Presenting a model to determine the equilibrium point in the Oligopoly

Presenting a model to determine the equilibrium point in the Oligopoly

Subject Areas :

Reza Basiri ¹ , Mansour Abedian ² , Saeed Aghasi ³ , Zahra Dashtlali ⁴

1 - Doctoral student of Management Department, Dahaghan Branch, Islamic Azad University, Dahaghan, Iran.
2 - Assistant Professor, Department of Industrial Engineering, Najaf Abad Branch, Islamic Azad University, Najaf Abad, Iran. (author responsible)
3 - Assistant Professor, Department of Management, Dehagan Branch, Islamic Azad University, Dehagan, Iran.
4 - Assistant Professor, Department of Management, Dehagan Branch, Islamic Azad University, Dehagan, Iran.

Received: 2023-10-24 Accepted : 2024-03-04 Published : 2024-12-29

Keywords: Price maker, price taker, Cournot&ndash, Nash equilibrium, oligopoly, game theory,

Abstract :

Oligopoly is one of the common structures of the market and is actually a state between pure competition and pure monopoly. The theoretical literature distinguishes between the behaviors of companies in adopting competitive pricing strategies. It is common to study models where all firms are price-makers or price-takers, but the simultaneous application of price-making and price-taking strategies by firms producing a similar product using game theory has not received much attention. Therefore, the purpose of this article is to use game theory with equilibrium concepts forward-looking equilibrium reasoning, and backward-looking individual learning simulation tools to investigate the behavior of companies. The results of the recent study showed that the Cournot-Nash model is a stable model for the real evaluation of pricing strategies in a dynamic oligopoly market. However, with a larger number of firms, a unilateral deviation from Cournot's behavior becomes profitable. In this paper, we have formally proved that the only possible stable market is the Cornot market, where every firm can be a price taker. Conversely, a market in which all firms accept only prices is never stable, and therefore Walrasian equilibrium is not applicable according to the findings. When there are no stable markets, the market does not evolve toward a fixed composition, but the number of price takers typically decreases. In such a situation, the market composition follows a cyclical pattern that is related to the stability or volatility of crude expectations.

References:

