Chapter

Algorithmic Game Theory

Volume 4997 of the series Lecture Notes in Computer Science pp 327-336

Is Shapley Cost Sharing Optimal?

  • Shahar DobzinskiAffiliated withThe School of Computer Science and Engineering, The Hebrew University of Jerusalem
  • , Aranyak MehtaAffiliated withGoogle, Inc.
  • , Tim RoughgardenAffiliated withDepartment of Computer Science, Stanford University
  • , Mukund SundararajanAffiliated withDepartment of Computer Science, Stanford University

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Abstract

We study the best guarantees of efficiency approximation achievable by cost-sharing mechanisms. Our main result is the first quantitative lower bound that applies to all truthful cost-sharing mechanisms, including randomized mechanisms that are only truthful in expectation, and only β-budget-balanced in expectation. Our lower bound is optimal up to constant factors and applies even to the simple and central special case of the public excludable good problem. We also give a stronger lower bound for a subclass of deterministic cost-sharing mechanisms, which is driven by a new characterization of the Shapley value mechanism. Finally, we show a separation between the best-possible efficiency guarantees achievable by deterministic and randomized cost-sharing mechanisms.