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The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games

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  • Tobias Harks

    (Department of Quantitative Economics, Maastricht University, 6200 MD Maastricht, The Netherlands)

  • Konstantin Miller

    (Telecommunication Networks Group, Technische Universität Berlin, 10587 Berlin, Germany)

Abstract

Resource allocation problems play a key role in many applications, including traffic networks, telecommunication networks, and economics. In most applications, the allocation of resources is determined by a finite number of independent players, each optimizing an individual objective function. An important question in all these applications is the degree of suboptimality caused by selfish resource allocation. We consider the worst-case efficiency of cost sharing methods in resource allocation games in terms of the ratio of the minimum guaranteed surplus of a Nash equilibrium and the maximal surplus. Our main technical result is an upper bound on the efficiency loss that depends on the class of allowable cost functions and the class of allowable cost sharing methods. We demonstrate the power of this bound by evaluating the worst-case efficiency loss for three well-known cost sharing methods: incremental cost sharing, marginal cost pricing, and average cost sharing.

Suggested Citation

  • Tobias Harks & Konstantin Miller, 2011. "The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games," Operations Research, INFORMS, vol. 59(6), pages 1491-1503, December.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:6:p:1491-1503
    DOI: 10.1287/opre.1110.0979
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    References listed on IDEAS

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    Cited by:

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    2. Fielbaum, Andres & Kucharski, Rafał & Cats, Oded & Alonso-Mora, Javier, 2022. "How to split the costs and charge the travellers sharing a ride? aligning system’s optimum with users’ equilibrium," European Journal of Operational Research, Elsevier, vol. 301(3), pages 956-973.
    3. Harks, Tobias & von Falkenhausen, Philipp, 2014. "Optimal cost sharing for capacitated facility location games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 187-198.
    4. Philipp von Falkenhausen & Tobias Harks, 2013. "Optimal Cost Sharing for Resource Selection Games," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 184-208, February.
    5. Zhenliang Liao & Phillip Hannam, 2013. "The Mekong Game: Achieving an All-win Situation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2611-2622, May.
    6. Vasilis Gkatzelis & Konstantinos Kollias & Tim Roughgarden, 2016. "Optimal Cost-Sharing in General Resource Selection Games," Operations Research, INFORMS, vol. 64(6), pages 1230-1238, December.

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