Marginal Utility and Cournot Stability Under Market Entry

Gerasimos Soldatos

doi:10.2478/sbe-2021-0015

.blurhash-client-img { display: none !important; }

Marginal Utility and Cournot Stability Under Market Entry

Studies in Business and Economics

Volume 16 (2021): Issue 1 (April 2021)

By: Gerasimos Soldatos

Open Access

|May 2021

Abstract

This paper introduces into the discussion of the stability of quantity-oligopoly equilibrium, the role that the slope of the marginal utility curve and of market entry in shaping the equilibrium and its stability. It does so by considering inverse multivariate linear demand functions and the notion of stability related to multivariate mean value theorem. The equilibrium cluster of Cournot sellers is determined by the stability dictated by this theorem and the rate of decline of the marginal utility of the product under consideration. Strategic complementarity is found to be the case under product heterogeneity, while the strategic substitutability associated with product homogeneity, induces a modification of Cournot limit theorem.

References

Al-khedhairi, Abdulrahman (2019), “Differentiated Cournot Duopoly Game with Fractional-order and its Discretization”, Engineering Computations, 36(3), 781-806.10.1108/EC-07-2018-0333
Search in Google Scholar Back to article
Al-Nowaihi, AN and Paul L. Levine (1985), “The Stability of the Cournot Oligopoly Model: A Reassessment”, Journal of Economic Theory, 35, 307-321.10.1016/0022-0531(85)90046-8
Search in Google Scholar Back to article
Amir, Rabah and Val E. Lambson (2000), “On the Effects of Entry in Cournot Markets”, Review of Economic Studies, 67(2), 235-254.10.1111/1467-937X.00129
Search in Google Scholar Back to article
Andaluz, Joaquin, Abdelalim A. Elsadany and Gloria Jarne (2020), “Dynamic Cournot Oligopoly Game based on General Isoelastic Demand”, Nonlinear Dynamics, 99, 1053-1063.10.1007/s11071-019-05333-7
Search in Google Scholar Back to article
Ardabili, Parinaz and Mingyan Liu, (2017), “On the Uniqueness and Stability of Equilibria of Network Games”, 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 280-286. https://parinazn.com/papers/conferences/allerton17_vi-net-games.pdf
Search in Google Scholar Back to article
Askar, Sameh S., Mona F. EL-Wakeel and M. A. Alrodaini (2018), “Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products”, Complexity, 2018 issue, 1-13.10.1155/2018/6526794
Search in Google Scholar Back to article
Barthel, Anne-Christine and Eric Hoffmann (2019),” On the Existence and Stability of Equilibria in N- firm Cournot-Bertrand Oligopolies”, Theory and Decision, 1-21. https://doi.Org/10.1007/sl1238-019-09739-y
Search in Google Scholar Back to article
Choné, Philippe and Laurent Linnemer (2019), “ The Quasilinear Quadratic Utility Model: An Overview”, CESifo Working Paper Series 7640. https://www.ifo.de/DocDL/cesifo1_wp7640.pdf10.2139/ssrn.3422221
Search in Google Scholar Back to article
Corchón, Luis C. and Marco A. Marini, eds. (2018), Handbook of Game Theory and Industrial Organization, Volume I: Theory, Edward Elgar Publishing: Cheltenham Glos, UK10.4337/9781788112789
Search in Google Scholar Back to article
Corchón, Luis C. and Ramon J. Torregrosa (2018), “Cournot Equilibrium Revisited”. Available at SSRN: https://ssrn.com/abstract=3205390 or http://dx.doi.org/10.2139/ssrn.320539010.2139/ssrn.3205390
Search in Google Scholar Back to article
Cournot, Antoine-Augustin (1897[1838]), Recherches sur les principes mathematiques de la theorie des richesses. Trans. Nathaniel T. Bacon, Researches Into The Mathematical Principles Of The Theory Of Wealth, Macmillan & Co: London. https://www3.nd.edu/~tgresik/IO/Cournot.pdf
Search in Google Scholar Back to article
Delbono, Flavio and Luca Lambertini (2018), “Cournot Conjectures under Price Competition”, International Journal of Economic Theory, 14(4), 295-301.10.1111/ijet.12159
Search in Google Scholar Back to article
Elsadany, Abdelalim A. (2017), “Dynamics of a Cournot Duopoly Game with Bounded Rationality based on Relative Profit Maximization”, Applied Mathematics and Computation, 294, 253-263.10.1016/j.amc.2016.09.018
Search in Google Scholar Back to article
