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A note on the nonuniqueness of the Equal Profit Method

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  • Dahlberg, Joen
  • Göthe-Lundgren, Maud
  • Engevall, Stefan

Abstract

When a set of players cooperate, they need to decide how the collective cost should be allocated among them. Cooperative game theory provides several methods or solution concepts, that can be used as a tool for cost allocation. In this note, we consider a specific solution concept called the Equal Profit Method (EPM). In some cases, a solution according to the EPM is any one of infinitely many solutions. That is, it is not always unique. This leads to a lack of clarity in the characterization of the solutions obtained by the EPM. We present a modified version of the EPM, which unlike its precursor ensures a unique solution. In order to illustrate the differences, we present some numerical examples and comparisons between the two concepts.

Suggested Citation

  • Dahlberg, Joen & Göthe-Lundgren, Maud & Engevall, Stefan, 2017. "A note on the nonuniqueness of the Equal Profit Method," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 84-89.
    • Handle: RePEc:eee:apmaco:v:308:y:2017:i:c:p:84-89
    DOI: 10.1016/j.amc.2017.03.018
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    References listed on IDEAS

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    Cited by:

    1. Basso, Franco & Guajardo, Mario & Varas, Mauricio, 2020. "Collaborative job scheduling in the wine bottling process," Omega, Elsevier, vol. 91(C).
    2. Gao, Evelyn & Sowlati, Taraneh & Akhtari, Shaghaygh, 2019. "Profit allocation in collaborative bioenergy and biofuel supply chains," Energy, Elsevier, vol. 188(C).
    3. Joen Dahlberg & Stefan Engevall & Maud Göthe-Lundgren & Kurt Jörnsten & Mikael Rönnqvist, 2019. "Incitements for transportation collaboration by cost allocation," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1009-1032, December.
    4. Chen, Yang & Park, Byungkwon & Kou, Xiao & Hu, Mengqi & Dong, Jin & Li, Fangxing & Amasyali, Kadir & Olama, Mohammed, 2020. "A comparison study on trading behavior and profit distribution in local energy transaction games," Applied Energy, Elsevier, vol. 280(C).
    5. Osicka, Ondrej & Guajardo, Mario & van Oost, Thibault, 2018. "Cooperative game-theoretic features of cost sharing in location-routing," Discussion Papers 2018/11, Norwegian School of Economics, Department of Business and Management Science.

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