Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies

Tasnádi, Attila (2012): Endogenous Timing of Moves in Bertrand-Edgeworth Triopolies.

Abstract

We determine the endogenous order of moves in which the firms set their prices in the framework of a capacity-constrained Bertrand-Edgeworth triopoly. A three-period timing game that determines the period in which the firms announce their prices precedes the price-setting stage. We show for the non-trivial case (in which the Bertrand-Edgeworth triopoly has only an equilibrium in non-degenerated mixedstrategies) that the firm with the largest capacity sets its price first, while the two other firms set their prices later. Our result extends a finding by Deneckere and Kovenock (1992) from duopolies to triopolies. This extension was made possible by Hirata's (2009) recent advancements on the mixed-strategy equilibria of Bertrand-Edgeworth games.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bertrand-Edgeworth, price leadership, oligopoly, timing games
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets

References

Allen, B., and M. Hellwig (1993): Bertrand-Edgeworth Duopoly with Proportional Demand. International Economic Review, 34, 39-60.

Bagh, A. (2010): Variational Convergence: Approximation and Existence of Equilibria in Discontinuous Games. Journal of Economic Theory, 145, 1244-1268.

Beckmann, M. (1965): Bertrand-Edgeworth Duopoly Revisited. In Operations Research-Verfahren, Vol. III, ed. by R. Henn, pp. 55-68. Hain, Meisenheim.

Boyer, M., and M. Moreaux (1987): Being a Leader or a Follower: Reflections on the Distribution of Roles in Duopoly. International Journal of Industrial Organization, 5, 175-192.

Cheviakov, A., and J. Hartwick (2005): Beckmann's Bertrand-Edgeworth duopoly example revisited. International Game Theory Review, 7, 1-12.

Dastidar, K., and D. Furth (2005): Endogenous price leadership in a duopoly: Equal products, unequal technology. International Journal of Economic Theory, 1, 189-210.

Davidson, C., and R. Deneckere (1986): Long-run Competition in Capacity, Shortrun Competition in Price and the Cournot Model. Rand Journal of Economics, 17, 404-415.

De Francesco, M., and N. Salvadori (2010): Bertrand-Edgeworth Games under Oligopoly with a Complete Characterization for the Triopoly. Munich Personal RePEc Archive, MPRA Paper No. 24087.

de Frutos, M.-A., and N. Fabra (2011): Endogenous capacities and price competition: The role of demand uncertainty. International Journal of Industrial Organization, 29, 399-411.

Deneckere, R., and D. Kovenock (1992): Price Leadership. Review of Economic Studies, 59, 143-162.

Dowrick, S. (1986): von Stackelberg and Cournot Duopoly: Choosing Roles. Rand Journal of Economics, 17, 251-260.

Gal-Or, E. (1985): First Mover and Second Mover Advantages. International Economic Review, 26, 649-653.

Gangopadhyay, S. (1993): Simultaneous vs Sequential Move Price Games: A Comparison of Equilibrium Payoffs. Indian Statistical Institute Discussion Paper No. 93-01.

Hamilton, J., and S. Slutsky (1990): Endogenous Timing in Duopoly Games: Stackelberg or Cournot Equilibria. Games and Economic Behavior, 2, 29-46.

Hirata, D. (2009): Asymmetric Bertrand-Edgeworth Oligopoly and Mergers. B.E. Journal of Theoretical Economics, 9, "Article 22".

Hviid, M. (1991): Capacity constrained duopolies, uncertain demand and nonexistence of pure strategy equilibria. European Journal of Political Economy, 7, 183-190.

Kreps, D. M., and J. A. Scheinkman (1983): Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes. Bell Journal of Economics, 14, 326-337.

Lepore, J. (2012): Cournot outcomes under Bertrand-Edgeworth competition with demand uncertainty. Journal of Mathematical Economics, 48, 177-186.

Levitan, R., and M. Shubik (1972): Price Duopoly and Capacity Constraints. International Economic Review, 13, 111-122.

Matsumura, T. (1999): Quantity-setting Oligopoly with Endogenous Sequencing. International Journal of Industrial Organization, 17, 289-296.

Matsumura, T. (2002): Market Instability in a Stackelberg Duopoly. Journal of Economics(Zeitschrift fur Nationalokonomie), 75, 199-210.

Osborne, M. J., and C. Pitchik (1986): Price Competition in a Capacity-Constrained Duopoly. Journal of Economic Theory, 38, 238-260.

Reynolds, S., and B. Wilson (2000): Bertrand-Edgeworth competition, demand uncertainty, and asymmetric outcomes. Journal of Economic Theory, 92, 122-141.

Tasnádi, A. (2010): Timing of Decisions in Oligopoly Games. VDM Publishing House, Saarbrucken, Germany.

van Damme, E., and S. Hurkens (1999): Endogenous Stackelberg Leadership. Games and Economic Behavior, 28, 105-129.

van Damme, E., and S. Hurkens (2004): Endogenous Price Leadership. Games and Economic Behavior, 47, 404-420.

Vives, X. (1986): Rationing Rules and Bertrand-Edgeworth Equilibria in Large Markets. Economics Letters, 21, 113-116.

Vives, X. (1999): Oligopoly Pricing: Old Ideas and New Tools. MIT Press, Cambridge MA.

von Stengel, B. (2010): Follower payoffs in symmetric duopoly games. Games and Economic Behavior, 69, 512-516.

Yano, M., and T. Komatsubara (2006): Endogenous price leadership and technological differences. International Journal of Economic Theory, 2, 365-383.

Yano, M., and T. Komatsubara (2012): Price Competition Or Tacit Collusion. KIER Discussion Paper No. 807.