Gao, Bingyuan and Yueping Du, (2018), Exploring General Equilibrium Points for Cournot Model, Discrete Dynamics in Nature and Society, 2018 issue, 1-7. https://www.hindawi.com/journals/ddns/2018/7630395/10.1155/2018/7630395
Search in Google Scholar Back to article
Garg, Vikas K. and Tommi Jaakkola (2017), “Local Aggregative Games”, 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA. https://papers.nips.cc/paper/7118-local-aggregative-games.pdf
Search in Google Scholar Back to article
Hahn, Frank H. (1962), “The Stability of the Cournot Oligopoly Solution”, Review of Economic Studies, 29, 329-333.10.2307/2296310
Search in Google Scholar Back to article
Hommes, Cars H., Marius I. Ochea, and Jan Tuinstra (2018), “Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics”, Dynamic Games and Applications, 8, 822-843.10.1007/s13235-018-0238-x
Search in Google Scholar Back to article
Kollias, Iraklis, Elias Camouzis and John Leventides (2017), “Global Analysis of Solutions on the Cournot-Theocharis Duopoly with Variable Marginal Costs”, Journal of Dynamics and Games, 4(1), 25-39.10.3934/jdg.2017002
Search in Google Scholar Back to article
Okuguchi, Koji and TakeshiYamazaki (2008), “Global Stability of Unique Nash Equilibrium in Cournot Oligopoly and Public Good Game”, Journal of Economic Dynamics and Control, 32(4), 1204-1211.10.1016/j.jedc.2007.05.003
Search in Google Scholar Back to article
Pecora, Nicolò and Mauro Sodini, (2018), “A Heterogenous Cournot Duopoly with Delay Dynamics: Hopf Bifurcations and Stability Switching Curves”, Communications in Nonlinear Science and Numerical Simulation, 58, 36-46.10.1016/j.cnsns.2017.06.015
Search in Google Scholar Back to article
Puu, Tönu, ed., (2018), Disequilibrium Economics: Oligopoly, Trade, and Macrodynamics, Springer: Berlin.10.1007/978-3-319-74415-5
Search in Google Scholar Back to article
Radi, Davide (2017), “Walrasian versus Cournot Behavior in an Oligopoly of Boundedly Rational Firms”, Journal of Evolutionary Economics, 27, 933-961.10.1007/s00191-017-0536-2
Search in Google Scholar Back to article
Sarafopoulos, Georges and Kosmas Papadopoulos (2018), “On the Stability of a Cournot Dynamic Game Under the Influence of Information”, in The Economies of the Balkan and the Eastern European Countries in the Changing World, KnE Social Sciences, 131-144. DOI 10.18502/kss.v3i 10.3534.
Search in Google Scholar Back to article
Shubik, Martin and Richard E. Levitan (1980), Market Structure and Behavior, Harvard U. Press: Cambridge, MA.10.4159/harvard.9780674433403
Search in Google Scholar Back to article
Theocharis, Reghinos D. (1960) On the Stability of the Cournot Solution on the Oligopoly Problem”, Review of Economic Studies, 27, 133-134.10.2307/2296135
Search in Google Scholar Back to article
Ueda, Masahiko (2019), “Effect of Information Asymmetry in Cournot Duopoly Game with Bounded Rationality”, Applied Mathematics and Computation, 362, 124535.10.1016/j.amc.2019.06.049
Search in Google Scholar Back to article
Yu, Weisheng, and Yu Yu, (2018), “The stability of Bayesian Nash Equilibrium of Dynamic Cournot Duopoly Model with Asymmetric Information”, Communications in Nonlinear Science and Numerical Simulation, 63, 101-116.10.1016/j.cnsns.2018.03.001
Search in Google Scholar Back to article
Zhou, Jie, Wei Zhou, Tong Chu, Ying-xiang Chang, and Meng-jia Huang, (2019), “Bifurcation, Intermittent Chaos and Multi-stability in a Two-stage Cournot Game with R&D Spillover and Product Differentiation”, Applied Mathematics and Computation, 341, 358-378.10.1016/j.amc.2018.09.004
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/sbe-2021-0015 | Journal eISSN: 2344-5416 | Journal ISSN: 1842-4120

Journal RSS Feed

Language: English

Page range: 187 - 197

Published on: May 26, 2021

Published by: Lucian Blaga University of Sibiu

In partnership with: Paradigm Publishing Services

Keywords:

Cournot equilibrium stability,

General quantity oligopoly,

Quasilinear quadratic utility,

Mean value theorem

Related subjects:

Business and economics,

Business management,

Management accounting, financial controlling, cost calculation, investment,

Management, organization, corporate governance,

Business development, change management, cooperation,

Entrepreneurship

© 2021 Gerasimos Soldatos, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 16 (2021): Issue 1 (April 2021)