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A note on topological aspects in dynamic games of resource extraction and economic growth theory

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  • Jaśkiewicz, Anna
  • Nowak, Andrzej S.

Abstract

We show that right-continuous monotone strategies used in Markov perfect equilibria for economic growth models and related dynamic games can be recognised as members of the Hilbert space of square integrable functions of the state variable. We provide an application of this result to a bequest game and point out that this result also holds for the class of left-continuous monotone functions. The result is fundamental for using the Schauder fixed point theorem. Furthermore, it considerably simplifies the classical approach, where such strategies are represented by non-negative measures on the state space.

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  • Jaśkiewicz, Anna & Nowak, Andrzej S., 2022. "A note on topological aspects in dynamic games of resource extraction and economic growth theory," Games and Economic Behavior, Elsevier, vol. 131(C), pages 264-274.
    • Handle: RePEc:eee:gamebe:v:131:y:2022:i:c:p:264-274
    DOI: 10.1016/j.geb.2021.11.011
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    References listed on IDEAS

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    3. Łukasz Balbus & Anna Jaśkiewicz & Andrzej S. Nowak, 2020. "Markov perfect equilibria in a dynamic decision model with quasi-hyperbolic discounting," Annals of Operations Research, Springer, vol. 287(2), pages 573-591, April.
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    11. 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.
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    More about this item

    Keywords

    Economic growth model; Bequest game; Monotone strategies; Locally convex space;
    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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