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Is Shapley cost sharing optimal?

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  • Dobzinski, Shahar
  • Mehta, Aranyak
  • Roughgarden, Tim
  • Sundararajan, Mukund

Abstract

A general approach to the design of budget-balanced cost-sharing mechanisms is to use the Shapley value, applied to the given cost function, to define payments from the players to the mechanism. Is the corresponding Shapley value mechanism “optimal” in some sense? We consider the objective of minimizing worst-case inefficiency subject to a revenue constraint, and prove results in three different regimes. First, for the public excludable good problem, the Shapley value mechanism minimizes the worst-case efficiency loss over all truthful, deterministic, and budget-balanced mechanisms that satisfy equal treatment. Second, even with randomization and approximate budget-balance allowed and dropping equal treatment, the worst-case efficiency loss of the Shapley value mechanism is within a constant factor of the minimum possible. Third, for no-deficit mechanisms, we prove a general positive result: for every monotone cost function, a suitable blend of the VCG and Shapley value mechanisms is no-deficit and enjoys good approximate efficiency guarantees.

Suggested Citation

  • Dobzinski, Shahar & Mehta, Aranyak & Roughgarden, Tim & Sundararajan, Mukund, 2018. "Is Shapley cost sharing optimal?," Games and Economic Behavior, Elsevier, vol. 108(C), pages 130-138.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:130-138
    DOI: 10.1016/j.geb.2017.03.008
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    References listed on IDEAS

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    3. Shichijo, Tatsuhiro & Fukuda, Emiko, 2021. "Cost-sharing mechanism for excludable goods with generalized non-rivalry," Journal of Economic Theory, Elsevier, vol. 193(C).

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    More about this item

    Keywords

    Shapley value; Cost-sharing mechanisms; Approximate efficiency;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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