination of local search algorithms with results for monotone submodular valuations, applied to the derived local optima.

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Notes

  1. 1.

    In some works on mechanism design, symmetric submodular functions have a different meaning and refer to the case where v(S) depends only on |S|. Here we have adopted the terminology of earlier literature on submodular optimization, e.g., [14].

  2. 2.

    The algorithm of [22] can be derandomized, but only assuming an oracle for the extension by expectation, of the objective function v.

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Authors and Affiliations

  1. Department of Informatics, Athens University of Economics and Business, Athens, Greece

    Georgios Amanatidis, Georgios Birmpas & Evangelos Markakis

Authors
  1. Georgios Amanatidis
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  2. Georgios Birmpas
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  3. Evangelos Markakis
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Correspondence to Evangelos Markakis .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Nikhil R. Devanur

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Amanatidis, G., Birmpas, G., Markakis, E. (2017). On Budget-Feasible Mechanism Design for Symmetric Submodular Objectives. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_1

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  • DOI: https://doi.org/10.1007/978-3-319-71924-5_1

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