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Efficient Money Burning in General Domains

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Abstract

We study mechanism design where the objective is to maximize the residual surplus, i.e., the total value of the outcome minus the payments charged to the agents, by truthful mechanisms. The motivation comes from applications where the payments charged are not in the form of actual monetary transfers, but take the form of wasted resources. We consider a general mechanism design setting with m discrete outcomes and n multidimensional agents. We present two randomized truthful mechanisms that extract an O(logm) fraction of the maximum social surplus as residual surplus. The first mechanism achieves an O(logm)-approximation to the social surplus, which is improved to an O(1)-approximation by the second mechanism. An interesting feature of the second mechanism is that it optimizes over an appropriately restricted space of probability distributions, thus achieving an efficient tradeoff between social surplus and the total amount of payments charged to the agents.

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Notes

  1. For example, we consider an instance with m agents and m outcomes, where each agent i has some value v i >0 only for outcome i and v 1=1, v 2=1−ε and v 3=⋯ = v m = ε, for any small ε>0. Then, the residual surplus of VCG is ε and the expected residual surplus of the random allocation is \(\varepsilon +\frac {2-\varepsilon }{m}\). Since the optimal social surplus is 1, any randomization between VCG and the random allocation yields an approximation ratio of Ω(1/ε).

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Acknowledgments

This research was partially supported by the project AlgoNow, co-financed by the European Union (European Social Fund - ESF) and Greek national funds, through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALES, investing in knowledge society through the European Social Fund, by NSF Award CCF-1101491, and by an award for Graduate Students in Theoretical Computer Science by the Simons Foundation. Part of this work was done while D. Tsipras was with the School of Electrical and Computer Engineering, National Technical University of Athens, Greece.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, National Technical University of Athens, 157 80, Athens, Greece

    Dimitris Fotakis

  2. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Dimitris Tsipras, Christos Tzamos & Emmanouil Zampetakis

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  1. Dimitris Fotakis
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  2. Dimitris Tsipras
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  3. Christos Tzamos
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  4. Emmanouil Zampetakis
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Correspondence to Dimitris Fotakis.

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Fotakis, D., Tsipras, D., Tzamos, C. et al. Efficient Money Burning in General Domains. Theory Comput Syst 59, 619–640 (2016). https://doi.org/10.1007/s00224-016-9720-2

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