COMPARATIVE STUDIES ON COOPERATIVE STOCHASTIC DIFFERENTIAL GAME AND DYNAMIC SEQUENTIAL GAME OF ECONOMIC MATURITY
Abstract
In the paper, we are encouraged to investigate the effect of game structure imposed on the minimum-time needed to economic maturity in a dynamic macroeconomic model. Indeed, we have established a basic framework for the comparative study of the cooperative stochastic differential game and dynamic sequential game of economic maturity. Moreover, in a simple stochastic growth model, closed-form solution of the minimum-time needed to economic maturity has been derived with the explicit condition, under which it is confirmed that cooperation between the representative household and the self-interested politician will definitely lead us to much faster economic maturity than that of sequential action, supplied, too. Finally, our model supports the comparative study of the minimum-time needed to economic maturity under different political-institution constraints.
References
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[44] Merton, R. C. (1975). An Asymptotic Theory of Growth under Uncertainty, Review of Economic Studies, 42: 375-393.
[45] North, D.C. (1990). Institutions, Institutional Change and Economic Performance. New York: Cambridge University Press.
[46] North, D.C. (1994). Economic Performance through Time, American Economic Review, 84: 359-368.
[47] Olson, M.C., (2000). Power and Prosperity: Outgrowing Communist and Capitalist Dictatorships. Basic Books, New York.
[48] Phelan, C., Stacchetti, E. (2001). Sequential Equilibria in a Ramsey Tax Model, Econometrica, 69: 1491- 1518.
[49] Phelps, E.S. (1961). The Golden Rule of Accumulation: A Fable for Growthmen, American Economic Review, 51: 638-643.
[50] Pohjola, M. (1983). Nash and Stackelberg Solution in a Differential Game Model of Capitalism, Journal of Economic Dynamics and Control, 6: 173-186.
[51] Øksendal, B. (2003). Stochastic Differential Equations. Berlin: Springer-Verlag, sixth edition.
[52] Øksendal, B., Sulem, A. (2005). Applied Stochastic Control of Jump Diffusions. Berlin: Springer-Verlag.
[53] Radner, R. (1961). Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem, Review of Economic Studies, 28: 98-104.
[54] Rebelo, S. (1991). Long-run Policy Analysis and Long-run Growth, Journal of Political Economy, 99: 500 -521.
[55] Sen, A. (1970). Interpersonal Aggregation and Partial Comparability, Econometrica, 38: 393-409.
[56] Simaan, M., and Cruz, J.B. (1973). On the Stackelberg Strategy in Nonzero-Sum Games, Journal Optimization Theory and Applications, 11: 533-555.
[57] Solow, R.M. (2003). Reflections on Growth and Development, Annals of Economics and Finance, 4: 219- 229.
[58] Song, Z., Storesletten, K. and Zilibotti, F. 2011. Growing Like China, American Economic Review, 101: 202- 241.
[59] Turnovsky, S.J. (2000). Fiscal Policy, Elastic Labor Supply, and Endogenous Growth, Journal of Monetary Economics, 45: 185-210.
[60] Wälde, K. (2011). Production Technologies in Stochastic Continuous Time Models, Journal of Economic Dynamics and Control, 35: 616-622.
[61] Williamson, O.E. (2000). The New Institutional Economics: Taking Stock, Looking Ahead, Journal of Economic Literature, 38: 595-613.
[62] Yared, P. (2010). Politicians, Taxes and Debt, Review of Economic Studies, 77: 806-840.
[63] Yeung, D.W.K., and Petrosyan, L. (2006). Cooperative Stochastic Differential Games. Springer, New York.
[2] Acemoglu, D., Golosov, M., Tsyvinski, A. (2010). Dynamic Mirrlees Taxation under Political Economy Constraint, Review of Economic Studies, 77: 841-881.
[3] Acemoglu, D., Golosov, M., Tsyvinski, A. (2011). Political economy of Ramsey taxation, Journal of Public Economics, 95: 467-475.
[4] Acemoglu, D., Johnson, S., and Robinson, J.A. (2005a). The Rise of Europe: Atlantic Trade, Institutional Change, and Economic Growth, American Economic Review, 95: 546-79.
[5] Acemoglu, D., Johnson, S., Robinson, J.A. (2005b). Institutions as a Fundamental Cause of Development. In Handbook of Economic Growth, ed. Philippe Aghion and Steven Durlauf, 386-472. Amsterdam, Holland: Elsevier.
