Oligopoly dynamics

Handbook of Research on Complexity

Volumn , Issue , 2009, Pages 124-168

  Kopel, Michael ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84881672191     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (140)

1. Agiza, H.N. (1999), "On the Analysis of Stability, Bifurcation, Chaos and Chaos Control of Kopel Map," Chaos, Solitons & Fractals, 10(11), 1909-16.
2. Agiza, H.N., G.I. Bischi, and M. Kopel (1999), "Multistability in a Dynamic Cournot Game With Three Oligopolists," Mathematics and Computers in Simulation, 51(1), 63-90.
3. Agliari, A., G.I. Bischi, and L. Gardini (2002), "Some Methods for the Global Analysis of Dynamic Games Represented by Iterated Noninvertible Maps," in T. Puu and I. Sushko (eds), Oligopoly Dynamics: Models and Tools, Springer, Berlin, Heidelberg, Ch. 3, pp. 31-83.
4. Agliari, A., L. Gardini, and T. Puu (2000), "The Dynamics of a Triopoly Game," Chaos, Solitons & Fractals, 11(15), 2531-60.
5. Agliari, A., L. Gardini, and T. Puu (2006), "Global Bifurcations in Duopoly When the Cournot Point is Destabilized via a Subcritical Neimark Bifurcation," International Game Theory Review, 8(1), 1-20.
6. Alexander, J.C., J.A. Yorke, Z. You, and I. Kan (1992), "Riddled Basins," International Journal of Bifurcations and Chaos, 2(4), 795-813.
7. Al-Nowaihi, A. and P.L. Levine (1985), "The Stability of the Cournot Oligopoly Model: A Reassessment," Journal of Economic Theory, 35(2), 307-21.
8. Amir, R. and J.Y. Jin (2001), "Cournot and Bertrand Equilibria Compared: Substitutability, Complementarity and Concavity," International Journal of Industrial Organization, 19(3-4), 303-17.
9. Amir, R. and V.E. Lambson (2000), "On the Effects of Entry in Cournot Markets," Review of Economic Studies, 67(2), 235-54.
10. Amir, R. and J. Wooders (1998), "Cooperation vs. Competition in R&D: The Role of Stability of Equilibrium," Journal of Economics, 67(1), 63-73.
11. Anderson, D.R., N.M. Myran, and D.L. White (2005), "Basins of Attraction in a Cournot Duopoly Model of Kopel," The Journal of Difference Equations and Applications, 11(10), 879-87.
12. Bertrand, J. (1883), "Theorie Mathématique de la Richesse Sociale", Journal des Savantes, 48(883), 499-508.
13. Binmore, K. (1992), Fun and Games. A Text on Game Theory, D.C. Heath, Lexington.
14. Bischi, G.I. and L. Gardini (1998), "Cycles and Bifurcations in Duopoly Games," in Quaderni dell' Istituto di Mathematica "E. Levi," University of Parma, No. 3.
15. Bischi, G.I. and M. Kopel (2001), "Equilibrium Selection in a Nonlinear Duopoly Game With Adaptive Expectations," Journal of Economic Behavior and Organization, 46(1), 73-100.
16. Bischi, G.I. and M. Kopel (2003a), "Long Run Evolution, Path Dependence and Global Properties of Dynamic Games: A Tutorial," Cubo Matemática Educacional, 5(3), 437-68.
17. Bischi, G.I. and M. Kopel (2003b), "Multistability and Path Dependence in a Dynamic Brand Competition Model," Chaos, Solitons & Fractals, 18(3), 561-76.
18. Bischi, G.I. and F. Lamantia (2002), "Nonlinear Duopoly Games with Positive Cost Externalities Due to Spillovers," Chaos, Solitons & Fractals, 13(4), 701-21.
19. Bischi, G.I. and A. Naimzada (1999), "Global Analysis of a Duopoly Game With Bounded Rationality," in Advances in Dynamic Games and Applications, Vol. 5, Birkhauser, Boston, pp. 361-85.
20. Bischi, G.I., C. Chiarella, and M. Kopel (2004), "The Long Run Outcomes and Global Dynamics of a Duopoly Game With Misspecified Demand Functions," International Game Theory Review, 6(3), 343-80.
