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The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy

Author

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  • Frank Huettner

    (ESMT European School of Management and Technology, Schlossplatz 1, 10178 Berlin, Germany)

  • Harald Wiese

    (Institut für Theoretische Volkswirtschaftslehre, Wirtschaftswissenschaftliche Fakultät, Universität Leipzig, Grimmaische Str. 12, 04009 Leipzig, Germany)

Abstract

A cooperative game with transferable utility (TU game) captures a situation in which players can achieve certain payoffs by cooperating. We assume that the players are part of a hierarchy. In the literature, this invokes the assumption that subordinates cannot cooperate without the permission of their superiors. Instead, we assume that superiors can force their subordinates to cooperate. We show how both notions correspond to each other by means of dual TU games. This way, we capture the idea that a superiors’ ability to enforce cooperation can be seen as the ability to neutralize her subordinate’s threat to abstain from cooperation. Moreover, we introduce the coercion value for games with a hierarchy and provide characterizations thereof that reveal the similarity to the permission value.

Suggested Citation

  • Frank Huettner & Harald Wiese, 2016. "The Need for Permission, the Power to Enforce, and Duality in Cooperative Games with a Hierarchy," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-12, December.
    • Handle: RePEc:wsi:igtrxx:v:18:y:2016:i:04:n:s0219198916500158
    DOI: 10.1142/S0219198916500158
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    References listed on IDEAS

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    More about this item

    Keywords

    Permission value; hierarchy; enforcement; duality;
    All these keywords.

    JEL classification:

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

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