Is Shapley Cost Sharing Optimal?

Authors:
Shahar Dobzinski;Aranyak Mehta;Tim Roughgarden;Mukund Sundararajan
Affiliations:
The School of Computer Science and Engineering, The Hebrew University of Jerusalem,;Google, Inc.,;Department of Computer Science, Stanford University, Stanford, 94305;Department of Computer Science, Stanford University, Stanford, 94305
Venue:
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Year:
2008

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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.