21. Bischi, G.I., H. Dawid, and M. Kopel (2003a), "Spillover Effects and the Evolution of Firm Clusters," Journal of Economic Behavior and Organization, 50(1), 47-75.
22. Bischi, G.I., H. Dawid, and M. Kopel (2003b), "Gaining the Competitive Edge Using Internal and External Spillovers: A Dynamic Analysis," Journal of Economic Dynamics and Control, 27(11), 2171-93.
23. Bischi G.I., M. Gallegati, and A. Naimzada (1999), "Symmetry-breaking Bifurcations and Representative Firm in Dynamic Duopoly Games," Annals of Operations Research, 89(1), 253-72.
24. Bischi, G.I., L. Gardini, and M. Kopel (2000), "Analysis of Global Bifurcations in a Market Share Attraction Model," Journal of Economic Dynamics and Control, 24(5-7), 855-79. Reprinted in J. B. Rosser, Jr. (ed.) (2004), Complexity in Economics, Vol I: Methodology, Interacting Agents, and Microeconomic Models, Edward Elgar, Cheltenham, UK and Northampton, MA, USA.
25. Bischi, G.I., L. Gardini, and M. Kopel (2006), "Noninvertible Maps and Complex Basin Boundaries in Dynamic Economic Models With Coexisting Attractors," Chaos and Complexity Letters, 2(1), 43-76.
26. Bischi, G.I., M. Kopel, and A. Naimzada (2001), "On a Rent-seeking Game Described by a Noninvertible Iterated Map With Denominator," Nonlinear Analysis, 47(8), 5309-24.
27. Bischi, G.I., M. Kopel, and F. Szidarovszky (2005), "Expectation-stock Dynamics in Multiagent Fisheries," Annals of Operations Research - Special Issue on Contributions to the Theory of Games, 137(1), 299-329.
28. Bischi, G.I., L. Stefanini, and L. Gardini (1998), "Synchronization, Intermittency and Critical Curves in a Duopoly Game", Mathematics and Computers in Simulation, 44(6), 559-85.
29. Bischi, G.I., C. Mammana, and L. Gardini (2000), "Multistability and Cyclic Attractors in Duopoly Games," Chaos, Solitons & Fractals, 11(4), 543-64.
30. Bischi, G.I., A.K. Naimzada, and L. Sbragia (2007), "Oligopoly Games With Local Monopolistic Approximation," Journal of Economic Behavior and Organization, 62(3), 371-88.
31. Bischi, G.I., C. Chiarella, M. Kopel, and F. Szidarovszky (2009), Nonlinear Oligopolies: Stability and Bifurcations, forthcoming, Springer, Berlin/Heidelberg/New York.
32. Bonanno, G. (1988), "Oligopoly Equilbria When Firms Have Local Knowledge of Demand," International Economic Review, 29(1), 45-55.
33. Bonanno, G. and E.C. Zeeman (1985), "Limited Knowledge of Demand and Oligopoly Equilibria," Journal of Economic Theory, 35(2), 276-83.
34. Bresnahan, T.F. (1981), "Duopoly Models with Consistent Conjectures," American Economic Review, 71(5), 934-45.
35. Brock, W.A. and C.H. Hommes (1997), "A Rational Route to Randomness," Econometrica, 65(5), 1059-95.
36. Bulow, J., J. Geanakoplos, and P. Klemperer (1985), "Holding Idle Capacity to Deter Entry," The Economic Journal, 95(1), 178-82.
37. Cheng, L. (1985), "Comparing Bertrand and Cournot Equilibria: A Geometric Approach," RAND Journal of Economics, 16(1), 146-52.
38. Chiarella, C. and F. Szidarovszky (2001), "The Nonlinear Cournot Model Under Uncertainty With Continuously Distributed Time Lags," Central European Journal of Operations Research, 9(3), 183-96.
39. Chiarella, C. and F. Szidarovszky (2004), "Dynamic Oligopolies Without Full Information and With Continuously Distributed Time Lags," Journal of Economic Behavior and Organization, 54(4), 495-511.
40. Chiarella, C. and F. Szidarovszky (2005), "On the Stability of Price-adjusting Oligopolies with Incomplete Information," International Journal of Systems Science, 36(8), 501-7.
