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Efficient quotient extensions of the Myerson value

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  • Daniel Li Li

    (Shanghai Business School)

  • Erfang Shan

    (Shanghai University)

Abstract

We propose an efficient extension of the Myerson value for games with communication graph structure. Define a quotient game on set of the components of the graph, in which each component acts as a component-player. Then, each player in a component receives his payoff according to the Myerson value and an equal share of the surplus of the Shapley value obtained by the component in the quotient game. We show that this efficient extension of the Myerson value can be characterized by quotient component efficiency, fair distribution of surplus within component and coherence with the Myerson value for connected graphs.

Suggested Citation

  • Daniel Li Li & Erfang Shan, 2020. "Efficient quotient extensions of the Myerson value," Annals of Operations Research, Springer, vol. 292(1), pages 171-181, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:1:d:10.1007_s10479-020-03634-4
    DOI: 10.1007/s10479-020-03634-4
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    References listed on IDEAS

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    1. van den Brink, René & Khmelnitskaya, Anna & van der Laan, Gerard, 2012. "An efficient and fair solution for communication graph games," Economics Letters, Elsevier, vol. 117(3), pages 786-789.
    2. Sylvain Béal & André Casajus & Frank Huettner, 2015. "Efficient extensions of the Myerson value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 819-827, December.
    3. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Hu, Xun-Feng & Li, Deng-Feng & Xu, Gen-Jiu, 2018. "Fair distribution of surplus and efficient extensions of the Myerson value," Economics Letters, Elsevier, vol. 165(C), pages 1-5.
    6. Béal, Sylvain & Casajus, André & Huettner, Frank, 2016. "On the existence of efficient and fair extensions of communication values for connected graphs," Economics Letters, Elsevier, vol. 146(C), pages 103-106.
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    Cited by:

    1. Rong Zou & Genjiu Xu & Dongshuang Hou, 2023. "Efficient extensions of the Myerson value based on endogenous claims from players," Annals of Operations Research, Springer, vol. 323(1), pages 287-300, April.
    2. Erfang Shan & Jilei Shi & Wenrong Lyu, 2023. "The efficient partition surplus Owen graph value," Annals of Operations Research, Springer, vol. 320(1), pages 379-392, January.

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