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Solidarity Value for Graph Games

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  • Daniel Li

    (Shanghai University)

  • Erfang Shan

    (Shanghai University)

Abstract

For cooperative games, the Shapley value is the most eminent allocation rule that represents the economic rationality, and the solidarity value takes into account social and psychological aspects. The (communication) graph game was developed by Myerson (1977), and the well-known Myerson value is the Shapley value for graph games. In this paper we propose the graph solidarity value for graph games, in which a player’s payoff is derived from the solidarity worths of connected coalitions and the surplus of components. We also recall the graph egalitarian value introduced by Béal et al. (2012) by giving different characteristic properties, from which we see that the graph solidarity value lies between the Myerson value and the graph egalitarian value.

Suggested Citation

  • Daniel Li & Erfang Shan, 2025. "Solidarity Value for Graph Games," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-13, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02709-1
    DOI: 10.1007/s10957-025-02709-1
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    References listed on IDEAS

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    1. 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.
    2. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    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.
    5. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    6. Rong Zou & Wenzhong Li & Marc Uetz & Genjiu Xu, 2023. "Two-step Shapley-solidarity value for cooperative games with coalition structure," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 1-25, March.
    7. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Fairness and fairness for neighbors: The difference between the Myerson value and component-wise egalitarian solutions," Economics Letters, Elsevier, vol. 117(1), pages 263-267.
    8. 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.
    9. 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.
    10. Casajus, André & Huettner, Frank, 2014. "Null, nullifying, or dummifying players: The difference between the Shapley value, the equal division value, and the equal surplus division value," Economics Letters, Elsevier, vol. 122(2), pages 167-169.
    11. 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.
    12. Wenzhong Li & Genjiu Xu & Rong Zou & Dongshuang Hou, 2022. "The allocation of marginal surplus for cooperative games with transferable utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 353-377, June.
    13. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
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