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A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism

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  • Balbus, Łukasz
  • Reffett, Kevin
  • Woźny, Łukasz

Abstract

We provide sufficient conditions for existence and uniqueness of a monotone, Lipschitz continuous Markov stationary Nash equilibrium (MSNE) and characterize its associated Stationary Markov equilibrium in a class of intergenerational paternalistic altruism models with stochastic production. Our methods are constructive, and emphasize both order-theoretic and geometrical properties of nonlinear fixed point operators, and relate our results to the construction of globally stable numerical schemes that construct approximate Markov equilibrium in our models. Our results provide a new catalog of tools for the rigorous analysis of MSNE on minimal state spaces for OLG economies with stochastic production and limited commitment.

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  • Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2013. "A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1019-1039.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:5:p:1019-1039
    DOI: 10.1016/j.jedc.2013.01.005
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    Cited by:

    1. Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2016. "Non-paternalistic intergenerational altruism revisited," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 27-33.
    2. Wozny Lukasz & Growiec Jakub, 2012. "Intergenerational Interactions in Human Capital Accumulation," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-47, June.
    3. Łukasz Balbus, 2020. "On recursive utilities with non-affine aggregator and conditional certainty equivalent," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 551-577, September.
    4. 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.
    5. Edward C. Prescott & Kevin L. Reffett, 2016. "Preface: Special Issue on Dynamic Games in Macroeconomics," Dynamic Games and Applications, Springer, vol. 6(2), pages 157-160, June.
    6. Yu, Meng & Zhang, Junnan, 2019. "Equilibrium in production chains with multiple upstream partners," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 1-10.
    7. Meng Yu & Junnan Zhang, 2019. "Equilibrium in Production Chains with Multiple Upstream Partners," Papers 1908.08208, arXiv.org.
    8. Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2015. "Existence of Stationary Markov Perfect Equilibria in Stochastic Altruistic Growth Economies," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 295-315, April.
    9. Jaśkiewicz, Anna & Nowak, Andrzej S., 2014. "Stationary Markov perfect equilibria in risk sensitive stochastic overlapping generations models," Journal of Economic Theory, Elsevier, vol. 151(C), pages 411-447.
    10. Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2020. "Equilibria in Altruistic Economic Growth Models," Dynamic Games and Applications, Springer, vol. 10(1), pages 1-18, March.

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    More about this item

    Keywords

    Stochastic games; Constructive methods; Intergenerational altruism;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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