Differential Games with (A) symmetric Players and Heterogeneous Strategies
DOI:
https://doi.org/10.6000/1929-7092.2016.05.15Keywords:
Differential game, Heterogeneous strategy, subgame perfect Markovian Nash Equilibrium, anticipating open-loop strategyAbstract
One family of heterogeneous strategies in differential games with (a)symmetric players is developed in which one player adopts an anticipating open-loop strategy and the other adopts a standard Markovian strategy. Via conjecturing principle, the anticipating open-loop strategic player plans her strategy based on the possible updating the rival player may take. These asymmetric strategies should be appropriate choices in some modelling circumstances and they frame one of the infinitely many non-degenerate Markovian Nash Equilibrium. Except the stationary path, this kind of strategy makes the study of short-run trajectory possible, which usually are not subgame perfect. However, the short-run non-perfection may provide very important policy suggestions.
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Basar, T. 1976. On the uniqueness of the Nash solution in linear-quadratic differential games. International Journal of Game Theory, 5(2/3), 65–90.
http://dx.doi.org/10.1007/BF01753310
Benchekroun, H. 2003. Unilateral production restrictions in a dynamic duopoly. Journal of Economic Theory, 111, 214-239.
http://dx.doi.org/10.1016/S0022-0531(03)00090-5
Benchekroun, H., A. Halsema and C. Withagen. 2009. On nonrenewable resource oligopolies: the asymmetric case. Journal of Economic Dynamic and Control, 33, 1867-1879.
http://dx.doi.org/10.1016/j.jedc.2009.03.008
Bertinelli, L., L. Marchiori, A. Tabakovic and B. Zou. 2015. Transboundary Pollution Abatement: The Impact of Unilateral Commitment in Differential Games. CREA DP 2015-02.
Dawid, H. and G. Feichtinger. 1996. Optimal allocation of drug control efforts: A differential game anaylsis. Journal of Optimization Theory and Application, 91(2), 279–297.
http://dx.doi.org/10.1007/BF02190097
Dockner, E. and G. Sorger. 1996. Existence and properties of equilibria for a dynamic game on productive assets. Journal of Economic Theory, 71, 209-227.
http://dx.doi.org/10.1006/jeth.1996.0115
Dockner, E., Jorgensen S., Van Long N., and G. Sorger. 2000. Differential games in economics and management: Cambridge University Press.
http://dx.doi.org/10.1017/CBO9780511805127
Easterly, W. and A. Kray. 2000. Small states, small problems ? Income, growth, and volatility in small states. World Development, 28 (11): 2013-2027.
http://dx.doi.org/10.1016/S0305-750X(00)00068-1
Fershtman, Ch. and M. Kamien. 1987. Dynamic duopolistic competition with sticky prices. Econometrica, 55(5), 1151-1164.
http://dx.doi.org/10.2307/1911265
Fershtman, Ch. and M. Kamien. 1990. Turnpike Properties in a Finite-Horizon Differential Game: Dynamic Duopoly with Sticky Prices. International Economics Review, 31(1), 49-60.
http://dx.doi.org/10.2307/2526627
Han, Y., Pieretti P., S. Zanaj and B. Zou. 2014. Asymmetric competition among Nation States-A differential game approach. Journal of Public Economics, 119, 71-79.
http://dx.doi.org/10.1016/j.jpubeco.2014.07.008
Itaya, J. and K. Shimomura. 2001. A dynamic conjectural variations model in the private provision of public goods: a differential game approach. Journal of Public Economics, 81, 153-172.
http://dx.doi.org/10.1016/S0047-2727(00)00111-0
Kamien, M. and N. Schwartz. 2003. Dynamic optimization. 2nd Edition and 7th Impression: Elsevier, North Holland.
Kuznets, S. 1960. Economic Growth of Small Nations. In The Economic Consequences of the Size of Nations. ed. E.A.G. Robinson. Proceedings of a Conference Held by the International Economic Associations: MacMillan, Toronto.
http://dx.doi.org/10.1007/978-1-349-15210-0_2
Long, N. 2010. A surveyy of Dynamic Games in Economics: World Scientific.
http://dx.doi.org/10.1142/9789814293044
Reinganum, J. and N. Stokey. 1985. Oligopoly extraction of a common perperty natureal esource: The importantce of the period of commitment in dynamic games. International Economic Review,39(1), 161-173.
http://dx.doi.org/10.2307/2526532
Reinganum, J. 1981. On the diffusion of new technology: A game theoretic approach. The Review of Economic Studies, 48(3), 395-405.
http://dx.doi.org/10.2307/2297153
Reynolds, S. 1987. Capacity investment, preemption and commitmnet in an infinite horizon model. International Economic Review, 28(1), 69-88.
http://dx.doi.org/10.2307/2526860
Shimomura, K. and J. F. Thisse. 2012. Competition among the big and the small. RAND Journal of Economics, RAND Corporation, 43(2), 329-347.
Sorger, G. 2015. Dynamic Economic Analysis: Deterministic Models in Discrete Time: Cambridge University Press.
Streeten, P. 1993. The Special Problems of Small Countries. World Development, 21(2): 197-202.
http://dx.doi.org/10.1016/0305-750X(93)90014-Z
Zissimos, B. and M. Wooders. 2008. Public good differentiation and the intensity of tax competition. Journal of Public Economics, 92, 1105-1121.
http://dx.doi.org/10.1016/j.jpubeco.2007.09.009
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Published
2016-05-30
How to Cite
Zou, B. (2016). Differential Games with (A) symmetric Players and Heterogeneous Strategies. Journal of Reviews on Global Economics, 5, 171–179. https://doi.org/10.6000/1929-7092.2016.05.15
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