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The apex power measure for directed networks

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  • René van den Brink

    (Department of Econometrics, Free University, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands)

Abstract

In this paper we provide an axiomatization of the Shapley value restricted to the class of apex games using an equal loss property which states that the payoff of an apex player and a non-apex player decrease by the same amount if we make this particular non-apex player a null player. We also generalize this axiomatization to the class of games that can be obtained as sums of apex games. After discussing these axiomatizations we apply apex games and their Shapley values in measuring relational power in directed networks. We conclude by mentioning how these results can be adapted to give axiomatizations of the Banzhaf value.

Suggested Citation

  • René van den Brink, 2002. "The apex power measure for directed networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 845-867.
    • Handle: RePEc:spr:sochwe:v:19:y:2002:i:4:p:845-867
    Note: Received: 17 February 1999/Accepted: 2 October 2002
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    Cited by:

    1. Arlegi, Ritxar & Dimitrov, Dinko, 2012. "Evolvement of influence in hierarchies," Economics Letters, Elsevier, vol. 117(2), pages 484-486.
    2. René Brink & Chris Dietz, 2014. "Games with a local permission structure: separation of authority and value generation," Theory and Decision, Springer, vol. 76(3), pages 343-361, March.
    3. René van den Brink & Frank Steffen, 2007. "Positional Power in Hierarchies," Tinbergen Institute Discussion Papers 07-038/1, Tinbergen Institute.
    4. Agnieszka Rusinowska & Rudolf Berghammer & Harrie de Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.
    5. Kong, Qianqian & Peters, Hans, 2023. "Power indices for networks, with applications to matching markets," European Journal of Operational Research, Elsevier, vol. 306(1), pages 448-456.
    6. Roland K. Cheo, 2007. "Adopting Shapley values to address embedding biases in contingent valuation studies," Applied Economics Letters, Taylor & Francis Journals, vol. 14(10), pages 765-768.
    7. Qianqian Kong & Hans Peters, 2021. "An issue based power index," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 23-38, March.

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