Commenced in January 2007
Paper Count: 32451
A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society
Abstract:This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1132647Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 847
 D. Acemoglu and J. Robinson. Economic Origins of Dictatorship and Democracy. Cambridge University Press. New York, 2006.
 D. Acemoglu, G. Egorov, and K. Sonin. Political model of social evolution. Proceedings of the National Academy of Sciences of the United States of American, 108 Suppl 4:21292–21296, 2011.
 D. Acemoglu, G. Egorov, and K. Sonin. Dynamics and stability of constitutions, coalitions and clubs. Am. Econ. Rev., 102(4), 2012.
 Jinhui H. Bai and Roger Lagunoff. On the Faustian dynamics of policy and political power. Review of Economic Studies, 78:17–48, 2011.
 S. Barber, M. Maschler, and J. Shalev. Voting for voters: A model of the electoral evolution. Games Econ. Behav., 37:40–78, 2001.
 L. D. Berkovitz. Two person zero sum differential games: an overview. In J. D. Grote, editor, The theory and application of differential games. D. Reidel Publishing Company, 1974.
 Bruce Bueno de Mesquita. Game theory, political economy, and the evolving study of war and peace. American Political Science Review, 4:638–642, 2006.
 R. J. Elliott. Introduction to differential games ii. stochastic games and parabolic equations. In J. D. Grote, editor, The theory and application of differential games. D. Reidel Publishing Company, 1974.
 A. Friedman. Differential Games. Wiley, 1971.
 Arieh Gavious and Shlomo Mizrahi. A signaling model of peaceful political change. Soc. Choice Welfare, 20:119–136, 2003.
 A. Gomes and P. Jehiel. Dynamic processes of social and economic interactions: On the persistence of inefficiencies. J. Polit. Econ., 113: 626–667, 2005.
 F. Huang. The coevolution of economic and political development from monarchy to democracy. International Economic Review, 53(4): 1341–1368, 2012.
 F. Huang. Why did universities precede primary schools? a political economy model of educational change. Economic Inquiry, 50:418–434, 2012.
 Paul E. Johnson. Formal theories of politics: The scope of mathematical modelling in political science. Mathl Comput. Modelling, 12(4/5): 397–404, 1989.
 Roger Lagunoff. Dynamic stability and reform of political institutions. Games and Economic Behavior, 67:569–583, 2009.
 Leonardo Martinez. A theory of political cycles. Journal of Economic Theory, 144:1166–1186, 2009.
 Nolan McCarty and Adam Meirowitz. Political Game Theory, An Introduction. Cambridge University Press, 2007.
 Akira Okada, Kenichi Sakakibara, and Koichi Suga. The dynamic transformation of political systems through social contract: a game theoretic approach. Soc. Choice Welf., 14:1–21, 1997.
 Lawrence Perko. Differential Equations and Dynamical Systems. 3 edition.
 A. W. Starr and Y. C. Ho. Further properties of nonzero-sum differential games. J. Optimization Theory and Applications, 3:207–219, 1969.
 K. Uchida. On existence of a nash equilibrium point in n-person nonzero sum stochastic differential games. SIAM J. Control Optim., 16:142–149, 1978.
 P. P. Varaiya. N-player stochastic differential games. SIAM J. Control Optim., 4:538–545, 1976.
 Eelco Zandberg, Jakob de Haan, and J. Paul Elhorst. The political economy of financial reform: How robust are Huang’s findings. J. Appl. Econ., 27:695–699, 2012.