Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality

Applied Mathematics and Computation

Volumn 271, Issue , 2015, Pages 259-268

  Peng, Yu ^a   Lu, Qian ^a  

^a SOUTHWEST UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Bifurcation; Bounded rationality; Chaotic; Stability; Stackelberg game

Indexed keywords

BIFURCATION (MATHEMATICS); COMPETITION; COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DYNAMICAL SYSTEMS; FEEDBACK; GAME THEORY; NONLINEAR DYNAMICAL SYSTEMS;

BACKWARD INDUCTION; BIFURCATION DIAGRAM; BOUNDED RATIONALITY; CHAOTIC; DISCRETE DYNAMICAL SYSTEMS; EQUILIBRIUM PROFITS; LOCAL STABILITY ANALYSIS; STACKELBERG GAMES;

STABILITY;

EID: 84942610432     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2015.08.138     Document Type: Article

References (36)

1. R. Gibbons A Primer in Game Theory 1992 Simon & Schuster New York
2. A.A. Cournot Researches into the Principles of the Theory of Wealth Irwin Paper Back Classics in Economics 1963
3. H. von Stackelberg Probleme der unvollkommenen konkurrenz Weltwirtschaftliches Archiv 48 1938 95 141
4. T. Puu Chaos in duopoly pricing Chaos Solit. Fract. 1 1991 573 581
5. T. Puu The chaotic duopolists revisited J. Econ. Behav. Organ. 37 1998 385 394
6. G.I. Bischi, and A. Naimzada Global Analysis of a Dynamic Duopoly Game with Bounded Rationality, in: Advanced in Dynamic Games and Application 5 1999 Birkhouser
7. G.I. Bischi, A.K. Naimzada, and L. Sbragia Oligopoly games with Local Monopolistic Approximation J. Econ. Behav. Organ. 62 2007 371 388
8. G.I. Bischi, L. Stefanini, and L. Gardini Synchronization intermittency and critical curves in a duopoly game Math. Comput. Simul. 44 1998 559 585
9. H.N. Agiza On the stability, bifurcations, chaos and chaos control of Kopel map Chaos Solit. Fract. 11 1999 1909 1916
10. H.N. Agiza, A.S. Hegazi, and A.A. Elsadany Complex dynamics and synchronization of duopoly game with bounded rationality Math. Comput. Simul. 58 2002 133 146
11. H.N. Agiza, and A.A. Elsadany Chaotic dynamics in nonlinear duopoly game with heterogeneous players Appl. Math. Comput. 149 2004 843 860
12. H.N. Agiza, and A.A. Elsadany Nonlinear dynamics in the Cournot duopoly game with heterogeneous players Phys. A 320 2003 512 524
13. H.N. Agiza, A.S. Hegazi, and A.A. Elsadany The dynamics of Bowley's model with bounded rationality Chaos Solit. Fract. 12 2001 1705 1717
14. E. Ahmed, H.N. Agiza, and S.Z Hassan On modifications of Puu's dynamical duopoly Chaos Solit. Fract. 7 2000 1025 1028
15. A.A. Elsadany Dynamics of a delayed duopoly game with bounded rationality Mathemat. Comput. Model. 52 2010 1479 1489
16. J.B. Rosser The development of complex oligopoly dynamics theory, in: Text Book Oligopoly Dynamics: Models and Tools 2002 Springer-Verleg
17. A. Naimzada, and L. Sbragia Oligopoly games with nonlinear demand and cost functions: Two boundedly rational adjustment processes Chaos Solit. Fract. 2 2006 707 722
18. H.N. Yao, and F. Xu Complex dynamics analysis for a duopoly advertising model with nonlinear cost Appl. Math. Comput. 180 2006 134 145
19. M.T. Yassen, and H.N. Agiza Analysis of a duopoly game with delayed baounded rationality Appl. Math. Comput. 138 2003 387 402
20. J. Zhang, Q. Da, and Y. Wang Analysis of nonlinear duopoly game with hetergeneous players Econ. Model. 24 2007 138 148
21. J. Du, and T. Huang New results on stable region of Nash equilibrium point of output game model Appl. Math. Comput. 192 2007 12 19
22. Z. Ding, Q. Li, D. Ge, and S. Jiang Research on dynamics in a resource extraction game with bounded rationality Appl. Math. Comput. 236 2014 628 634
23. J. Du, T. Huang, and Z. Sheng Anaylsis of decision-making in economic chaos control Nonlinear Anal.: Real World Appl. 10 2009 2493 2501
24. Z. Sheng, T. Huang, J. Du, Q. Mei, and H. Haung Study on self-adaptive proportional control method for a class of output models Discrete Contin. Dyn. Syst. Ser. B 11 2009 459 477
25. H. Simon Rational choice and the structure of the environment Psychol. Rev. 63 1956 129 138
26. James Pita, Manish Jain, Milind Tambe, Fernando Ordóñez, and Sarit Kraus Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition Artif. Intel. 174 2010 1142 1171
27. E. Ott, C. Grebogi, and J.A. Yorke Controlling chaos Phys. Rev. Lett. 64 1990 1196 1199
28. J. Holyst, and K. Urbanowicz Chaos control in economical model by time-delayed feedback method Phys. A 287 2000 587 598
29. J. Ding, Q. Mei, and H. Yao Dynamics and adaptive control of a duopoly advertising model based on heterogeneous expectations Nonlinear Dyn. 67 1 2012 129 138
30. E.M. Elabbasy, H.N. Agiza, and A.A. Elsadany Analysis of nonlinear triopoly game with heterogeneous players Comput. Math. Appl. 57 2009 488 499
31. A.A. Elabbasy, H.N. Agiza, and E.M. Elsadany Complex dynamics and chaos control of heterogeneous quadropoly game Comput. Math. Appl. 219 2013 11110 11118
32. Z. Ding, Q. Hang, and H. Yang Analysis of the dynamics of multi- team Bertrand game with heterogeneous players Int. J. Syst. Sci. 42 2010 1047 1056
33. Z. Ding, Q. Li, S. Jiang, and X. Wang Dynamics in a Cournot investment game with heterogeneous players Comput. Math. Appl. 256 2015 939 950
34. X.S. Luo, G.R. Chen, B.H. Wang, J.Q. Fang, Y.L. Zou, and H.J. Quan Control of period-doubling bifurcation and chaos in a discrete nonlinear system by the feedback of states and parameter adjustment Acta. Phys. Sin. Ch Ed. 52 2003 790 794
35. X. Pu, and J. Ma Complex dynamics and chaos control in nonlinear four-oligopolist game with different expectations Int. J. Bifurcat. Chaos 23 3 2013 1350053
36. Z. Ding, Q. Li, S. Jiang, and X. Wang Dynamics in a Cournot investment game with heterogeneous players Comput. Math. Appl. 256 2015 939 950