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Tree solutions and standardness for cycle-free graph games

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  • Li, Daniel Li
  • Shan, Erfang

Abstract

The average tree solution for cycle-free graph games is uniquely determined by component efficiency and component fairness. Component fairness states that the average changes of payoffs for players in two separated components of a tree are equal when a link is broken. Thus a small part of players, particularly a player who is linked only to one of other players, may influence the game greatly. Replacing component fairness with total component fairness that counts changes of payoffs of players in total, we propose the total tree solution. This solution is characterized by component efficiency and component standardness.

Suggested Citation

  • Li, Daniel Li & Shan, Erfang, 2023. "Tree solutions and standardness for cycle-free graph games," Economics Letters, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:ecolet:v:222:y:2023:i:c:s0165176522004293
    DOI: 10.1016/j.econlet.2022.110955
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    References listed on IDEAS

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    1. Shan, Erfang & Zhang, Guang & Dong, Yanxia, 2016. "Component-wise proportional solutions for communication graph games," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 22-28.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. Liying Kang & Anna Khmelnitskaya & Erfang Shan & Dolf Talman & Guang Zhang, 2021. "The average tree value for hypergraph games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 437-460, December.
    4. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
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    More about this item

    Keywords

    Cooperative game; Tree solution; Component fairness; Component standardness;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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