41. Corchon, L.C. and A. Mas-Colell (1996), "On the Stability of Best Reply and Gradient Systems with Applications to Imperfectly Competitive Models," Economics Letters, 51(1), 59-65.
42. Cournot, A. (1838), Researches into the Principles of the Theory of Wealth, English translation, 1963, Irwin Paperback Classics in Economics, Ch. VII.
43. Cox, J.C. and M. Walker (1998), "Learning to Play Cournot Duopoly Strategies," Journal of Economic Behavior and Organization, 36(2), 141-61.
44. Dana, R.-A. and L. Montrucchio (1986), "Dynamic Complexity in Duopoly Games," Journal of Economic Theory, 40(1), 40-56.
45. Dana, R.-A. and L. Montrucchio (1987), "On Rational Dynamic Strategies in Infinite Horizon Models Where Agents Discount the Future," Journal of Economic Behavior and Organization, 8(3), 497-511.
46. Dawid, H. (2007), "Evolutionary Game Dynamics and the Analysis of Agent-based Imitation Models: The Long Run, the Medium Run and the Importance of a Global Analysis," Journal of Economic Dynamics and Control, 31(5), 2108-33.
47. Day, R.H. (1994), Complex Economic Dynamics, Vol. I: An Introduction to Dynamical Systems and Market Mechanisms, MIT Press, Cambridge, MA.
48. Dixit, A. (1986), "Comparative Statics for Oligopoly," International Economic Review, 27(1), 107-22.
49. Dockner, E., S. Jorgensen, N. van Long, and G. Sorger (2000), Differential Games in Economics and Management Science, Cambridge University Press, New York.
50. Ellison, G. (2000), "Basins of Attraction, Long Run Stochastic Stability, and the Speed of Step-by-step Evolution," Review of Economic Studies, 67(1), 17-45.
51. Fisher, F.M. (1961), "The Stability of the Cournot Oligopoly Solution: The Effects of Speeds of Adjustment and Increasing Marginal Costs," Review of Economic Studies, 28, 125-35.
52. Friedman, J.W. (1977), Oligopoly and the Theory of Games, North-Holland, Amsterdam.
53. Friedman, J.W. (1982), "Oligopoly Theory," in Handbook of Mathematical Economics, Vol. II, K.J. Arrow and M.D. Intriligator (eds), North-Holland, Amsterdam, Ch. 11.
54. Friedman, D. (1991), "Evolutionary Games in Economics," Econometrica, 59(3), 637-66.
55. Friedman, D. (1998), "On Economic Applications of Evolutionary Game Theory," Journal of Evolutionary Economics, 8(1), 15-43.
56. Friedman, J.W. and C. Mezzetti (2002), "Bounded Rationality, Dynamic Oligopoly, and Conjectural Variations," Journal of Economic Behavior and Organization, 49(3), 287-306.
57. Fudenberg, D. and D.K. Levine (1998), The Theory of Learning in Games, MIT Press, Cambridge, MA.
58. Fudenberg, D. and J. Tirole (1992), Game Theory, MIT Press, Cambridge, MA.
59. Furth, D. (1986), "Stability and Instability in Oligopoly," Journal of Economic Theory, 40(2), 197-228.
60. Gal-Or, E. (1985), "First Mover and Second Mover Advantages," International Economic Review, 26(3), 649-53.
61. Grebogi, C., S.W. McDonald, E. Ott, and J.A. Yorke (1983), "Final State Sensitivity: An Obstruction to Predictability," Physics Letters, 99A, 415-18.
62. Grosser, J. (1999), "Multiple Equilibria, Equilibrium Selection and Economic Policy," Zeitschrift für Wirtschafts- und Sozialwissenschaften, 119, 191-204.
63. Hadar, J (1966), "Stability of Oligopoly with Product Differentiation," Review of Economic Studies, 33(1), 57-60.
64. Hahn, F.H. (1962), "The Stability of the Cournot Oligopoly Solution," Review of Economic Studies, 29(4), 329-31.
65. Hamilton, J. and S. Slutsky (1990), "Endogenous Timing in Duopoly Games: Stackelberg or Cournot Equilibria," Games and Economic Behavior, 2(1), 29-46.
66. Hathaway, N.J., J.A. Rickard, and T.D. Howroyd (1979), "Dynamic Stackelberg Stability," Economics Letters, 2(3), 209-13.
