Dynamic Price Competition with Price Adjustment Costs and Product Differentiation
AbstractWe study a discrete time dynamic game of price competition with spatially differentiated products and price adjustment costs. We characterise the Markov perfect and the open-loop equilibrium of our game. We find that in the steady state Markov perfect equilibrium, given the presence of adjustment costs, equilibrium prices are always higher than prices at the repeated static Nash solution, even though, adjustment costs are not paid in steady state. This is due to intertemporal strategic complementarity in the strategies of the firms and from the fact that the cost of adjusting prices adds credibility to high price equilibrium strategies. On the other hand, the stationary open-loop equilibrium coincides always with the static solution. Furthermore, in contrast to continuous time games, we show that the stationary Markov perfect equilibrium converges to the static Nash equilibrium when adjustment costs tend to zero. Moreover, we obtain the same convergence result when adjustment costs tend to infinity.
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Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2003.120.
Date of creation: Dec 2003
Date of revision:
Price adjustment costs; Difference game; Markov perfect equilibrium; Open-loop equilibrium;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
This paper has been announced in the following NEP Reports:
- NEP-COM-2004-09-12 (Industrial Competition)
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- Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-99, May.
- Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-64, September.
- Akerlof, George A & Yellen, Janet L, 1985. "Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?," American Economic Review, American Economic Association, vol. 75(4), pages 708-20, September.
- Lapham, Beverly & Ware, Roger, 1994. "Markov puppy dogs and related animals," International Journal of Industrial Organization, Elsevier, vol. 12(4), pages 569-593, December.
- Maskin, Eric & Tirole, Jean, 2001.
"Markov Perfect Equilibrium: I. Observable Actions,"
Journal of Economic Theory,
Elsevier, vol. 100(2), pages 191-219, October.
- Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
- Slade, Margaret E., 1999. "Sticky prices in a dynamic oligopoly: An investigation of (s,S) thresholds," International Journal of Industrial Organization, Elsevier, vol. 17(4), pages 477-511, May.
- Driskill, Robert A. & McCafferty, Stephen, 1989. "Dynamic duopoly with adjustment costs: A differential game approach," Journal of Economic Theory, Elsevier, vol. 49(2), pages 324-338, December.
- Jensen, Henrik & Lockwood, Ben, 1998.
"A note on discontinuous value functions and strategies in affine-quadratic differential games,"
Elsevier, vol. 61(3), pages 301-306, December.
- Jensen, H. & Lockwood, B., 1995. "A Note on Discontinuous Value Functions and Strategies in Affine-Quadratic Differential Games," Discussion Papers 9514, Exeter University, Department of Economics.
- Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
- Jun, Byoung & Vives, Xavier, 2001. "Incentives in Dynamic Duopoly," CEPR Discussion Papers 2899, C.E.P.R. Discussion Papers.
- Karp, Larry & Perloff, Jeffrey M, 1988.
"Open-loop and feedback models of dynamic oligopoly,"
Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series
qt7pn779rc, Department of Agricultural & Resource Economics, UC Berkeley.
- Karp, Larry S. & Perloff, Jeffrey M., 1993. "Open-loop and feedback models of dynamic oligopoly," International Journal of Industrial Organization, Elsevier, vol. 11(3), pages 369-389, September.
- Fudenberg, Drew & Tirole, Jean, 1984. "The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look," American Economic Review, American Economic Association, vol. 74(2), pages 361-66, May.
- Lockwood, Ben, 1996. "Uniqueness of Markov-perfect equilibrium in infinite-time affine-quadratic differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 20(5), pages 751-765, May.
- Rotemberg, Julio J, 1982. "Sticky Prices in the United States," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1187-1211, December.
- Mankiw, N Gregory, 1985. "Small Menu Costs and Large Business Cycles: A Macroeconomic Model," The Quarterly Journal of Economics, MIT Press, vol. 100(2), pages 529-38, May.
- AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," CORE Discussion Papers 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Piga, Claudio A. G., 2000. "Competition in a duopoly with sticky price and advertising," International Journal of Industrial Organization, Elsevier, vol. 18(4), pages 595-614, May.
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