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Outside option values for network games

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  • Belau, Julia

Abstract

Various political, economic and social situations of cooperation and bargaining can be modeled by cooperative games. Cooperation potential and the outcome of cooperation are often influenced by the structure of how agents are related to each other, that is, by a network structure. Extending Myerson (1977)’s model of restricted communication, Jackson and Wolinsky (1996) introduced the setting of network games which is more flexible, for example in the distinction between the outcome of communication paths. The contribution of this paper is the analysis of outside-option-sensitive allocation rules in the network game setting. More precisely, we provide definitions and axiomatizations of outside-option-sensitive extensions of the Myerson value and the Position value for network games, the graph-χ-value and the kappa value for network games, respectively. These values have not been analyzed in the network game framework so far and, in contrast to their counterparts by means of restricted communication, we justify the values following the simple aspects used in the original axiomatization of the Shapley value. In addition, we also find such a justification of the Myerson value for network games. In all axiomatizations, we do not require any conditions on the network.

Suggested Citation

  • Belau, Julia, 2016. "Outside option values for network games," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 76-86.
    • Handle: RePEc:eee:matsoc:v:84:y:2016:i:c:p:76-86
    DOI: 10.1016/j.mathsocsci.2016.09.005
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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. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
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    5. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
    6. André Casajus, 2009. "Networks and outside options," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 1-13, January.
    7. Julia Belau, 2011. "Outside Options In Probabilistic Coalition Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 417-442.
    8. 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.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Marco Slikker, 2005. "Link Monotonic Allocation Schemes," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 473-489.
    11. Navarro, Noemi, 2007. "Fair allocation in networks with externalities," Games and Economic Behavior, Elsevier, vol. 58(2), pages 354-364, February.
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    Cited by:

    1. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    2. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    3. Daniel Li Li & Erfang Shan, 2021. "Cooperative games with partial information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 297-309, March.
    4. Julia Belau, 2018. "The class of ASN-position values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 65-99, January.
    5. Daniel Li Li & Erfang Shan, 2022. "Safety of links with respect to the Myerson value for communication situations," Operational Research, Springer, vol. 22(3), pages 2121-2131, July.

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