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Local versions of Tarski's theorem for correspondences

Author

Listed:
  • Łukasz Balbus
  • Wojciech Olszewski
  • Kevin Reffett
  • Łukasz Woźny

Abstract

For a strong set order increasing (resp., strongly monotone) upper order hemicontinuous correspondence mapping a complete lattice A into itself (resp., a sigma-complete lattice into itself), we provide conditions for tight fixed-point bounds for sufficiently large iterations starting from any initial point in A. Our results prove a local version of the Veinott-Zhou generalization of Tarski’s theorem, as well as provide a new global version of the Tarski-Kantorovich principle for correspondences.

Suggested Citation

  • Łukasz Balbus & Wojciech Olszewski & Kevin Reffett & Łukasz Woźny, 2023. "Local versions of Tarski's theorem for correspondences," KAE Working Papers 2023-085, Warsaw School of Economics, Collegium of Economic Analysis.
    • Handle: RePEc:sgh:kaewps:2023085
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    File URL: http://hdl.handle.net/20.500.12182/1144
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    References listed on IDEAS

    as
    1. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    2. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2015. "Time consistent Markov policies in dynamic economies with quasi-hyperbolic consumers," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 83-112, February.
    3. Li, Huiyu & Stachurski, John, 2014. "Solving the income fluctuation problem with unbounded rewards," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 353-365.
    4. Echenique, Federico & Edlin, Aaron, 2004. "Mixed equilibria are unstable in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 118(1), pages 61-79, September.
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    More about this item

    Keywords

    monotone iterations on correspondences; Tarski's fixed-point theorem; Veinott-Zhou version of Tarski’s theorem for correspondences; Tarski-Kantorovich principle for correspondences; adaptive learning;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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