[6] Aghion, P. (2004). Growth and Development: A Schumpeterian Approach, Annals of Economics and Finance, 5: 1-25.
[7] Akerlof, G.A. (1997). Social Distance and Social Decisions, Econometrica, 65: 1005-1027.
[8] Amable, B. (2003).The Diversity of Modern Capitalism. Oxford: Oxford University Press.
[9] Barro, R.J. (1973). The Control of Politicians: an Economic Model, Public Choice, 14: 19-42.
[10] Barro, R.J. (1990). Government Spending in a Simple Model of Endogenous Growth, Journal of Political Economy, 98: 103-125.
[11] Başar, T., Haurie, A., Ricci, G. (1985). On the Dominance of Capitalism Leadership in a Feedback-Stackelberg Solution of a Differential Game Model of Capitalism, Journal of Economic Dynamics and Control, 9: 101-125.
[12] Buchanan, J.M., Tullock, G. (1962). The Calculus of Consent. University of Michigan Press, Michigan.
[13] Chakraborty, S. (2004). Endogenous Lifetime and Economic Growth, Journal of Economic Theory, 116: 119-137.
[14] Chamley, C. (1986). Optimal Taxation of Capital Income in General Equilibrium with Infinite Lives, Econometrica, 54: 607-622.
[15] Chang, F., Malliaris, A.G. (1987). Asymptotic Growth under Uncertainty: Existence and Uniqueness, Review of Economic Studies, 54: 169-174.
[16] Chari, V.V., Kehoe, P.J. (1990). Sustainable Plans, Journal of Political Economy, 98: 783-802.
[17] Chari, V.V., Kehoe, P.J. (1993). Sustainable Plans and Mutual Default, Review of Economic Studies, 60: 175-195.
[18] Coase, R.H. (1988). The Firm, the Market and the Law. Chicago: University of Chicago Press.
[19] Dai, D.(2012). Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology, Annals of Economics and Finance, 13: 389-431.
[20] Dai, D. (2013). Modeling the Minimum Time Needed to Economic Maturity, Economic Research Guardian, 3: 2-21.
[21] Dai, D., Shen, K., Ma, R. (2013). A Case against Zero Capital-Income Taxation, Frontiers of Economics, China, 8: 65-91.
[22] de la Croix, D., Ponthiere, G. (2010). On the Golden Rule of Capital Accumulation under Endogenous Longevity, Mathematical Social Sciences, 59: 227-238.
[23] Farhi, E., Werning, I. (2008). The Political Economy of Nonlinear Capital Taxation. Mimeo, Harvard and MIT.
[24] Ferejohn, J. (1986). Incumbent Performance and Electoral Control, Public Choice, 50: 5-25.
[25] Fischer, S. (1980). Dynamic Inconsistency, Cooperation, and the Benevolent Dissembling Government, Journal of Economic Dynamics and Control, 2: 93-107.
[26] Harsanyi, J. (1955). Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility, Journal of Political Economy, 63: 309-321.
[27] Hoel, M. (1978). Distribution and Growth as a Differential Game between Workers and Capitalists, International Economic Review, 19: 335-350.
[28] Hurwicz, L. (1996). Institutions as Families of Game-forms, Japanese Economic Review, 47: 13-132.
[29] Jeanblanc, M., Lakner, P., and Kadam, A. (2004). Optimal Bankruptcy Time and Consumption/ Investment Policies on an Infinite Horizon with a Continuous Debt Repayment until Bankruptcy, Mathematics of Operations Research, 29: 649-671.
[30] Jones, L.E., Manuelli, R.E., Rossi, P.E. (1993). Optimal Taxation in Models of Endogenous Growth, Journal of Political Economy, 101: 485-517.
[31] Judd, K. (1985). Redistributive Taxation in a Simple Perfect Foresight Model, Journal of Public Economics, 78: 59-83.
[32] Kaitala, V., Pohjola, M. (1990). Economic Development and Agreeable Redistribution in Capitalism: Efficient Game Equilibria in a Two-Class Neoclassical Growth Model, International Economic Review, 31, 421-438.
[33] Kalai, E. (1977). Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons, Econometrica, 45: 1623-1630.
[34] Karatzas, I., Wang, H. (2000). Utility Maximization with Discretionary Stopping, SIAM Journal on Control and Optimization, 39: 306-329.
[35] Klein, P., Krusell, P., Rios-Rull, J.-V. (2008). Time-Consistent Public Policy, Review of Economic Studies, 75: 789-808.