- Abdou, D. & Raafat , A. (2022). Insight from the automotive industry – the case of the Mercedes s-class in the united state.‏
- Alós-Ferrer, C., 2004. Cournot versus Walras in dynamic oligopolies with memory. Int. J. Ind. Organiz. 22 (2), 193–217.
- Anufriev, M., Hommes, C., 2012. Evolutionary selection of individual expectations and aggregate outcomes in asset pricing experiments. Am. Econ. J. 4 (4), 35–64.
- Anufriev, M., Kopányi, D., Tuinstra, J., 2013. Learning cycles in Bertrand competition with differentiated commodities and competing learning rules. J. Econ. Dyn. Control 37 (12), 2562–2581.
- Anufriev, M. and Kopányi, D., 2018. Oligopoly game: Price makers meet price takers. Journal of economic dynamics and control, 91, pp.84-103.
- Arifovic, J., 1994. Genetic algorithm learning and the cobweb model. J. Econ. Dyn. Control 18 (1), 3–28.
- Arifovic, J., Maschek, M.K., 2006. Revisiting individual evolutionary learning in the cobweb model–an illustration of the virtual spite-effect. Comput. Econ. 28 (4), 333–354.
- Betrand, J. (1883). Theorie math ematique de la richesse sociale. Journal des savants, 499-508.‏
- Bimpikis, K., Ehsani, S., Ilkılı¸c, R., 2019. Cournot competition in networked markets. Management Science 65(6), 2467–2481
- Bischi, G.-I., Chiarella, C., Kopel, M., 2004. The long run outcomes and global dynamics of a duopoly game with misspecified demand functions. Int. Game Theory Rev. 6 (03), 343–379.
- Bischi, G.I., Chiarella, C., Kopel, M., Szidarovszky, F., 2009. Nonlinear Oligopolies: Stability and Bifurcations. Springer Science & Business Media.
- Bischi, G.I., Lamantia, F., Radi, D., 2015. An evolutionary Cournot model with limited market knowledge. J. Econ. Behav. Org. 116, 219–238.
- Bischi, G.I., Naimzada, A.K., Sbragia, L., 2007. Oligopoly games with local monopolistic approximation. J. Econ. Behav. Org. 62 (3), 371–388.
- Bray, M.M., Savin, N.E., 1986. Rational expectations equilibria, learning, and model specification.Econometrica 54 (5), 1129–1160.
- Brock, W., Hommes, C., 1997. A rational route to randomness. Econometrica 65 (5), 1059–1095.
- Camerer, C., Ho, T.H., 1999. Experience-weighted attraction learning in normal form games. Econometrica 67 (4), 827–874.
- Chletsos, M., Saiti, A., 2019. Hospitals as suppliers of healthcare services. In: Strategic Management and Economics in Health Care, pp. 179–205. Springer.
- Chiarella, C., 1988. The cobweb model: its instability and the onset of chaos. Econ. Model. 5 (4), 377–384.
- Chiarella, C., Szidarovszky, F., 2004. Dynamic oligopolies without full information and with continuously distributed time lags. J. Econ. Behav. Org. 54 (4).495–511.
- Colombo, L., & Labrecciosa, P. (2020). Dynamic oligopoly pricing with reference-price effects. European Journal of Operational Research, 288(3), 1006-1016.‏
- Cournot, A.-A., 1838. Recherches sur les principes mathématiques de la théorie des richesses par Augustin Cournot. Hachette, Paris. (English translation:-Researches into the Mathematical Principles of the Theory of Wealth. Kelley,New York, 1960).
- Dou, W.W., Ji, Y. and Wu, W., 2022. The oligopoly Lucas tree. The Review of Financial Studies, 35(8), pp.3867-3921.
- Droste, E., Hommes, C., Tuinstra, J., 2002. Endogenous fluctuations under evolutionary pressure in Cournot competition. Games Econ. Behav. 40 (2), 232–269.
- Erev, I., Roth, A.E., 1998. Predicting how people play games: reinforcement learning in experimental games with unique, mixed strategy equilibria. Am.
Econ. Rev. 88 (4), 848–881.
- Hahn, F.H., 1962. The stability of the Cournot oligopoly solution. Rev. Econ. Stud. 29 (4), 329–331.
- Hommes, C., 2013. Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems. Cambridge University Press. Hommes, C.H., 1994. Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand. J. Econ. Behav. Org. 24 (3), 315–335.
- Hommes, C.H., Ochea, M.I., Tuinstra, J., 2018. Evolutionary competition between adjustment processes in Cournot oligopoly: instability and complex dynamics. J. Dyn. Games Appl. doi:10.1007/s13235-018-0238-x.
- Huang, W., 2002. On the incentive for price-taking behavior. Manag. Decis. 40 (7), 682–692.
- Huang, W., 2003. A naive but optimal route to Walrasian behavior in oligopolies. J. Econ. Behav. Org. 52 (4), 553–571.
- Huang, W., 2007. Profitability analysis of price-taking strategy in disequilibrium. Discrete Dyn. Nat. Soc. 2007.
- Kirman, A., 1983. On mistaken beliefs and resultant equilibria. In: Frydman, R., Phelps, E. (Eds.), Individual Forecasting and Collective Outcomes. Cambridge
University Press, pp. 147–166.
-Kirman, A., 2011. Complex Economics: Individual and Collective Rationality. Routledge.
- Jokar-Dehoie, M., Zare, M., Niknam, T., Aghaei, J., Pourbehzadi, M., Javidi, G. and Sheybani, E., 2022. Game Theory-Based Bidding Strategy in the Three-Level Optimal Operation of an -Aggregated Microgrid in an Oligopoly Market. IEEE Access, 10, pp.104719-104736.
- Kirschen, D.S., Strbac, G.: Fundamentals of Power System Economics. John Wiley & Sons, (2018)
- Liu, Q. and Chow, J.Y., 2022. Efficient and stable data-sharing in a public transit oligopoly as a coopetitive game. Transportation Research Part B: Methodological, 163, pp.64-87.
- Li, X., Wang, Y., Zhu, M. and Ma, J., 2022. Research on the Complexity of Oligopoly Game under Business Interruption Insurance of the Engineering Project. Mathematical Problems in Engineering, 2022.
- Liu, L., 2022. Approximate Nash Equilibrium Learning for n-Player Markov Games in Dynamic Pricing. arXiv preprint arXiv:2207.06492.
- McFadden, D., 1981. Econometric models of probabilistic choice. In: Manski, C.F., McFadden, D. (Eds.), Structural Analysis of Discrete Data with Econometric
Applications. MIT Press: Cambridge, MA.
- Muth, J.F., 1961. Rational expectations and the theory of price movements. Econometrica 29 (3), 315–335.
- Nerlove, M., 1958. Adaptive expectations and cobweb phenomena. Q. J. Econ. 72(2), 227–240.
- Prado, N., & Blavatsky, B. (2021). Imagination, Selves, and Knowledge of Self: Pessoa's Dreams in The Book of Disquiet. In Epistemic Uses of Imagination (pp. 298-318). Routledge.‏
- Semmler, W., Di Bartolomeo, G., Fard, B.M. and Braga, J.P., 2022. Limit pricing and entry game of renewable energy firms into the energy sector. Structural Change and Economic Dynamics, 61, pp.179-190.
- Szidarovszky, F. (Eds.), Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications. Springer, pp. 249–268.
- Taywade, K., Goldsmith, J., Harrison, B., & Bagh, A. (2023). Multi-armed Bandit Algorithms for Cournot Games.‏
- Yuan, J., & Zhu, J. (2023). Analysis of heterogeneous duopoly game with information asymmetry based on extrapolative mechanism. Studies in Nonlinear Dynamics & Econometrics, 27(5), 635-648.
- Yuri, T., Jernigan, R. W., Brumfield, R. T., Bhagabati, N. K., & Braun, M. J. (2009). The effect of marker choice on estimated levels of introgression across an avian (Pipridae: Manacus) hybrid zone. Molecular Ecology, 18(23), 4888-4903.‏
- Vall´ee, T., Yıldızo˘glu, M., 2009. Convergence in the finite Cournot oligopoly with social and individual learning. Journal of Economic Behavior & Organization 72(2), 670–690.
- Vega-Redondo, F., 1997. The evolution of Walrasian behavior. Econometrica 65 (2), 375–384.
- Vriend, N.J., 2000. An illustration of the essential difference between individual and social learning, and its consequences for computational analyses. Journal of economic dynamics and control 24(1), 1–19 [12].
- Zhang, Y., Gu, C., Yan, X. and Li, F., 2020. Cournot oligopoly game-based local energy trading considering renewable energy uncertainty costs. Renewable Energy, 159, pp.1117-1127.