Abstract
We investigate a dynamic oligopoly game with price adjustments. We show that the subgame perfect equilibria are characterized by larger output and lower price levels than the open-loop solution. The individual (and industry) output at the closed-loop equilibrium is larger than its counterpart at the feedback equilibrium. Therefore, firms prefer the open-loop equilibrium to the feedback equilibrium, and the latter to the closed-loop equilibrium. The opposite applies to consumers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Basar and G. J. Olsder, Dynamic noncooperative game theory. Academic Press, San Diego (1982); second edition (1995).
S. Clemhout and H. Y. Wan, Jr., A class of trilinear differential games. J. Optim. Theory Appl. 14(1974), 419–424.
E. J. Dockner and A. A. Haug, Tariffs and quotas under dynamic duopolistic competition. J. Int. Economics 29(1990), 147–159.
The closed loop motive for voluntary export restraints. Canad. J. Economics 3(1991), 679–685.
E. J. Dockner, G. Feichtinger, and S. Jørgensen, Tractable classes of nonzero-sum open-loop Nash differential games: Theory and examples. J. Optim. Theory Appl. 45(1985), 179–197.
R. Driskill and S. McCafferty, Dynamic duopoly with adjustment costs: A differential game approach. J. Econom. Theory 69(1989), 324–338.
C. Fershtman, Identification of classes of differential games for which the open-loop is a degenerated feedback Nash equilibrium. J. Optim. Theory Appl. 55(1987), 217–231.
C. Fershtman and M. I. Kamien, Dynamic duopolistic competition with sticky prices. Econometrica 55(1987), 1151–1164.
Turnpike properties in a finite-horizon differential game: Dynamic duopoly with sticky prices. Int. Econom. Review 31(1990), 49–60.
C. Fershtman, M. Kamien, and E. Muller, Integral games: Theory and applications. In: Dynamic Economic Models and Optimal Control (G. Feichtinger, ed.), Amsterdam, North-Holland (1992), pp. 297–311.
A. Mehlmann, Applied Differential Games. Plenum Press, New York (1988).
A. Mehlmann and R. Willing, On nonunique closed-loop Nash equilibria for a class of differential games with a unique and degenerate feedback solution. J. Optim. Theory Appl. 41(1983), 463–472.
C. Piga, Competition in a duopoly with sticky price and advertising. Int. J. Industrial Organization 18(2000), 595–614.
J. Reinganum, A class of differential games for which the closed loop and open loop Nash equilibria coincide. J. Optim. Theory Appl. 36(1982), 253–262.
S. S. Reynolds, Capacity investment, preemption and commitment in an infinite horizon model. Int. Econom. Review 28(1987), 69–88.
M. Simaan and T. Takayama, Game theory applied to dynamic duopoly problems with production constraints. Automatica 14(1978), 161–166.
A. M. Spence, Investment strategy and growth in a new market. Bell J. Economics 10(1979), 1–19.
A. W. Starr and Y. C. Ho, Nonzero-sum differential games. J. Optim. Theory Appl. 3(1969), 184–208.
S. Tsutsui and K. Mino, Nonlinear strategies in dynamic duopolistic competition with sticky prices. J. Econom. Theory 52(1990), 136–161.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cellini, R., Lambertini, L. Dynamic Oligopoly with Sticky Prices: Closed-Loop, Feedback, and Open-Loop Solutions. Journal of Dynamical and Control Systems 10, 303–314 (2004). https://doi.org/10.1023/B:JODS.0000034432.46970.64
Issue Date:
DOI: https://doi.org/10.1023/B:JODS.0000034432.46970.64