TY - JOUR
T1 - A constructive geometrical approach to the uniqueness of Markov stationary equilibrium in stochastic games of intergenerational altruism
AU - Balbus, Łukasz
AU - Reffett, Kevin
AU - Woźny, Łukasz
N1 - Funding Information:
The authors thank Rabah Amir, Ken Judd, David Levine, Andrzej Nowak, Ed Prescott, Manuel Santos the anonymous referees at this journal, as well as the attendees at our presentation at the 13th International Symposium on Dynamic Games and Applications in Wrocław, Poland, for helpful conversations on issues relating to this paper. The usual caveats apply. Reffett gratefully acknowledges the Paris School of Economics during the Summer of 2008 , as well as the Dean's Summer Grant Program at ASU in the Summer of 2010 for financial support. Woźny acknowledges financial support from the Fulbright Program 2006–2007 ; SGH Dean's Grant for Young Researchers 2008 as well as Arizona State University, USA for hosting during the writing of this paper.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013/5
Y1 - 2013/5
N2 - 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.
AB - 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.
KW - Constructive methods
KW - Intergenerational altruism
KW - Stochastic games
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U2 - 10.1016/j.jedc.2013.01.005
DO - 10.1016/j.jedc.2013.01.005
M3 - Article
AN - SCOPUS:84875373537
SN - 0165-1889
VL - 37
SP - 1019
EP - 1039
JO - Journal of Economic Dynamics and Control
JF - Journal of Economic Dynamics and Control
IS - 5
ER -