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An Efficient and Fair Solution for Communication Graph Games

Author

Listed:
  • Rene van den Brink

    (VU University Amsterdam, the Netherlands)

  • Anna Khmelnitskaya

    (Russian Academy of Sciences, St Petersburg, Russia)

  • Gerard van der Laan

    (VU University Amsterdam, the Netherlands)

Abstract

This discussion paper resulted in a publication in 'Economics Letters' , 2012, 117, 786-789. 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 component balancedness. This latter axiom compares for every component in the communication graph the total payoff to the players of this component in the game itself to the total payoff of these players when applying the solution to the subgame induced by this component.

Suggested Citation

  • Rene van den Brink & Anna Khmelnitskaya & Gerard van der Laan, 2011. "An Efficient and Fair Solution for Communication Graph Games," Tinbergen Institute Discussion Papers 11-052/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20110052
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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.
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    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. 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.
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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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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. Shi, Jilei & Shan, Erfang, 2020. "Weighted component-wise solutions for graph games," Economics Letters, Elsevier, vol. 192(C).
    13. 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.
    14. 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.
    15. 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.
    16. Hu, Xun-Feng, 2019. "Coalitional surplus desirability and the equal surplus division value," Economics Letters, Elsevier, vol. 179(C), pages 1-4.
    17. 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.
    18. 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.
    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

    TU game; communication graph; Myerson value; fairness; efficiency;
    All these keywords.

    JEL classification:

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

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