A Constructive Geometrical Approach to the Uniqueness of Markov Stationary Equilibrium in Stochastic Games of Intergenerational Altruism
University of Zielona Gora - Institute of Mathematics
Arizona State University - Department of Economics
Lukasz Patryk Wozny
Warsaw School of Economics - Department of Applied and Theoretical Economics
May 3, 2011
We provide sufficient conditions for existence and uniqueness of a monotone, Lipschitz continuous Markov stationary Nash equilibrium and implied invariant distribution 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, hence can be used to build globally stable asymptotically uniformly consistent numerical schemes for approximate solutions via Picard iterations on approximate versions of our operators. Our results provide hence a new catalog of tools for rigorous analysis of Markov stationary equilibrium on minimal state spaces for overlapping generations with stochastic production, without commitment.
Number of Pages in PDF File: 50
Keywords: stochastic games, constructive methods, intergenerational altruism
JEL Classification: C62, C73, D91, 040working papers series
Date posted: May 5, 2011
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