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An efficient and fair solution for communication graph games

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  • van den Brink, René
  • Khmelnitskaya, Anna
  • van der Laan, Gerard

Abstract

We introduce an efficient solution for games with communication graph structures and show that it is characterized by efficiency, fairness and a new axiom called fair distribution of the surplus.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecolet:v:117:y:2012:i:3:p:786-789
    DOI: 10.1016/j.econlet.2012.08.026
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    References listed on IDEAS

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    1. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 505-514, November.
    2. 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.
    3. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    4. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    5. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    6. Yoshio Kamijo, 2009. "A Two-Step Shapley Value For Cooperative Games With Coalition Structures," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 207-214.
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    Citations

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    Cited by:

    1. Guang Zhang & Erfang Shan & Liying Kang & Yanxia Dong, 2017. "Two efficient values of cooperative games with graph structure based on $$\tau $$ τ -values," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 462-482, August.
    2. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2021. "Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations," Annals of Operations Research, Springer, vol. 302(1), pages 23-47, July.
    3. 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.
    4. Sylvain Béal & André Casajus & Frank Huettner, 2018. "Efficient extensions of communication values," Annals of Operations Research, Springer, vol. 264(1), pages 41-56, May.
    5. 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.
    6. René Brink & Anna Khmelnitskaya & Gerard Laan, 2016. "An Owen-type value for games with two-level communication structure," Annals of Operations Research, Springer, vol. 243(1), pages 179-198, August.
    7. Erfang Shan & Zhiqiang Yu & Wenrong Lyu, 2023. "Union-wise egalitarian solutions in cooperative games with a coalition structure," 4OR, Springer, vol. 21(3), pages 533-545, September.
    8. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    9. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    10. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2019. "Cohesive efficiency in TU-games: Two extensions of the Shapley value," Working Papers 2019-03, CRESE.
    11. 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.
    12. Hu, Xun-Feng, 2019. "Coalitional surplus desirability and the equal surplus division value," Economics Letters, Elsevier, vol. 179(C), pages 1-4.
    13. Aguiar, Victor H. & Pongou, Roland & Tondji, Jean-Baptiste, 2018. "A non-parametric approach to testing the axioms of the Shapley value with limited data," Games and Economic Behavior, Elsevier, vol. 111(C), pages 41-63.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Shi, Jilei & Shan, Erfang, 2020. "Weighted component-wise solutions for graph games," Economics Letters, Elsevier, vol. 192(C).
    19. 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.

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    More about this item

    Keywords

    Game theory; TU game; Communication graph; Myerson value;
    All these keywords.

    JEL classification:

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

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