A Dynamic Game Theory Model for Analyzing Competition in the Oligopoly Markets

Document Type : Original Article


1 Ph.D Student, Islamic Azad University, Tehran North Branch.

2 Assistatnt Professor, Islamic Azad University, Tehran North Branch

3 Assistatnt Professor, Buein Zahra Technical University.


Privatization has led to the formation dynamic competition in markets, such as airline service providers with a limited number of suppliers and a large number of customers (oligopoly markets). Suppliers of goods and services in these markets are considering the behavior of competitors to determine the amount of products and advertisements in order to maximize their benefits. This paper investigates a differential oligopoly game model under open loop and close loop structures. By applying mathematical validation of the optimal levels of production (supply) and advertising cost, the proposed model used to analyze the market for airline services, and it is shown that parameters such as sticky price, substitutability among goods and advertising promotional efficiency on supply and advertising are effective in achieving sustainable equilibrium in such markets. Sensitivity analysis of the parameters in the proposed model shows that in open loop strategy when companies in an oligopoly market do not agree any agreement in all stages of competition, they will suffer a lot of financial burden.


1. Abdoli, G. (2012). Game theory and its applications, Third Edition. Tehran, Iranian Student Book Agency (In Persian).
2. Barati, M. (2017). The Effect of Supply Chain Relationship Management on the Competitiveness of Small and Medium Enterprises of Automobile Industry, Industrial Management Perspective7(26), 123-141 (In Persian).
3. Cellini, R. & Lambertini, L. (2002). A differential game approach to investment in product differentiation, Journal of Economic Dynamics and Control, 27(1), 51-62.
4. Cellini, R. & Lambertini, L. (2003). Capacity accumulation and utilization in a differential duopoly game. working paper from Dipartimento Scienze Economiche, Universita’ di Bologna.
5. Cellini, R. & Lambertini, L. (2003). Advertising in a differential oligopoly game. Journal of Optimization Theory and Applications, 116(1), 61-81.
6. Cellini, R. & Lambertini, L. (2004). Dynamic oligopoly with sticky prices: closed-loop, feedback, and open-loop solutions. Journal of Dynamical and Control Systems, 10(3), 303-314.
7. Cellini, R. & Lambertini, L. (2007). A differential oligopoly game with differentiated goods and sticky prices. European Journal of Operational Research, 176, 1131-1144.
8. Dastgerdi Yeganeh, V. (2010). Game Theory, Encyclopedia of City Economics, 8, 134-140 (In Persian).
9. Delbono, F. & Lambertini, L. (2016). Ranking Bertrand, Cournot and supply function equilibria in oligopoly. Energy Economics, 60, 73-85.
10. Dong, L., Narasimhan, C. & Zhu, K. (2009). Product line pricing in a supply chain. Management Science, 55 (10), 1704-1717.
11. Dragone, D., Lambertini, L. & Palestini, A. (2011). On the feedback solution of a differential oligopoly game with capacity adjustment. IFAC Proceedings, 44, 6795-6799.
12. Driskill, R. & McCafferty, S. (1989). Dynamic duopoly with adjustment costs: A differential game approach. Journal of Economic Theory, 69, 324–338.
13. Faraji Dizaji, S. (2010). Microeconomic theory, Iran University of Economic Science, Tehran.
14. Faruqi, F.A. (2017). Dierential Game Theory with Applications to Missiles and Autonomous Systems Guidance. John Wiley & Sons Ltd.
15. Fershtman, C. & Kamien, M. I. (1987). Dynamic duopolistic competition with sticky prices, Econometrica, 55: 1151-1164.
16. Friesz. T. L. (2010). Dynamic Optimization and Differential Games. Springer US.
17. Grauberger, W. & Kimms, A. (2016). Airline revenue management games with simultaneous price and quantity competition. Computers & Operations Research75, 64-75.
18. Grosset, L. & Viscolani, B. (2015). Open-Loop Nash Equilibrium in Erickson's Oligopoly Model. Nonlinear Analysis and Differential Equations, 4, 167-172.
19. Hespanha, J. P. (2017). Noncooperative Game Theory an Introduction for Engineering and Computer Scientists. Princeton University Press.
20. Hu, G., Wang, L., Chen, Y. & Bidanda, B. (2015). An oligopoly model to analyze the market and social welfare for green manufacturing industry. Journal of Cleaner Production, 85, 94–103.
21. Jergensen, S., Dockner, E., Van Long, N. & Sorger, G. (2000). Differential Games in Economics and Management Science. Cambridge University Press, 77-91.
22. Khodad Kashi, F., Zaranejad, M. & Usefi Hajiabad, R. (2015). Investigating the interaction between the level of focus, profitability, research and development and advertising in the factories, The Economic Research, 15(3), 175-194 (In Persian).
