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Axiomatic Approach to Farsighted Coalition Formation

Author

Listed:
  • Mert Kimya
Abstract
We provide the first axiomatic treatment of two of the most fundamental far-sighted solution concepts. We then extend our analysis to include an axiomatization of the stable set to the extent that it is farsighted. In fi nite abstract games a solution is the largest consistent set if and only if it is maximally supportable and nonempty. In any abstract game a solution is the farsighted stable set if and only if it is minimally supportable, consistent, conversely consistent and nonempty in finite horizon games. We call the stable set that does not suffer from Harsanyi (1974)'s critique of myopia the Harsanyi stable set. In any abstract game a solution is the Harsanyi stable set if and only if it is simply supportable, consistent, weakly conversely consistent and it satisfi es restricted nonemptiness. The axioms of consistency and converse consistency are the adaptations of the frequently used principles of consistency and converse consistency to a farsighted framework. The axioms of maximal supportability, minimal supportability and simple supportability relate to the commonly held expectations that support these solutions as their stationary states.

Suggested Citation

  • Mert Kimya, 2024. "Axiomatic Approach to Farsighted Coalition Formation," Working Papers 2024-03, University of Sydney, School of Economics.
    • Handle: RePEc:syd:wpaper:2024-03
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    References listed on IDEAS

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    1. Bloch, Francis & van den Nouweland, Anne, 2021. "Myopic and farsighted stable sets in 2-player strategic-form games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 663-683.
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    9. Licun Xue, 1998. "Coalitional stability under perfect foresight," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 603-627.
    10. Kimya, Mert, 2022. "Farsighted objections and maximality in one-to-one matching problems," Journal of Economic Theory, Elsevier, vol. 204(C).
    11. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    12. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2021. "Implementation in largest consistent set via rights structures," Games and Economic Behavior, Elsevier, vol. 128(C), pages 202-212.
    13. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    14. Dutta, Bhaskar & Vartiainen, Hannu, 2020. "Coalition formation and history dependence," Theoretical Economics, Econometric Society, vol. 15(1), January.
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    17. Hirai, Toshiyuki & Watanabe, Naoki & Muto, Shigeo, 2019. "Farsighted stability in patent licensing: An abstract game approach," Games and Economic Behavior, Elsevier, vol. 118(C), pages 141-160.
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