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Stable Markov perfect equilibria in the asymmetric differential-game duopoly with a renewable resource

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  • Yuankan Huang

    (Tokyo Institute of Technology)

  • Takehiro Inohara

    (Tokyo Institute of Technology)

Abstract

We derive an ordinary differential equations (ODE) system from the Hamilton–Jacob–Bellman (HJB) equation in an asymmetric differential-game duopoly with a renewable resource. We show the ODE system admits asymmetric stable Markov perfect equilibria (MPEs) passing through removable singularities. This result relaxes restriction of solving the HJB equation, so that nonlinear stable MPEs can be derived under various asymmetric setups. We also give multiple numerical examples to exhibit bigger difference in firms’ profit functions and discount rates may lead to lower steady states for the asymmetric MPEs.

Suggested Citation

  • Yuankan Huang & Takehiro Inohara, 2023. "Stable Markov perfect equilibria in the asymmetric differential-game duopoly with a renewable resource," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 45-63, April.
    • Handle: RePEc:spr:etbull:v:11:y:2023:i:1:d:10.1007_s40505-022-00230-6
    DOI: 10.1007/s40505-022-00230-6
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    More about this item

    Keywords

    Asymmetric differential games; Dynamic duopoly; Renewable resource; Markov perfect equilibria; Ordinary differential systems; Removable singularities;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation

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