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A Mean Field Capital Accumulation Game with HARA Utility

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  • Minyi Huang

Abstract

This paper introduces a mean field modeling framework for consumption-accumulation optimization. The production dynamics are generalized from stochastic growth theory by addressing the collective impact of a large population of similar agents on efficiency. This gives rise to a stochastic dynamic game with mean field coupling in the dynamics, where we adopt a hyperbolic absolute risk aversion (HARA) utility functional for the agents. A set of decentralized strategies is obtained by using the Nash certainty equivalence approach. To examine the long-term behavior we introduce a notion called the relaxed stationary mean field solution. The simple strategy computed from this solution is used to investigate the out-of-equilibrium behavior of the mean field system. Interesting nonlinear phenomena can emerge, including stable equilibria, limit cycles and chaos, which are related to the agent’s sensitivity to the mean field. Copyright Springer Science+Business Media New York 2013

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  • Minyi Huang, 2013. "A Mean Field Capital Accumulation Game with HARA Utility," Dynamic Games and Applications, Springer, vol. 3(4), pages 446-472, December.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:4:p:446-472
    DOI: 10.1007/s13235-013-0092-9
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    1. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    3. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    4. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    5. Łukasz Balbus & Andrzej S. Nowak, 2004. "Construction of Nash equilibria in symmetric stochastic games of capital accumulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 267-277, October.
    6. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    7. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    8. Dockner, Engelbert J. & Nishimura, Kazuo, 2005. "Capital accumulation games with a non-concave production function," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 408-420, August.
    9. Robert J. Barro & Xavier Sala-I-Martin, 1992. "Public Finance in Models of Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 645-661.
    10. Hamidou Tembine & Quanyan Zhu & Tamer Basar, 2011. "Risk-sensitive mean field stochastic differential games," Post-Print hal-00643547, HAL.
    11. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    12. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    13. Jerusalem D. Levhari & T. N. Srinivasan, 1969. "Optimal Savings under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(2), pages 153-163.
    14. Liu, Wen-Fang & Turnovsky, Stephen J., 2005. "Consumption externalities, production externalities, and long-run macroeconomic efficiency," Journal of Public Economics, Elsevier, vol. 89(5-6), pages 1097-1129, June.
    15. repec:dau:papers:123456789/6046 is not listed on IDEAS
    16. Duffie, Darrell & Fleming, Wendell & Soner, H. Mete & Zariphopoulou, Thaleia, 1997. "Hedging in incomplete markets with HARA utility," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 753-782, May.
    17. Lambson, Val Eugene, 1984. "Self-enforcing collusion in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 34(2), pages 282-291, December.
    18. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2008. "Markov Perfect Industry Dynamics With Many Firms," Econometrica, Econometric Society, vol. 76(6), pages 1375-1411, November.
    19. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    20. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    21. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
    22. David Cass, 1965. "Optimum Growth in an Aggregative Model of Capital Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(3), pages 233-240.
    23. Olson, Lars J. & Roy, Santanu, 2000. "Dynamic Efficiency of Conservation of Renewable Resources under Uncertainty," Journal of Economic Theory, Elsevier, vol. 95(2), pages 186-214, December.
    24. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    25. Mendelssohn, Roy & Sobel, Matthew J., 1980. "Capital accumulation and the optimization of renewable resource models," Journal of Economic Theory, Elsevier, vol. 23(2), pages 243-260, October.
    26. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    27. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    28. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
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