23. Kobayashi, S. (2014). On a Dynamic Model of Cooperative and Noncooperative R and D in Oligopoly with Spillovers.Dynamic Games and Applications, 5, 599–61.
24. Lambertini, L. & Mantovani, A. (2006). Identifying reaction functions in differential oligopoly games. Mathematical Social Sciences, 52 (3), 252-271.
25. Lambertini, L.  & Mantovani, A. (2014). Feedback equilibria in a dynamic renewable resource oligopoly: pre-emption, voracity and exhaustion. International Journal of Management and Economics, 46, 134–146.
26. Liang, Z. & Peng, Y. (2016). A game theory based analysis of decision making for green retrofit under different occupancy types. Journal of Cleaner Production137, 1300-1312.
27. Ma, M., Zuo, Y., Liu, K. & Qi, Y. (2015). Forest Insurance Market Participants’ Game Behavior in China: An Analysis Based on Tripartite Dynamic Game Model, Journal of Industrial Engineering and Management, 8, 5-7.
28. Mahmoudinia, D., Dallali Esfahani, Engwerda, J. R. & Dastjerdi, R. (2016). Game theory and its role in determining optimal policies and strategic interaction between fiscal and monetary policymakers (Application of differential game theory and stackelberg games), Quarterly Journal of Applied Economics Studies5(18), 1-34 (In Persian).
29. Milan, M. (1996). Games, Strategies & Managers: How Managers Can Use Game Theory to Make Better Business Decision. Oxford University Press, USA, 246.
30. Mosleh Shirazi, A.N. & Khalifeh, M. (2015). Measuring global competitiveness of Iran compared to countries using a two-stage model of data envelopment analysis, Industrial Management Perspective19, 119-137 (In Persian).
31. Navidi, H. (2010). An Ordinal Game Theroic Approach for Competitive Multi 50 Criteria Supplier Selection. International Conference on Future Industrial Engineering and Application, 412-415.
32. Piga, A. (2000). Competition in a duopoly with sticky price and advertising. International Journal of Industrial Organization, 18, 595-614.
33. Prasad, A., Sethia, S. P. & Niak, P.A. (2012). Understanding the impact of churn in dynamic oligopoly market. Automatica, 48(11), 2882-2887.
34. Raoufinia, M., Baradaran, V. & Shahrjerdi, R. (2018). A Dynamic Differential Game with Sticky Price and Advertising, Kybernetes (Impress) doi.org/10.1108/K-02-2018-0067.
35. Runyan, P., Heping, W. & Zhengping. W. (2000). Decision-making of Aircraft Optimum Configuration Utilizing Multi-dimensional Game Theory. Chinese Journal of Aeronautics, 23, 194-197.
36. Sethi, S. & Thompson, J. (2006). Optimal control theory applications to Management Science and Economics, springer.
37. Shahikitash, M. & Mohammadzadeh, A. (2014). Gain sensitivity of conjecture changes in a multilateral monopoly structure based on the Iwata approach, Journal of Agricultural Economics and Development, 28 (3), 272-281 (In Persian).
38. Simaan, M. & Takayama, T. (1978). Game theory applied to dynamic duopoly problems with production constraints. Automatica.14, 161-166.
39. Staelin, R. (1986). Channel efficiency, incentive compatibility, transfer pricing, and market structure: an equilibrium analysis of channel relationships. In: Bucklin, L., Carman, J. (Eds.), Research in Marketing, 8, JAI Press, Greenwich, CT, 181-223.
40. Taleizadeh, A. & Mohammadi, R. (2015). Optimizing sales prices and advertising costs in a two-tier supply chain, including a manufacturer and two retailers, Industrial Management Perspective, 18, 107-127 (In Persian).
41. Van Long, N. (2010). A Survey of Dynamic Games in Economics. World Scientific Publishing.
42. Wei, W. & Hansen, M. (2007). Airlines’ competition in aircraft size and service frequency in duopoly markets. Transportation Research Part E: Logistics and Transportation Review, 43 (4)409-424.
43. Wiszniewska-Matyszkiel, A., Bodnar, M., & Mirota, F. (2014). Dynamic oligopoly with sticky prices: off-steady-state analysis. Dynamic Games and Applications, 5(4), 1-31.
44. Wu, Z. X., Zhang, B.X., Li, S., & Wang, X. (2009). Dynamic Duopolistic Competition with Sticky Prices and Advertising in Product Differentiation Market: A Feedback Nash Equilibrium. International Conference on Information Engineering and Computer Science (ICIECS), 19-20 December 2009 1: 1-770, IEEE, Wuhan, China.
45. Xiao, W., Zhang, B., Li, S.; &Wang, X. (2009). Dynamic Duopolistic Competition with Sticky Prices and Advertising in Product Differentiation Market: A Feedback Nash Equilibrium. International Conference on Information Engineering and Computer Science, Wuhan, China.
46. Zito, P., Salvo, G. & La Franca, L. (2011). Modelling Airlines Competition on Fares and Frequencies of Service by Bi-level Optimization. Procedia Social and Behavioral Sciences, 20, 1080-1089.