Stationary Markovian Equilibrium in Altruistic Stochastic OLG Models with Limited Commitment

55 Pages Posted: 25 Aug 2011 Last revised: 27 Jan 2012

See all articles by Lukasz Balbus

Lukasz Balbus

University of Zielona Gora - Institute of Mathematics

Kevin Reffett

Arizona State University - Department of Economics

Lukasz Patryk Wozny

Warsaw School of Economics - Quantitative Economics Department; Warsaw School of Economics (SGH)

Date Written: August 25, 2011

Abstract

We introduce a new class of in nite horizon altruistic stochastic OLG models with capital and labor, but without commitment between the generations. Under mild regularity conditions, for economies with either bounded or unbounded state spaces, continuous monotone Markov perfect Nash equilibrium (henceforth MPNE) are shown to exist, and form an antichain. Further, for each such MPNE, we can also construct a corresponding stationary Markovian equilibrium invariant distribution. We then show for many versions of our economies found in applied work in macroeconomics, unique MPNE exist relative to the space of bounded measurable functions. We also relate all of our results to those obtained by promised utility/continuation methods based upon the work of Abreu et al. (1990). As our results are constructive, we can provide characterizations of numerical methods for approximating MPNE, and we construct error bounds. Finally, we provide a series of examples to show the potential applications and limitations of our results.

Keywords: stochastic games, Markov perfect Nash equilibrium, constructive methods, commitment

JEL Classification: C62, C73, D91, 040

Suggested Citation

Balbus, Lukasz and Reffett, Kevin L. and Wozny, Lukasz Patryk, Stationary Markovian Equilibrium in Altruistic Stochastic OLG Models with Limited Commitment (August 25, 2011). Available at SSRN: https://ssrn.com/abstract=1916819 or http://dx.doi.org/10.2139/ssrn.1916819

Lukasz Balbus

University of Zielona Gora - Institute of Mathematics ( email )

65-246 Zielona Góra
Poland

Kevin L. Reffett

Arizona State University - Department of Economics ( email )

Tempe, AZ 85287-3806
United States

Lukasz Patryk Wozny (Contact Author)

Warsaw School of Economics - Quantitative Economics Department ( email )

Warsaw
Poland

Warsaw School of Economics (SGH) ( email )

aleja Niepodleglosci 162
PL-Warsaw, 02-554
Poland

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