[36] Kocherlakota, N.R. (2005). Zero Expected Wealth Taxes: a Mirrlees Approach to Dynamic Optimal Taxation, Econometrica, 73: 1587-1621.
[37] Kurz, M., (1965). Optimal Paths of Capital Accumulation under the Minimum Time Objective, Econometrica, 33: 42-66.
[38] Kydland, F., and Prescott, E.C. (1977). Rules Rather than Discretion: The Inconsistency of Optimal Plans, Journal of Political Economy, 85: 473-492.
[39] Lancaster, K. (1973). The Dynamic Inefficiency of Capitalism, Journal of Political Economy, 81: 1092- 1109.
[40] Leong, C.K., Huang, W. (2010). A Stochastic Differential Game of Capitalism, Journal of Mathematical Economics, 46: 552-561.
[41] McKenzie, L. (1963a). The Dorfman-Samuelson-Solow Turnpike Theorem, International Economic Review, 4: 29-43.
[42] McKenzie, L., (1963b). Turnpike Theorems for a Generalized Leontief Model, Econometrica, 31: 165- 180.
[43] McKenzie, L. (1976). Turnpike Theory, Econometrica, 44: 841-865.
[44] Merton, R. C. (1975). An Asymptotic Theory of Growth under Uncertainty, Review of Economic Studies, 42: 375-393.
[45] North, D.C. (1990). Institutions, Institutional Change and Economic Performance. New York: Cambridge University Press.
[46] North, D.C. (1994). Economic Performance through Time, American Economic Review, 84: 359-368.
[47] Olson, M.C., (2000). Power and Prosperity: Outgrowing Communist and Capitalist Dictatorships. Basic Books, New York.
[48] Phelan, C., Stacchetti, E. (2001). Sequential Equilibria in a Ramsey Tax Model, Econometrica, 69: 1491- 1518.
[49] Phelps, E.S. (1961). The Golden Rule of Accumulation: A Fable for Growthmen, American Economic Review, 51: 638-643.
[50] Pohjola, M. (1983). Nash and Stackelberg Solution in a Differential Game Model of Capitalism, Journal of Economic Dynamics and Control, 6: 173-186.
[51] Øksendal, B. (2003). Stochastic Differential Equations. Berlin: Springer-Verlag, sixth edition.
[52] Øksendal, B., Sulem, A. (2005). Applied Stochastic Control of Jump Diffusions. Berlin: Springer-Verlag.
[53] Radner, R. (1961). Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem, Review of Economic Studies, 28: 98-104.
[54] Rebelo, S. (1991). Long-run Policy Analysis and Long-run Growth, Journal of Political Economy, 99: 500 -521.
[55] Sen, A. (1970). Interpersonal Aggregation and Partial Comparability, Econometrica, 38: 393-409.
[56] Simaan, M., and Cruz, J.B. (1973). On the Stackelberg Strategy in Nonzero-Sum Games, Journal Optimization Theory and Applications, 11: 533-555.
[57] Solow, R.M. (2003). Reflections on Growth and Development, Annals of Economics and Finance, 4: 219- 229.
[58] Song, Z., Storesletten, K. and Zilibotti, F. 2011. Growing Like China, American Economic Review, 101: 202- 241.
[59] Turnovsky, S.J. (2000). Fiscal Policy, Elastic Labor Supply, and Endogenous Growth, Journal of Monetary Economics, 45: 185-210.
[60] Wälde, K. (2011). Production Technologies in Stochastic Continuous Time Models, Journal of Economic Dynamics and Control, 35: 616-622.
[61] Williamson, O.E. (2000). The New Institutional Economics: Taking Stock, Looking Ahead, Journal of Economic Literature, 38: 595-613.
[62] Yared, P. (2010). Politicians, Taxes and Debt, Review of Economic Studies, 77: 806-840.
[63] Yeung, D.W.K., and Petrosyan, L. (2006). Cooperative Stochastic Differential Games. Springer, New York.
Published
2013-06-30
How to Cite
DAI, Darong; YIN, Jun.
COMPARATIVE STUDIES ON COOPERATIVE STOCHASTIC DIFFERENTIAL GAME AND DYNAMIC SEQUENTIAL GAME OF ECONOMIC MATURITY.
Theoretical and Practical Research in Economic Fields, [S.l.], v. 4, n. 1, p. 25-60, june 2013.
ISSN 2068-7710.
Available at: <https://journals.aserspublishing.eu/tpref/article/view/1175>. Date accessed: 12 july 2025.
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