TY - JOUR
T1 - Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment
AU - Balbus, Łukasz
AU - Reffett, Kevin
AU - Woźny, Łukasz
N1 - Funding Information:
We thank Rabah Amir, Manjira Datta, Len Mirman, Adrian Peralta-Alva, and Ed Prescott for helpful conversations as well as an anonymous referee for important points. We also thank participants of our sessions at XIXth European Workshop on General Equilibrium Theory, Kraków, as well as at the 4th International Conference on Game Theory and Management, St. Petersburg for helpful comments. Reffett thanks the Dean’s Summer Grant Program at ASU for generous financial support of this research. All the usual caveats apply.
PY - 2012/3
Y1 - 2012/3
N2 - We introduce a new class of infinite 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 etal. (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.
AB - We introduce a new class of infinite 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 etal. (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.
KW - Commitment
KW - Constructive methods
KW - Markov perfect Nash equilibrium
KW - Stochastic games
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U2 - 10.1016/j.jmateco.2012.02.002
DO - 10.1016/j.jmateco.2012.02.002
M3 - Article
AN - SCOPUS:84858747327
SN - 0304-4068
VL - 48
SP - 115
EP - 132
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
IS - 2
ER -