IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

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

  • Balbus, Łukasz
  • Reffett, Kevin
  • Woźny, Łukasz

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0165188913000134
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 37 (2013)
Issue (Month): 5 ()
Pages: 1019-1039

as
in new window

Handle: RePEc:eee:dyncon:v:37:y:2013:i:5:p:1019-1039
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Adrian Peralta-Alva & Manuel S. Santos, 2009. "Problems in the numerical simulation of models with heterogeneous agents and economic distortions," Working Papers 2009-036, Federal Reserve Bank of St. Louis.
  2. Coleman, Wilbur John, II, 1991. "Equilibrium in a Production Economy with an Income Tax," Econometrica, Econometric Society, vol. 59(4), pages 1091-1104, July.
  3. Susan Athey & Andrew Atkeson & Patrick J. Kehoe, 2004. "The optimal degree of discretion in monetary policy," Staff Report 326, Federal Reserve Bank of Minneapolis.
  4. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  5. Christopher Phelan & Ennio Stacchetti, 1999. "Sequential equilibria in a Ramsey tax model," Staff Report 258, Federal Reserve Bank of Minneapolis.
  6. Bernheim, B Douglas & Ray, Debraj, 1987. "Economic Growth with Intergenerational Altruism," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 227-41, April.
  7. Albert Marcet & Ramon Marimon, 2011. "Recursive Contracts," Economics Working Papers ECO2011/15, European University Institute.
  8. Andrzej Nowak, 2006. "On perfect equilibria in stochastic models of growth with intergenerational altruism," Economic Theory, Springer, vol. 28(1), pages 73-83, 05.
  9. Leonard J Mirman & Olivier F. Morand & Kevin L. Reffett, 2004. "A Qualitative Approach to Markovian Equilibrium in Infinite Horizon Economies with Capital," Levine's Bibliography 122247000000000224, UCLA Department of Economics.
  10. Kydland, Finn E. & Prescott, Edward C., 1980. "Dynamic optimal taxation, rational expectations and optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 79-91, May.
  11. Matthias Messner & Nicola Pavoni, 2004. "On the Recursive Saddle Point Method," Levine's Bibliography 122247000000000050, UCLA Department of Economics.
  12. Zhigang Feng & Jianjun Miao & Adrian Peralta-Alva & Manual Santos, 2009. "Numerical Simulation of Nonoptimal Dynamic Equilibrium Models," Working Papers 0912, University of Miami, Department of Economics.
  13. Rustichini, Aldo, 1998. "Dynamic Programming Solution of Incentive Constrained Problems," Journal of Economic Theory, Elsevier, vol. 78(2), pages 329-354, February.
  14. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-91, June.
  15. AMIR , Rabah, 1994. "Strategic Intergenerational Bequests with Stochastic Convex Production," CORE Discussion Papers 1994025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Andrew Atkeson, 2010. "International lending with moral hazard and risk of repudiation," Levine's Working Paper Archive 200, David K. Levine.
  17. AMIR , Rabah, 1995. "Continuous Stochastic Games of Capital Accumulation with Convex Transition," CORE Discussion Papers 1995009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  18. repec:spr:compst:v:62:y:2005:i:1:p:3-22 is not listed on IDEAS
  19. Laitner, John, 1979. "Household Bequests, Perfect Expectations, and the National Distribution of Wealth," Econometrica, Econometric Society, vol. 47(5), pages 1175-93, September.
  20. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
  21. K. Hinderer, 2005. "Lipschitz Continuity of Value Functions in Markovian Decision Processes," Mathematical Methods of Operations Research, Springer, vol. 62(1), pages 3-22, 09.
  22. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  23. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, 07.
  24. Peleg, Bezalel & Yaari, Menahem E, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 391-401, July.
  25. John Laitner, 2002. "Wealth Inequality and Altruistic Bequests," American Economic Review, American Economic Association, vol. 92(2), pages 270-273, May.
  26. Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
  27. Loury, Glenn C, 1981. "Intergenerational Transfers and the Distribution of Earnings," Econometrica, Econometric Society, vol. 49(4), pages 843-67, June.
  28. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-63, September.
  29. repec:spr:compst:v:66:y:2007:i:3:p:513-530 is not listed on IDEAS
  30. Laitner, John, 1979. "Household Bequest Behaviour and the National Distribution of Wealth," Review of Economic Studies, Wiley Blackwell, vol. 46(3), pages 467-83, July.
  31. Andrzej Nowak, 2003. "On a new class of nonzero-sum discounted stochastic games having stationary Nash equilibrium points," International Journal of Game Theory, Springer, vol. 32(1), pages 121-132, December.
  32. Horst, Ulrich, 2005. "Stationary equilibria in discounted stochastic games with weakly interacting players," Games and Economic Behavior, Elsevier, vol. 51(1), pages 83-108, April.
  33. Leininger, Wolfgang, 1986. "The Existence of Perfect Equilibria in a Model of Growth with Altruism between Generations," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 349-67, July.
  34. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:37:y:2013:i:5:p:1019-1039. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.