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A Cooperative Game Theory of Noncontiguous Allies

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  • Daniel G. Arce M.
  • Todd Sandler

Abstract

This paper develops a cooperative game‐theoretic representation of alliances with noncontiguous members that is based on cost savings from reducing overlapping responsibilities and sequestering borders. For various scenarios, three solutions (the Shapley value, nucleolus, and core's centroid) are found and compared. Even though their underlying ethical norm varies, the solutions are often identical for cases involving contiguous allies and for rectangular arrays of noncontiguous allies. When transaction costs and/or alternative spatial configurations are investigated, they may then differ. In all cases the cooperative approach leads to a distribution of alliance costs that need not necessarily coincide with the traditional emphasis on gross domestic product size as a proxy for deterrence value (the exploitation hypothesis). Instead, burdens can now be defined based upon a country's spatial and strategic location within the alliance.

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  • Daniel G. Arce M. & Todd Sandler, 2001. "A Cooperative Game Theory of Noncontiguous Allies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(4), pages 391-411, October.
    • Handle: RePEc:bla:jpbect:v:3:y:2001:i:4:p:391-411
    DOI: 10.1111/1097-3923.00075
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    Cited by:

    1. Arce M., Daniel G. & Sandler, Todd, 2003. "Health-promoting alliances," European Journal of Political Economy, Elsevier, vol. 19(2), pages 355-375, June.
    2. Dan Kovenock & Brian Roberson, 2012. "Coalitional Colonel Blotto Games with Application to the Economics of Alliances," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 14(4), pages 653-676, August.
    3. David Rietzke & Brian Roberson, 2013. "The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 937-956, April.
    4. Michael Finus & Bianca Rundshagen, 2009. "Membership rules and stability of coalition structures in positive externality games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(3), pages 389-406, March.

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