67. Hosomatsu, Y. (1969), "A Note on the Stability Conditions in Cournot's Dynamic Market Solution When Neither the Actual Market Demand Function nor the Production Levels of Rivals are Known," Review of Economic Studies, 36(105), 117-22.
68. Hotelling, H. (1929), "Stability in Competition," Economic Journal, 39(153), 41-57.
69. Howroyd, T.D. and J.A. Rickard (1981), "Cournot Oligopoly and Output Adjustment Costs," Economics Letters, 7(2), 113-17.
70. Howroyd, T.D. and A.M. Russell (1984), "Cournot Oligopoly Models with Time Delays," Journal of Mathematical Economics, 13(2), 97-103.
71. Huck, S., H.-T. Normann, and J. Oechssler (1999), "Learning in Cournot Oligopoly - An Experiment," The Economic Journal, 109(454), C80-C95.
72. Katz, M.L. and C. Shapiro (1985), "Network Externalities, Competition, and Compatibility," American Economic Review, 75(3), 424-40.
73. Kirman, A.P. (1975), "Learning by Firms About Demand Conditions," in Adaptive Economic Models, R.H. Day and T. Groves (eds), Academic Press, New York, pp. 137-56.
74. Kirman, A.P. (1983), "On Mistaken Beliefs and Resultant Equilibria" in Individual Forecasting and Aggregate Outcomes, R. Frydman and E.S. Phelps (eds), Cambridge University Press, Cambridge, UK, pp. 147-66.
75. Kirman, A.P. (1995), "Learning in Oligopoly: Theory, Simulation, and Experimental Evidence," in Learning and Rationality in Economics, A. Kirman and M. Salmon (eds), Blackwell, Oxford, pp. 127-78.
76. Kopel, M. (1996), "Simple and Complex Adjustment Dynamics in Cournot Duopoly Models," Chaos, Solitons & Fractals, 7(12), 2031-48. Reprinted in J.B. Rosser, Jr. (ed.) (2004), Complexity in Economics, Vol I: Methodology, Interacting Agents, and Microeconomic Models, Edward Elgar, Cheltenham, UK and Northampton, MA, USA.
77. Krelle, W. (1976), Preistheorie, Part 1: Monopol- und Oligopoltheorie, J.C.B. Mohr (Paul Siebeck), Tübingen.
78. Krugman, P. (1991), "History Versus Expectations," Quarterly Journal of Economics, 106(2), 651-67.
79. Kruse, J.B., S. Rassenti, S.R. Reynolds, and V.L. Smith (1994), "Bertrand-Edgeworth Competition in Experimental Markets," Econometrica, 62(2), 343-71.
80. Léonard, D. and K. Nishimura (1999), "Nonlinear Dynamics in the Cournot Model Without Full Information," Annals of Operations Research, 89(1), 165-73.
81. Levin, D. (1988), "Stackelberg, Cournot and Collusive Monopoly: Performance and Welfare Comparisons," Economic Inquiry, 26(2), 317-30.
82. Lorenz, H.-W. (1992), "Multiple Attractors, Complex Basin Boundaries, and Transient Motion in Deterministic Economic Systems," in G. Feichtinger (ed.), Dynamic Economic Models and Optimal Control, North-Holland, Amsterdam, pp. 411-30.
83. Lorenz, H.-W. (1993), Nonlinear Dynamical Economics and Chaotic Motion, Springer, Berlin/ Heidelberg/New York.
84. Mailath, G.J. (1998), "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, 36(3), 1347-74.
85. Martin, S. (2002), Advanced Industrial Economics, Blackwell Publishing, Oxford.
86. Matsumoto, A. and Y. Nonaka (2006), "Statistical Dynamics in a Chaotic Cournot Model With Complementary Goods," Journal of Economic Behavior and Organization, 61(4), 769-83.
87. McDonald, S.W., C. Grebogi, E. Ott, and J.A. Yorke (1985), "Fractal Basin Boundaries," Physica, 17D, 125-53.
88. McManus, M. and R.E. Quandt (1961), "Comments on the Stability of the Cournot Oligopoly Model," Review of Economic Studies, 28(2), 136-9.
