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

Łukasz Balbus, Kevin Reffett, Łukasz Woźny

Research output: Contribution to journalArticle

15 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1019-1039
Number of pages21
JournalJournal of Economic Dynamics and Control
Volume37
Issue number5
DOIs
StatePublished - May 1 2013

Keywords

  • Constructive methods
  • Intergenerational altruism
  • Stochastic games

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics

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