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Discrete time dynamic oligopolies with adjustment constraints
1. | Department of Economics, University of Colorado, Boulder, CO 80309-0256, United States |
2. | Department of Economics, Society, Politics, Università degli Studi di Urbino, 61029 Urbino, Italy |
3. | Department of Applied Mathematics, University of Pécs, Pécs, 7624, Hungary |
References:
[1] |
R. Amir, Cournot oligopoly and the theory of supermodular games, Games and Economic Behavior, 15 (1996), 132-148.
doi: 10.1006/game.1996.0062. |
[2] |
R. Amir and V. E. Lambson, On the effects of entry in Cournot markets, Review of Economic Studies, 67 (2000), 235-254.
doi: 10.1111/1467-937X.00129. |
[3] |
G. I. Bischi, C. Chiarella, M. Kopel and F. Szidarovszky, Nonlinear Oligopolies: Stability and Bifurcations, Springer-Verlag, Berlin-Heidelberg-New York, 2010.
doi: 10.1007/978-3-642-02106-0. |
[4] |
G. I. Bischi, L. Gardini and U. Merlone, Impulsivity in binary choices and the emergence of periodicity, Discrete Dynamics in Nature and Society, (2009), Article ID 407913, 22 pages.
doi: 10.1155/2009/407913. |
[5] |
A. Dal Forno, L. Gardini and U. Merlone, Ternary choices in repeated games and border collision bifurcations, Chaos Solitons & Fractals, 45 (2012), 294-305.
doi: 10.1016/j.chaos.2011.12.003. |
[6] |
R. Day, Complex Economic Dynamics, MIT Press, Cambridge, 1994. |
[7] |
M. di Bernardo, C. J. Budd, A. R. Champneys and P. Kowalczyk, Piecewise-smooth Dynamical Systems: Theory and Applications, Applied Mathematical Sciences 163, Springer-Verlag, London, 2008. |
[8] |
T. Bresnahan and V. Ramey, Output Fluctuations at the Plant Level, Quaterly Journal of Economics, 109 (1994), 593-624.
doi: 10.2307/2118415. |
[9] |
C. Fershtman and M. Kamien, Dynamic duopolistic competition with sticky prices, Econometrica, 55 (1987), 1151-1164.
doi: 10.2307/1911265. |
[10] |
L. Gardini, I. Sushko and A. Naimzada, Growing through chaotic intervals, Journal of Economic Theory, 143 (2008), 541-557.
doi: 10.1016/j.jet.2008.03.005. |
[11] |
L. Gardini, U. Merlone and F. Tramontana, Inertia in binary choices: Continuity breaking and big-bang bifurcation points, Journal of Economic Behavior & Organization, 80 (2011), 153-167.
doi: 10.1016/j.jebo.2011.03.004. |
[12] |
W. Huang and R. Day, Chaotically switching bear and bull markets: The derivation of stock price distributions from behavioral rules, in Nonlinear Dynamics and Evolutionary Economics (eds. R. Day, and P. Chen), Oxford University Press, 1993. |
[13] |
W. Novshek, On the existence of Cournot equilibrium, Review of Economic Studies, 52 (1985), 85-98.
doi: 10.2307/2297471. |
[14] |
H. E. Nusse and J. A. Yorke, Border-collision bifurcations including period two to period three for piecewise smooth systems, Physica D, 57 (1992), 39-57.
doi: 10.1016/0167-2789(92)90087-4. |
[15] |
H. E. Nusse and J. A. Yorke, Border-collision bifurcation for piecewise smooth one-dimensional maps, Int. J. Bifurcation Chaos, 5 (1995), 189-207.
doi: 10.1142/S0218127495000156. |
[16] |
K. Okuguchi, Expectations and Stability in Oligopoly Models, Springer-Verlag, Berlin-Heidelberg-New York, 1976. |
[17] |
K. Okuguchi and F. Szidarovszky, The Theory of Oligopoly with Multi-product Firms, Lecture Notes in Economics and Mathematical Systems, 342, Springer-Verlag, Berlin, 1990.