89. McMillan, J. (1984), "Collusion, Competition, and Conjectures," Canadian Journal of Economics, 17(4), 788-805.
90. Moulin, H. (1982), Game Theory for the Social Sciences, New York University Press, New York.
91. Okuguchi, K. (1964), "The Stability of the Cournot Oligopoly Solution: A Further Generalization," Review of Economic Studies, 31(2), 143-45.
92. Okuguchi, K. (1968), "The Stability of Price Adjusting Oligopoly: The Effects of Adaptive Expectations," Southern Economic Journal, 35(1), 34-6.
93. Okuguchi, K. (1969), "On the Stability of Price Adjusting Oligopoly Equilibrium under Product Differentation," Southern Economic Journal, 35(3), 244-6.
94. Okuguchi, K. (1970), "Adaptive Expectations in an Oligopoly Model," Review of Economic Studies, 37(2), 233-7.
95. Okuguchi, K. (1976), Expectations and Stability in Oligopoly Models, Lecture Notes in Economics and Mathematical Systems, Springer, Heidelberg.
96. Okuguchi, K. (1978), "The Stability of Price-adjusting Oligopoly with Conjectural Variations," Zeitschrift für Nationalökonomie, 38, 55-60.
97. Okuguchi, K. (1979), "On the Stability of the Stackelberg Oligopoly Equilibrium," Economics Letters, 3(4), 321-5.
98. Okuguchi, K. (1987), "Equilibrium Prices in the Bertrand and Cournot Oligopolies," Journal of Economic Theory, 42(1), 128-39.
99. Okuguchi, K. and F. Szidarovszky (1989), "On Sequential Stability of Equilibrium," in Computing and Computers for Control Systems, P. Borne et al. (eds), J.C. Baltzer, Basel, pp. 357-9.
100. Okuguchi, K. and F. Szidarovszky (1999), The Theory of Oligopoly with Multi-product Firms, 2nd, revised and enlarged edn, Springer, Berlin.
101. Puu, T. (1991), "Chaos in Duopoly Pricing," Chaos, Solitons & Fractals, 1(6), 573-81.
102. Puu, T. (1996), "Complex Dynamics With Three Oligopolists," Chaos, Solitons & Fractals, 7(12), 2075-81.
103. Puu, T. (1998), "The Chaotic Duopolist Revisited," Journal of Economic Behavior and Organization, 33(3), 385-94.
104. Puu, T. (2001), "Bertrand Oligopoly Revisited," Discrete Dynamics in Nature and Society, 6(1), 1-10.
105. Puu, T. (2003), Attractors, Bifurcations & Chaos: Nonlinear Phenomena in Economics, 2nd edn, Springer, Berlin, Heidelberg.
106. Puu, T. and I. Sushko (2002), Oligopoly Dynamics: Models and Tools, Springer, Berlin.
107. Quandt, R.E. (1967), "On the Stability of Price Adjusting Oligopoly," Southern Economic Journal, 33, 332-6.
108. Rand, D. (1978), "Exotic Phenomena in Games and Duopoly Models," Journal of Mathematical Economics, 5(2), 173-84.
109. Richter, H. and A. Stolk (2004), "Control of the Triple Chaotic Attractor in a Cournot Triopoly Model," Chaos, Solitons & Fractals, 20(2), 409-13.
110. Rickard, J.A. (1980), "Stability Properties in a Dynamic Stackelberg Oligopoly Model," Economic Record, 56(164), 253-6.
111. Rosser Jr., J.B. (1999), "On the Complexities of Complex Economic Dynamics," Journal of Economic Perspectives, 13(4), 169-92.
112. Rosser, J.B., Jr. (2000), From Catastrophe to Chaos: A General Theory of Economic Discontinuities. Mathematics, Microeconomics, Macroeconomics, and Finance, 2nd edn, Kluwer Academic Publishers, Boston.
113. Rosser, J.B., Jr. (2002), "The Development of Complex Oligopoly Dynamics Theory," in Puu, T. and I. Sushko (eds), Oligopoly Dynamics: Models and Tools, Springer, Berlin, Heidelberg, Ch. 2, pp. 15-29.
114. Rosser Jr., J.B. (2004), Complexity in Economics, Vols. I-III, Edward Elgar, Cheltenham, UK and Northampton, MA, USA.
