A Dynamic Cournot Model with Brownian Motion
ABSTRACT
In this paper we develop a stochastic version of a dynamic Cournot model. The model is dynamic because firms are slow to adjust output in response to changes in their economic environment. The model is stochastic because management may make errors in identifying the best course of action in a dynamic setting. We capture these behavioral errors with Brownian motion. The model demonstrates that the limiting output level of the game is a random variable, rather than a constant that is found in the non-stochastic case. In addition, the limiting variance in firm output is smaller with more firms. Finally, the model predicts that firm failure is more likely in smaller markets and for firms that are smaller and less efficient at managing errors.
In this paper we develop a stochastic version of a dynamic Cournot model. The model is dynamic because firms are slow to adjust output in response to changes in their economic environment. The model is stochastic because management may make errors in identifying the best course of action in a dynamic setting. We capture these behavioral errors with Brownian motion. The model demonstrates that the limiting output level of the game is a random variable, rather than a constant that is found in the non-stochastic case. In addition, the limiting variance in firm output is smaller with more firms. Finally, the model predicts that firm failure is more likely in smaller markets and for firms that are smaller and less efficient at managing errors.
Cite this paper
Youn, H. and Tremblay, V. (2015) A Dynamic Cournot Model with Brownian Motion. Theoretical Economics Letters, 5, 56-65. doi: 10.4236/tel.2015.51009.
Youn, H. and Tremblay, V. (2015) A Dynamic Cournot Model with Brownian Motion. Theoretical Economics Letters, 5, 56-65. doi: 10.4236/tel.2015.51009.
References
[1] Shy, O. (1995) Industrial Organization: Theory and Applications. MIT Press, Cambridge. [2] Tremblay, V.J. and Tremblay, C.H. (2012) New Perspectives on Industrial Organization: With Contributions from Behavioral Economics and Game Theory. Springer, Berlin. http://dx.doi.org/10.1007/978-1-4614-3241-8 [3] Friedman, J.W. (1971) A Noncooperative Equilibrium for Supergames. Review of Economic Studies, 28, 1-12. http://dx.doi.org/10.2307/2296617 [4] Driskill, R.A. and McCafferty, S. (1989) Dynamic Duopoly with Adjustment Costs: A Differential Game Approach. Journal of Economic Theory, 49, 324-338. http://dx.doi.org/10.1016/0022-0531(89)90085-9 [5] Fisher, F. (1961) The Stability of Cournot Oligopoly Solutions: The Effects of Speeds of Adjustment and Increasing Marginal Costs. Review of Economic Studies, 28, 125-135. http://dx.doi.org/10.2307/2295710 [6] Maskin, E. and Tirole, J. (1987) A Theory of Dynamic Oligopoly, III: Cournot Competition. European Economic Review, 31, 947-968. http://dx.doi.org/10.1016/0014-2921(87)90008-0 [7] Dockner, E. (1992) A Dynamic Theory of Conjectural Variations. Journal of Industrial Economics, 11, 377-394. http://dx.doi.org/10.2307/2950530 [8] Spiegler, R. (2011) Bounded Rationality and Industrial Organization. Oxford University Press, Oxford. [9] Oksendal, B. (2002) Stochastic Differential Equations: An Introduction with Applications. 5th Edition, Springer, Berlin. [10] Dunne, T., Roberts, M. and Samuelson, L. (1988) Patterns of Firm Entry and Exit in USA Manufacturing Industries. Rand Journal of Economics, 19, 495-515. http://dx.doi.org/10.2307/2555454 [11] Tremblay, V.J. and Tremblay, C.H. (2005) The USA Brewing Industry: Data and Economic Analysis, MIT Press, Cambridge. [12] Grimmett, G.R. and Stirzaker, D.R. (2001) Probability and Random Processes. Oxford University Press, Oxford.
[1] Shy, O. (1995) Industrial Organization: Theory and Applications. MIT Press, Cambridge. [2] Tremblay, V.J. and Tremblay, C.H. (2012) New Perspectives on Industrial Organization: With Contributions from Behavioral Economics and Game Theory. Springer, Berlin. http://dx.doi.org/10.1007/978-1-4614-3241-8 [3] Friedman, J.W. (1971) A Noncooperative Equilibrium for Supergames. Review of Economic Studies, 28, 1-12. http://dx.doi.org/10.2307/2296617 [4] Driskill, R.A. and McCafferty, S. (1989) Dynamic Duopoly with Adjustment Costs: A Differential Game Approach. Journal of Economic Theory, 49, 324-338. http://dx.doi.org/10.1016/0022-0531(89)90085-9 [5] Fisher, F. (1961) The Stability of Cournot Oligopoly Solutions: The Effects of Speeds of Adjustment and Increasing Marginal Costs. Review of Economic Studies, 28, 125-135. http://dx.doi.org/10.2307/2295710 [6] Maskin, E. and Tirole, J. (1987) A Theory of Dynamic Oligopoly, III: Cournot Competition. European Economic Review, 31, 947-968. http://dx.doi.org/10.1016/0014-2921(87)90008-0 [7] Dockner, E. (1992) A Dynamic Theory of Conjectural Variations. Journal of Industrial Economics, 11, 377-394. http://dx.doi.org/10.2307/2950530 [8] Spiegler, R. (2011) Bounded Rationality and Industrial Organization. Oxford University Press, Oxford. [9] Oksendal, B. (2002) Stochastic Differential Equations: An Introduction with Applications. 5th Edition, Springer, Berlin. [10] Dunne, T., Roberts, M. and Samuelson, L. (1988) Patterns of Firm Entry and Exit in USA Manufacturing Industries. Rand Journal of Economics, 19, 495-515. http://dx.doi.org/10.2307/2555454 [11] Tremblay, V.J. and Tremblay, C.H. (2005) The USA Brewing Industry: Data and Economic Analysis, MIT Press, Cambridge. [12] Grimmett, G.R. and Stirzaker, D.R. (2001) Probability and Random Processes. Oxford University Press, Oxford.