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Heterogeneous triopoly game with isoelastic demand function. (English) Zbl 1242.91150
Summary: We analyze a triopolistic market with heterogeneous firms when the demand function is isoelastic. We consider the same heterogeneous firms as {\it E. M. Elabbasy, H. N. Agiza} and {\it A. A. Elsadany} [Comput. Math. Appl. 57, No. 3, 488--499 (2009; Zbl 1165.91324)] introducing a nonlinearity in the demand function instead of the cost function. Stability conditions of the two equilibrium points and complex dynamics are studied. The main novelty consists of the double route to chaos, via period-doubling bifurcations and via Neimark-Sacker bifurcation. The two routes have important differences from the economic point of view.

91B69Heterogeneous agent models in economics
91A23Differential games (game theory)
91A25Dynamic games
Full Text: DOI
[1] Cournot, A.: Recherches sur les Principes Mathématiques de la Thé orie des Richesses. Hachette, Paris (1838)
[2] Agiza, H.N., Elsadany, A.A.: Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Physica, A 320, 512--524 (2003) · Zbl 1010.91006 · doi:10.1016/S0378-4371(02)01648-5
[3] Agiza, H.N., Elsadany, A.A.: Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Appl. Math. Comput. 149, 843--860 (2004) · Zbl 1064.91027 · doi:10.1016/S0096-3003(03)00190-5
[4] Bischi, G.I., Chiarella, C., Kopel, M., Szidarovszky, F.: Nonlinear Oligopolies: Stability and Bifurcations. Springer, New York (2009) · Zbl 1182.91001
[5] Zhang, J., Da, Q., Wang, Y.: Analysis of nonlinear duopoly game with heterogeneous players. Econ. Model. 24, 138--148 (2007) · doi:10.1016/j.econmod.2006.06.007
[6] Angelini, A., Dieci, R., Nardini, F.: Bifurcation analysis of a dynamic duopoly model with heteregeneous costs and behavioral rules. Math. Comput. Simul. 79, 3179--3196 (2009) · Zbl 1169.91347 · doi:10.1016/j.matcom.2009.04.001
[7] Tramontana, F.: Heterogeneous duopoly with isoelastic demand function. Econ. Model. 27, 350--357 (2010) · doi:10.1016/j.econmod.2009.09.014
[8] Puu, T.: Complex dynamics with three oligopolists. Chaos Solitons Fractals 7, 2075--2081 (1996) · doi:10.1016/S0960-0779(96)00073-2
[9] Agliari, A., Gardini, L., Puu, T.: The dynamics of a triopoly Cournot game. Chaos Solitons Fractals 11, 2531--2560 (2000) · Zbl 0998.91035 · doi:10.1016/S0960-0779(99)00160-5
[10] Agliari, A., Gardini, L., Puu, T.: Global bifurcations of basins in a triopoly game. Int. J. Bifurc. Chaos 12, 2175--2207 (2002) · Zbl 1043.37514 · doi:10.1142/S0218127402005789
[11] Elabbasy, E.M., Agiza, H.N., Elsadany, A.A., El-Metwally, H.: The dynamics of triopoly game with heterogeneous players. Int. J. Nonlinear Sci. 3, 83--90 (2007)
[12] Elabbasy, E.M., Agiza, H.N., Elsadany, A.A.: Analysis of nonlinear triopoly game with heterogeneous players. Comput. Math. Appl. 57, 488--499 (2009) · Zbl 1165.91324 · doi:10.1016/j.camwa.2008.09.046
[13] Puu, T.: Chaos in duopoly pricing. Chaos Solitons Fractals 1, 573--581 (1991) · Zbl 0754.90015 · doi:10.1016/0960-0779(91)90045-B
[14] Dixit, A.: Comparative statics for oligopoly. Int. Econ. Rev. 27, 107--122 (1986) · Zbl 0584.90012 · doi:10.2307/2526609
[15] Farebrother, R.W.: Simplified Samuelson conditions for cubit and quartic equations. Manch. Sch. Econ. Soc. Stud. 41, 396--400 (1973) · doi:10.1111/j.1467-9957.1973.tb00090.x
[16] Gandolfo, G.: Economic Dynamics: Methods and Models. Advanced Textbooks in Economics, vol. 16, 2nd edn. North-Holland, Amsterdam (1980) · Zbl 0464.90001
[17] Elaydi, S.N.: An Introduction to Difference Equations. Springer, New York (2005) · Zbl 1071.39001
[18] Okuguchi, K., Irie, K.: The Shur and Samuelson conditions for a cubic equation. Manch. Sch. Econ. Soc. Stud. 58, 414--418 (1990) · doi:10.1111/j.1467-9957.1990.tb00431.x