115. Russell, A., J.A. Rickard, and T.D. Howroyd (1986), "The Effects of Delays on the Stability and Rate of Convergence to Equilibrium of Oligopolies," Economic Record, 62(177), 194-8.
116. Sato, R. and K. Nagatani (1967), "The Stability of Oligopoly with Conjectural Variations," Review of Economic Studies, 34(4), 409-16.
117. Scherer, F.M. (1996), "Heinrich von Stackelberg's Marktform und Gleichgewicht," Journal of Economic Studies, 23(5/6), 58-70.
118. Schoonbeek, L. (1996), "Higher Order Lags in Price-adjusting Oligopoly," Economic Theory, 7(3), 547-55.
119. Schoonbeek, L. (1997), "A Dynamic Stackelberg Model with Production-adjustment Costs," Journal of Economics, 66(3), 271-82.
120. Seade, J. (1980), "The Stability of Cournot Revisited," Journal of Economic Theory, 23(1), 15-27.
121. Shapiro, C. (1989), "Theories of Oligopoly Behavior," in Handbook of Industrial Organization Vol. I, R. Schmalensee and R. Willig (eds), North-Holland, Amsterdam, Ch. 6.
122. Shy, O. (1995), Industrial Organization - Theory and Applications, MIT Press, Cambridge, MA.
123. Singh, N. and X. Vives (1984), "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, 15(4), 546-54.
124. Slade, M.E. (1994), "What Does an Oligopoly Maximize?," The Journal of Industrial Economics, 42(1), 45-61.
125. Szidarovszky, F. and W. Li (2000), "A Note on the Stability of Cournot-Nash Equilibrium: The Multiproduct Case with Adaptive Expectations," Journal of Mathematical Economics, 33, 101-7.
126. Szidarovszky, F. and K. Okuguchi (1988), "A Linear Oligopoly Model With Adaptive Expectations: Stability Reconsidered," Journal of Economics, 48, 79-82.
127. Szidarovszky, F. and K. Okuguchi (1993), "Dynamic Oligopoly With Complete Information," Belgian Journal of Operations Research, Statistics and Computer Science, 33, 13-44.
128. Szidarovszky, F. and J. Yen (1991), "Stability of a Special Oligopoly Market," PU.M.A. Series B, 2(2-3), 93-100.
129. Szidarovszky, F. and J. Yen (1995), "Dynamic Cournot Oligopolies With Production Adjustment Costs," Journal of Mathematical Economics, 24, 95-101.
130. Szidarovszky, F., S. Rassenti, and J. Yen (1992), "Modified Cournot Expectations in Dynamic Oligopolies," PU.M.A. Series B, 3(2-4), 143-50.
131. Tarr, D.G. (1975), "The Effects of Adaptive Expectations on the Stability of Price Adjusting Oligopoly," Southern Economic Journal, 41(4), 673-7.
132. Theocharis, R.D. (1960), "On the stability of the Cournot Solution on the Oligopoly Problem," Review of Economic Studies, 27(2), 133-4.
133. Tirole, J. (1988), The Theory of Industrial Organization, MIT Press, Cambridge, MA.
134. Van Huyck, J.B., J.P. Cook, and R.C. Battalio (1997), "Adaptive Behavior and Coordination Failure," Journal of Economic Behavior and Organization, 32(4), 483-503.
135. Veendorp, E.C.H. and A. Vessal (1978), "Price Adjusting Oligopoly for the n-Seller Case," Southern Economic Journal, 45(2), 502-7.
136. Vives, X. (1985), "On the Efficiency of Bertrand and Cournot Equilibria with Product Differentiation," Journal of Economic Theory, 36(1), 166-75.
137. Vives, X. (1999), Oligopoly Pricing: Old Ideas and New Tools, MIT Press, Cambridge, MA.
138. von Stackelberg, H. (1934), Marktform und Gleichgewicht, Springer, Wien.
139. Wirl, F., M. Kopel, and G. Feichtinger (1999), "Threshold Advertising Rules in a Duopoly Framework," Central European Journal of Operations Research, 7, 39-52.
140. Zhang, A. and Y. Zhang (1996), "Stability of a Cournot-Nash Equilibrium: The Multiproduct Case," Journal of Mathematical Economics, 26(1), 441-62.