doi: 10.1007/978-3-662-02622-9. |
[18] |
T. Puu and I. Sushko (eds.), Oligopoly Dynamics, Models and Tools, Springer Verlag, New York, 2002. |
[19] |
T. Puu and I. Sushko (eds.), Business Cycle Dynamics, Models and Tools, Springer Verlag, New York, 2006. |
[20] |
D. Radi, L. Gardini and V. Avrutin, The role of constraints in a segregation model: The symmetric case, Chaos, Solitons & Fractals, 66 (2014), 103-119.
doi: 10.1016/j.chaos.2014.05.009. |
[21] |
D. Radi, L. Gardini and V. Avrutin, The role of constraints in a segregation model: The asymmetric Case, Discrete Dynamics in Nature and Society, (2014), Art. ID 569296, 17 pp.
doi: 10.1155/2014/569296. |
[22] |
M. Simaan and T. Takayama, Game theory applied to dynamic duopoly problems with production constraint, Automatica, 14 (1978), 161-166.
doi: 10.1016/0005-1098(78)90022-5. |
[23] |
I. Sushko and L. Gardini, Degenerate bifurcations and border collisions in piecewise smooth 1D and 2D maps, Int. J. Bif. and Chaos, 20 (2010), 2045-2070.
doi: 10.1142/S0218127410026927. |
[24] |
I. Sushko, L. Gardini and K. Matsuyama, Superstable credit cycles and u-sequence, Chaos Solitons & Fractals, 59 (2014), 13-27.
doi: 10.1016/j.chaos.2013.11.006. |
[25] |
F. Tramontana, F. Westerhoff and L. Gardini, On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders, J. Econ. Behav. Organ., 74 (2010), 187-205.
doi: 10.1016/j.jebo.2010.02.008. |
[26] |
F. Tramontana, L. Gardini and F. Westerhoff, Heterogeneous speculators and asset price dynamics: Further results from a one-dimensional discontinuous piecewise-linear model, Computational Economics, 38 (2011), 329-347.
doi: 10.1007/s10614-011-9284-9. |
[27] |
Z. T. Zhusubaliyev and E. Mosekilde, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems, World Scientific, Singapore, 2003. |
show all references
References:
[1] |
R. Amir, Cournot oligopoly and the theory of supermodular games, Games and Economic Behavior, 15 (1996), 132-148.
doi: 10.1006/game.1996.0062. |
[2] |
R. Amir and V. E. Lambson, On the effects of entry in Cournot markets, Review of Economic Studies, 67 (2000), 235-254.
doi: 10.1111/1467-937X.00129. |
[3] |
G. I. Bischi, C. Chiarella, M. Kopel and F. Szidarovszky, Nonlinear Oligopolies: Stability and Bifurcations, Springer-Verlag, Berlin-Heidelberg-New York, 2010.
doi: 10.1007/978-3-642-02106-0. |
[4] |
G. I. Bischi, L. Gardini and U. Merlone, Impulsivity in binary choices and the emergence of periodicity, Discrete Dynamics in Nature and Society, (2009), Article ID 407913, 22 pages.
doi: 10.1155/2009/407913. |
[5] |
A. Dal Forno, L. Gardini and U. Merlone, Ternary choices in repeated games and border collision bifurcations, Chaos Solitons & Fractals, 45 (2012), 294-305.
doi: 10.1016/j.chaos.2011.12.003. |
[6] |
R. Day, Complex Economic Dynamics, MIT Press, Cambridge, 1994. |
[7] |
M. di Bernardo, C. J. Budd, A. R. Champneys and P. Kowalczyk, Piecewise-smooth Dynamical Systems: Theory and Applications, Applied Mathematical Sciences 163, Springer-Verlag, London, 2008. |
[8] |
T. Bresnahan and V. Ramey, Output Fluctuations at the Plant Level, Quaterly Journal of Economics, 109 (1994), 593-624.
doi: 10.2307/2118415. |
[9] |
C. Fershtman and M. Kamien, Dynamic duopolistic competition with sticky prices, Econometrica, 55 (1987), 1151-1164.
doi: 10.2307/1911265. |
[10] |
L. Gardini, I. Sushko and A. Naimzada, Growing through chaotic intervals, Journal of Economic Theory, 143 (2008), 541-557.
