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

Yuankan Huang () and Takehiro Inohara ()
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Yuankan Huang: Tokyo Institute of Technology
Takehiro Inohara: Tokyo Institute of Technology

Economic Theory Bulletin, 2023, vol. 11, issue 1, No 3, 45-63

Abstract: 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.

Keywords: Asymmetric differential games; Dynamic duopoly; Renewable resource; Markov perfect equilibria; Ordinary differential systems; Removable singularities (search for similar items in EconPapers)
JEL-codes: C73 L13 Q2 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s40505-022-00230-6

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