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Stochastic bequest games

Author

Listed:
  • Balbus, Łukasz
  • Jaśkiewicz, Anna
  • Nowak, Andrzej S.

Abstract

In this paper, we prove the existence of a stationary Markov perfect equilibrium for a stochastic version of the bequest game. A novel feature in our approach is the fact that the transition probability need not be non-atomic and therefore, the deterministic production function is not excluded from consideration. Moreover, in addition to the common expected utility we also deal with a utility that takes into account an attitude of the generation towards risk.

Suggested Citation

  • Balbus, Łukasz & Jaśkiewicz, Anna & Nowak, Andrzej S., 2015. "Stochastic bequest games," Games and Economic Behavior, Elsevier, vol. 90(C), pages 247-256.
  • Handle: RePEc:eee:gamebe:v:90:y:2015:i:c:p:247-256
    DOI: 10.1016/j.geb.2015.02.017
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    References listed on IDEAS

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    1. Amir, Rabah, 1996. "Strategic Intergenerational Bequests with Stochastic Convex Production," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 367-376, August.
    2. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    4. Wolfgang Leininger, 1986. "The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 349-367.
    5. Kohlberg, Elon, 1976. "A model of economic growth with altruism between generations," Journal of Economic Theory, Elsevier, vol. 13(1), pages 1-13, August.
    6. Anderson, Evan W. & Hansen, Lars Peter & Sargent, Thomas J., 2012. "Small noise methods for risk-sensitive/robust economies," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 468-500.
    7. Harris, Christopher & Laibson, David, 2001. "Dynamic Choices of Hyperbolic Consumers," Econometrica, Econometric Society, vol. 69(4), pages 935-957, July.
    8. 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.
    9. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
    10. Dutta, Prajit K & Sundaram, Rangarajan, 1992. "Markovian Equilibrium in a Class of Stochastic Games: Existence Theorems for Discounted and Undiscounted Models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 197-214, April.
    11. Andrzej Nowak, 2006. "On perfect equilibria in stochastic models of growth with intergenerational altruism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 73-83, May.
    12. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
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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. Cingiz, Kutay & Flesch, Janos & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2016. "Perfect Information Games where Each Player Acts Only Once," Research Memorandum 036, Maastricht University, Graduate School of Business and Economics (GSBE).

    More about this item

    Keywords

    Stochastic game; Bequest game; Stationary Markov perfect equilibrium; Entropic risk measure;

    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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