Vernasca, Gianluigi (2003) Dynamic price competition with price adjustment costs and product differentiation. Working Paper. University of Warwick, Department of Economics, Coventry.

Preview

PDF WRAP_Vernasca_twerp681.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (173Kb)

Abstract

We 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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Markov processes, Price maintenance -- Costs, Difference algebra, Equilibrium (Economics), Adjustment costs, Product differentiation
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	July 2003
Number:	No.681
Number of Pages:	24
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	[1] Akerlof, G. and J. Yellen (1985), “Can Small Deviations from Rationality Make Significant Differences to Economic Equilibria?”, American Economic Review 75, pp. 708-721. [2] Amir, R. (2001), “Stochastic Games in Economics and Related Fields: an Overview”, CORE Discussion Paper 2001/60. [3] Basar, T. and G.J. Olsder (1995), Dynamic Noncooperative Game Theory, Acadenic Press: New York. [4] Cellini, R. and L. Lambertini (2001.a), “Dynamic Oligopoly with Sticky Prices: Closed-Loop, Feedback and Open-Loop Solutions”, Working Paper, Dipartimento di Scienze Economiche, Universita’ degli Studi di Bologna. [5] Cellini, R. and L. Lambertini (2001.b), “Di¤erential oligopoly Games where the Closed-Loop Memoryless and the Open-Loop Equilibria Coincide”, Working Paper, Dipartimento di Scienze Economiche, Universita’ degli Studi di Bologna. [6] Cheney W. and D. Kincaid (1999), Numerical Mathematics and Computing, Brooks/Cole Publishing, Pacific Grove, CA. [7] Doganouglu, T. (1999), “Dynamic Price Competition with Persistent Consumer Tastes”, University of Bonn, mimeo. [8] Driskill R.A. and S. McCa¤erty (1989), “Dynamic Duopoly with Adjustment Costs: A Differential Game Approach”, Journal of Economic Theory, vol. 49, pp. 324-338. [9] Fershtman, C. and M. Kamien (1987), “Dynamic Duopolistic Competition with Sticky Prices”, Econometrica, vol. 55, no. 5, pp. 1151-1164. [10] Fudenberg, D. and J. Tirole (1984), “The Fat-Cat Effect, the Puppy-Dog ploy, and the Lean and Hungry Look”, American Economic Review, Papers and Proceedings 74, pp. 361-389. [11] Fudenberg, D. and J. Tirole (1991), Game Theory, The MIT Press: Cambridge, MA. [12] Jensen, H. and B. Lokwood (1998), “A Note on Discontinuous Value Functions and Strategies in A¢ne-Quadratic Differential Games”, Economic Letters 61, pp. 301-306. [13] Judd, K.L. (1989), “Cournot vs. Bertrand: A Dynamic Resolution”, University of Stanford, mimeo. [14] Jun, B. and X. Vives (1999), “Strategic Incentive in Dynamic Duopoly”, mimeo. [15] Karp, L. and J. Perloff (1993), “Open-loop and Feedback Models of Dynamic Oligopoly”, International Journal of Industrial Organization, vol. 11, pp. 369-389. [16] Kreps, D. and J. Scheinkman (1983), “Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes”, Bell Journal of Economics, vol.14, pp.326-337. [17] Lapham, B. and R. Ware (1994), “Markov Puppy Dogs and Related Animals”, International Journal of Industrial Organization, vol. 12, pp. 569-593. [18] Leonard D. and N. Van Long (1998), Optimal Control Theory and Static Optimization in Economics, Cambridge University Press: Cambridge, UK. [19] Lockwood, B. (1996), “Uniqueness of Markov Perfect Equilibrium in In finite Time A¢ne-Quadratic Differential Games”, Journal of Economics Dynamics and Control, vol.20, pp. 751-765. [20] Mankiw, G. (1985), “Small Menu Costs and Large Business Cycles: Macroeconomic Model of Monopoly”, Quarterly Journal of Economics 100, pp. 529-539. [21] Maskin, E. and J. Tirole (1987), “A Theory of DynamicOligopoly III”, European Economic Review 31, pp. 947-968. [22] Maskin, E. and J. Tirole (1988), “A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles”, Econometrica, vol.56, no. 3, pp. 571-599. [23] Maskin, E. and J. Tirole (2001), “Markov Perfect Equilibrium: I. Observable Actions”, Journal of Economic Theory, vol.100, pp. 191-219. [24] Papavassilopoulos G.P., J.V. Medanic, and J.B. Cruz (1979), “On the Existence of Nash Strategies and Solutions to Coupled Riccati Equations in Linear-Quadratic Games”, Journal of Optimization Theory and Applications, vol.28, no. 1, pp.49-76. [25] Piga, C. (2000), “Competition in a Duopoly with Sticky Prices and Advertising”, International Journal of Industrial Organization 18, pp. 595-614. [26] Reinganum, J. and N. Stokey (1985), “Olygopoly Extraction of a Common Property Natural Resource: The Importance of the Period of Commitment in Dynamic Games”, International Economic Review, vol. 26, pp. 161-173. [27] Reynolds, S.S. (1991), “Dynamic Oligopoly with capacity Adjustment Costs”, Journal of Economic Dynamics and Control, vol. 15, no. 3, pp. 491-514. [28] Rotemberg, J.J. (1982), “Sticky Prices in the United States”, Journal of Political Economy, vol. 90, no. 6, pp. 1187-1211. [29] Slade, M.E. (1999), “Sticky Prices in a Dynamic Oligopoly: An Investigation of (s; S ) Thresholds”, International Journal of Industrial Organization, vol. 17, pp. 477-511. [30] Tirole, J. (1988), The Theory of Industrial Organization,MIT Press: Cambridge, MA. [31] Zeeuw,A. and J. Van der Ploeg (1991), “Difference Games and Policy Evaluation: A Conceptual Framework”, Oxford Economic Papers, vol. 43, pp. 612-636.
URI:	http://wrap.warwick.ac.uk/id/eprint/1509

Request changes to a record

Actions (login required)

View Item