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Minimal farsighted instability

Author

Listed:
  • de Callataÿ, Pierre
  • Mauleon, Ana

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Vannetelbosch, Vincent

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

We propose the notion of minimal farsighted instability to determine the states that are more likely to emerge in the long run when agents are farsighted. A state is mini‐ mally farsighted unstable if there is no other state which is more farsightedly stable. To formulate what it means to be more farsightedly stable, we compare states by comparing (in the set inclusion or cardinal sense) their sets of farsighted defeating states. We next compare states in terms of their absorbtiveness by comparing both their sets of farsighted defeating states (i.e. in terms of their stability) and their sets of farsighted defeated states (i.e. in terms of their reachability). A state is maximally farsighted absorbing if there is no other state which is more farsightedly absorbing. We provide general results for characterizing minimally farsighted unstable states and maximally farsighted absorbing states, and we study their relationships with alternative notions of farsightedness. Finally, we use experimental data to show the relevance of the new solution concepts.

Suggested Citation

  • de Callataÿ, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2024. "Minimal farsighted instability," LIDAM Reprints CORE 3286, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3286
    DOI: https://doi.org/10.1007/s00182-024-00887-2
    Note: In: International Journal of Game Theory, 2024, vol. 53(2), p. 493-523
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    as
    1. Battal Doğan & Lars Ehlers, 2022. "Robust Minimal Instability of the Top Trading Cycles Mechanism," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 556-582, November.
    2. Jean-François Caulier & Ana Mauleon & Vincent Vannetelbosch, 2013. "Contractually stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 483-499, May.
    3. Page, Frank Jr. & Wooders, Myrna H. & Kamat, Samir, 2005. "Networks and farsighted stability," Journal of Economic Theory, Elsevier, vol. 120(2), pages 257-269, February.
    4. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent J., 2004. "Rationalizability for social environments," Games and Economic Behavior, Elsevier, vol. 49(1), pages 135-156, October.
    5. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    6. Gilles Grandjean & Ana Mauleon & Vincent Vannetelbosch, 2011. "Connections Among Farsighted Agents," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 935-955, December.
    7. Chenghong Luo & Ana Mauleon & Vincent Vannetelbosch, 2021. "Network formation with myopic and farsighted players," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1283-1317, June.
    8. Debraj Ray & Rajiv Vohra, 2015. "The Farsighted Stable Set," Econometrica, Econometric Society, vol. 83(3), pages 977-1011, May.
    9. Atila Abdulkadiroğlu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2020. "Efficiency, Justified Envy, and Incentives in Priority-Based Matching," American Economic Review: Insights, American Economic Association, vol. 2(4), pages 425-442, December.
    10. Jean-François Caulier & Ana Mauleon & Jose Sempere-Monerris & Vincent Vannetelbosch, 2013. "Stable and efficient coalitional networks," Review of Economic Design, Springer;Society for Economic Design, vol. 17(4), pages 249-271, December.
    11. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2020. "Matching with myopic and farsighted players," Journal of Economic Theory, Elsevier, vol. 190(C).
    12. Debraj Ray & Rajiv Vohra, 2019. "Maximality in the Farsighted Stable Set," Econometrica, Econometric Society, vol. 87(5), pages 1763-1779, September.
    13. 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.
    14. Bloch, Francis & Jackson, Matthew O., 2007. "The formation of networks with transfers among players," Journal of Economic Theory, Elsevier, vol. 133(1), pages 83-110, March.
    15. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    16. Kirchsteiger, Georg & Mantovani, Marco & Mauleon, Ana & Vannetelbosch, Vincent, 2016. "Limited farsightedness in network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 97-120.
    17. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2019. "Stability of networks under horizon-K farsightedness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 177-201, July.
    18. Kimya, Mert, 2020. "Equilibrium coalitional behavior," Theoretical Economics, Econometric Society, vol. 15(2), May.
    19. Effrosyni Diamantoudi & Licun Xue, 2003. "Farsighted stability in hedonic games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 39-61, August.
    20. Ana Mauleon & Simon Schopohl & Akylai Taalaibekova & Vincent Vannetelbosch, 2022. "Coordination on networks with farsighted and myopic agents," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 509-536, November.
    21. Qianfeng Tang & Yongchao Zhang, 2021. "Weak stability and Pareto efficiency in school choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 533-552, March.
    22. Dogan, Battal & Ehlers, Lars, 2021. "Minimally unstable Pareto improvements over deferred acceptance," Theoretical Economics, Econometric Society, vol. 16(4), November.
    23. Ana Mauleon & Vincent Vannetelbosch, 2004. "Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers," Theory and Decision, Springer, vol. 56(3), pages 291-324, May.
    24. P. Jean-Jacques Herings & Ana Mauleon & Vincent Vannetelbosch, 2010. "Coalition Formation among Farsighted Agents," Games, MDPI, vol. 1(3), pages 1-13, September.
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    More about this item

    Keywords

    Social environments ; States ; Stability comparisons ; Farsighted players;
    All these keywords.

    JEL classification:

    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D20 - Microeconomics - - Production and Organizations - - - General

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