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Analysis of decision-making in economic chaos control. (English) Zbl 1163.91331
Summary: In some economic chaotic systems, players are concerned about whether their performance is improved besides taking some methods to control chaos. In the face of chaos occurring in competition, whether one player takes controlling measures or not affects not only their own earning but also other opponents’ income. An output duopoly competing evolution model with bounded rationality is introduced in this paper. Using modern game theory, decision-making analyses about chaos control of the model are taken by taking aggregate profits as players’ payoff. It is found that the speed of players’ response to the market and whether the decisive parameters are in the stable region of the Nash equilibrium or not have a distinct influence on the results of the game. The impact of cost function’ type on results of the game is also found. The mechanism of influences is discovered by using numerical simulation.

91B06Decision theory
Full Text: DOI
[1] Agiza, H. N.; Hegazi, A. S.; Elsadany, A. A.: Complex dynamics and synchronization of a duopoly game with bounded rationality. Mathematics and computers in simulation 58, 133-146 (2002) · Zbl 1002.91010
[2] Agiza, H. N.; Hegazi, A. S.; Elsadany, A.: The dynamics of bowley’s model with bounded rationality. Chaos, solitons and fractals 12, 1705-1717 (2001) · Zbl 1036.91004
[3] Ahmed, E.; Agiza, H. N.: Dynamics of a cournot game with n-competitors. Chaos solitons and fractals 9, No. 9, 1513-1517 (1998) · Zbl 0952.91004
[4] Ahmed, E.; El-Misiery, A.; Agiza, H. N.: On controlling chaos in an inflation-unemployment dynamical system. Chaos solitons and fractals 10, 1567-1570 (1999) · Zbl 0958.91042
[5] Andrievskii, B. R.; Fradkov, A. L.: Control of chaos: methods and applications.i. Method. Automation and remote control 64, No. 5, 673-713 (2003) · Zbl 1107.37302
[6] Andrievskii, B. R.; Fradkov, A. L.: Control of chaos: methods and applications.ii. Application. Automation and remote control 65, No. 4, 505-533 (2004) · Zbl 1115.37315
[7] Bischi, G. I.; Naimzada, A.: Global analysis of a dynamic duopoly game with bounded rationality. Dynamics games and application 5 (1999) · Zbl 0957.91027
[8] Du, J. G.; Sheng, Z. H.; Yao, H. X.: Study on straight-line stabilization method for class of chaotic economic model. Journal of systems engineering in chinese 20, No. 4, 335-343 (2005) · Zbl 1154.91546
[9] Gallas, J. A. C; Nusse, H. E.: Periodicity versus chaos in the dynamics of cobweb models. Journal of economic behavior and organization 29, 447-464 (1996)
[10] Harsanyi, J. C.; Selten, R. A.: A general theory of equilibrium selection in games. (1988) · Zbl 0693.90098
[11] Hassan, S. Z.: On delayed dynamical duopoly. Applied mathematics and computation 151, 275-286 (2004) · Zbl 1088.91028
[12] He, X. Z.; Westerhoff, F. H.: Commodity markets, price limiters and speculative price dynamics. Journal of economic dynamics and control 29, No. 9, 1577-1596 (2005) · Zbl 1198.91161
[13] Holyst, J. A.; Urbanowicz, K.: Chaos control in economical model by time-delayed feedback method. Physical A 287, 587-598 (2000)
[14] Kass, L.: Stabilizing chaos in a dynamical macroeconomic model. Journal of economic behavior and organization 33, 313-332 (1998)
[15] Kopel, M.: Improving the performance of an economic system: controlling chaos. Journal of evolutionary economics 7, 269-289 (1997)
[16] Li, X.; Ying, J.; Chen, G. R.: Complexity and synchronization of the world trade web. Physica A 328, 287-296 (2003) · Zbl 1058.91065
[17] Mao, J. M.; Liu, Z. R.; Yang, L.: Straight-line stabilization. Physics review E 62, No. 4, 4846-4849 (2000)
[18] Wieland, C.; Westerhoff, F. H.: Exchange rate dynamics, central bank interventions and chaos control methods. Journal of economic behavior and organization 58, No. 1, 117-132 (2005)
[19] Xu, H. B.; Wang, G. R.; Chen, S. G.: Controlling chaos by a modified straight-line stabilization method. The European physical journal B 22, 65-69 (2001)
[20] Yassen, M. T.; Agiza, H. N.: Analysis of a duopoly game with delayed bounded rationality. Applied mathematics and computation 138, 387-402 (2003) · Zbl 1102.91021