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

Łukasz Balbus, Kevin Reffett and Łukasz Woźny

Journal of Economic Dynamics and Control, 2013, vol. 37, issue 5, 1019-1039

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.

Keywords: Stochastic games; Constructive methods; Intergenerational altruism (search for similar items in EconPapers)
JEL-codes: C62 C73 D91 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.jedc.2013.01.005

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