doi: 10.1016/j.jet.2008.03.005. |
[11] |
L. Gardini, U. Merlone and F. Tramontana, Inertia in binary choices: Continuity breaking and big-bang bifurcation points, Journal of Economic Behavior & Organization, 80 (2011), 153-167.
doi: 10.1016/j.jebo.2011.03.004. |
[12] |
W. Huang and R. Day, Chaotically switching bear and bull markets: The derivation of stock price distributions from behavioral rules, in Nonlinear Dynamics and Evolutionary Economics (eds. R. Day, and P. Chen), Oxford University Press, 1993. |
[13] |
W. Novshek, On the existence of Cournot equilibrium, Review of Economic Studies, 52 (1985), 85-98.
doi: 10.2307/2297471. |
[14] |
H. E. Nusse and J. A. Yorke, Border-collision bifurcations including period two to period three for piecewise smooth systems, Physica D, 57 (1992), 39-57.
doi: 10.1016/0167-2789(92)90087-4. |
[15] |
H. E. Nusse and J. A. Yorke, Border-collision bifurcation for piecewise smooth one-dimensional maps, Int. J. Bifurcation Chaos, 5 (1995), 189-207.
doi: 10.1142/S0218127495000156. |
[16] |
K. Okuguchi, Expectations and Stability in Oligopoly Models, Springer-Verlag, Berlin-Heidelberg-New York, 1976. |
[17] |
K. Okuguchi and F. Szidarovszky, The Theory of Oligopoly with Multi-product Firms, Lecture Notes in Economics and Mathematical Systems, 342, Springer-Verlag, Berlin, 1990.
doi: 10.1007/978-3-662-02622-9. |
[18] |
T. Puu and I. Sushko (eds.), Oligopoly Dynamics, Models and Tools, Springer Verlag, New York, 2002. |
[19] |
T. Puu and I. Sushko (eds.), Business Cycle Dynamics, Models and Tools, Springer Verlag, New York, 2006. |
[20] |
D. Radi, L. Gardini and V. Avrutin, The role of constraints in a segregation model: The symmetric case, Chaos, Solitons & Fractals, 66 (2014), 103-119.
doi: 10.1016/j.chaos.2014.05.009. |
[21] |
D. Radi, L. Gardini and V. Avrutin, The role of constraints in a segregation model: The asymmetric Case, Discrete Dynamics in Nature and Society, (2014), Art. ID 569296, 17 pp.
doi: 10.1155/2014/569296. |
[22] |
M. Simaan and T. Takayama, Game theory applied to dynamic duopoly problems with production constraint, Automatica, 14 (1978), 161-166.
doi: 10.1016/0005-1098(78)90022-5. |
[23] |
I. Sushko and L. Gardini, Degenerate bifurcations and border collisions in piecewise smooth 1D and 2D maps, Int. J. Bif. and Chaos, 20 (2010), 2045-2070.
doi: 10.1142/S0218127410026927. |
[24] |
I. Sushko, L. Gardini and K. Matsuyama, Superstable credit cycles and u-sequence, Chaos Solitons & Fractals, 59 (2014), 13-27.
doi: 10.1016/j.chaos.2013.11.006. |
[25] |
F. Tramontana, F. Westerhoff and L. Gardini, On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders, J. Econ. Behav. Organ., 74 (2010), 187-205.
doi: 10.1016/j.jebo.2010.02.008. |
[26] |
F. Tramontana, L. Gardini and F. Westerhoff, Heterogeneous speculators and asset price dynamics: Further results from a one-dimensional discontinuous piecewise-linear model, Computational Economics, 38 (2011), 329-347.
doi: 10.1007/s10614-011-9284-9. |
[27] |
Z. T. Zhusubaliyev and E. Mosekilde, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems, World Scientific, Singapore, 2003. |
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