zbMATH — the first resource for mathematics

Price leadership in a duopoly with capacity constraints and product differentiation. (English) Zbl 0774.90012
This paper investigates a duopoly model with two capacity constrained firms whose products are imperfect substitutes. Demand is assumed to be linear and symmetric between the two products, and costs are assumed to be equal to zero. Competition is in prices, and rationing is efficient. The firms play a “Stackelberg” game in which one of the firms chooses its price before the other firm. The authors calculate the subgame- perfect equilibria of this game. They then identify values of the two capacities for which both firms have identical preferences with respect to the question who should move first and who should move second. They show that the relevant capacity values are those for which both firms’ capacities are “relatively large”, and “differ significantly” from each other, and that both firms would then (weakly or strictly) prefer the firm with the larger capacity to move first. The authors argue that for these capacity values one would expect a model with endogenous sequencing for moves to generate this order of moves.
The paper is presented as an extension of recent work of R. J. Deneckere and the second author [Rev. Econ. Stud. 59, No. 1, 143-162 (1992; Zbl 0751.90017)]. Deneckere and the second author consider the case in which the two firms’ products are identical. In this case, the two firms’ preferences with respect to the question who should be the leader may be identical even if their capacities do not differ significantly.

91B24 Microeconomic theory (price theory and economic markets)
91B26 Auctions, bargaining, bidding and selling, and other market models
91A65 Hierarchical games (including Stackelberg games)
91A40 Other game-theoretic models
Full Text: DOI
[1] d’Aspremont, C., and Gabszewicz, J.J. (1985): ?Quasi-Monopolies.?Economica 52: 141-151. · doi:10.2307/2554416
[2] Bös, D., and Nett, L. (1990): ?Privatisation, Price Regulation, and Market Entry. An Asymmetric Multistage Duopoly Model.?Journal of Economics 51: 221-257. · Zbl 0701.90013
[3] Boyer, M., and Moreaux, M. (1987a): ?Being a Leader or a Follower: Reflections on the Distribution of Roles in Duopoly.?International Journal of Industrial Organization 5: 175-192. · doi:10.1016/S0167-7187(87)80018-8
[4] ? (1987b): ?On Stackelberg Equilibria with Differentiated Products: The Critical Role of the Strategy Space.?Journal of Industrial Economics 26: 217-230.
[5] Deneckere, R., and Kovenock, D. (1992): ?Price Leadership.?Review of Economic Studies 59: 143-162. · Zbl 0751.90017 · doi:10.2307/2297930
[6] Dixon, H. (1987a): ?The General Theory of Household and Market Contingent Demand.?The Manchester School 55: 287-304. · doi:10.1111/j.1467-9957.1987.tb01303.x
[7] ? (1987b): ?Approximate Bertrand Equilibria in a Replicated Industry.?Review of Economic Studies 54: 47-62. · Zbl 0609.90011 · doi:10.2307/2297445
[8] Dowrick, S. (1986): ?Von Stackelberg and Cournot Duopoly: Choosing Roles.?Rand Journal of Economics 17: 251-260. · doi:10.2307/2555388
[9] Gal-Or, E. (1985): ?First Mover and Second Mover Advantages.?International Economic Review 26: 649-653. · Zbl 0573.90106 · doi:10.2307/2526710
[10] Glicksberg, I. (1952): ?A Further Generalization of the Kakutani Fixed Point Theorem with Application of Nash Equilibrium Points.?Proceedings of the AMS 3: 170-174. · Zbl 0046.12103
[11] Harris, R. (1985): ?Why Voluntary Export Restraints are ?Voluntary?.?Canadian Journal of Economics 18: 799-809. · doi:10.2307/135091
[12] Kreps, D., and Scheinkman, J. (1983): ?Quantity Pre-commitment and Bertrand Competition Yields Cournot Outcomes.?Bell Journal of Economics 14: 326-337. · doi:10.2307/3003636
[13] Krishna, K. (1983): ?Trade Restrictions as Facilitating Practices.? Discussion Paper No. 55, Woodrow Wilson School, Princeton University.
[14] ? (1972): ?Trade Restrictions as Facilitating Practices.?,Journal of International Economics 26: 251-270. · doi:10.1016/0022-1996(89)90003-2
[15] Levitan, R., and Shubik, M. (1972): ?Price Duopoly and Capacity Constraints.?International Economic Review 13: 111-113. · Zbl 0234.90002 · doi:10.2307/2525908
[16] Ono, Y. (1982): ?The Equilibrium of Duopoly in a Market of Homogeneous Goods.?Economica 45: 287-295. · doi:10.2307/2553073
[17] ? (1987): ?Price Leadership: A Theoretical Analysis.?Economica 49: 11-20. · doi:10.2307/2553520
[18] Osborne, M., and Pitchik, C. (1986): ?Price Competition in a Capacity-Constrained Duopoly.?Journal of Economic Theory 38: 238-260. · Zbl 0603.90023 · doi:10.1016/0022-0531(86)90117-1
[19] Scherer, F. M. (1980):Industrial Market Structure and Economic Performance. Chicago, IL: Rand McNally. (2nd ed.)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.