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Subgame perfect Nash equilibrium for dynamic pricing competition with finite planning horizon

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  • Niloofar Fadavi

Abstract

Having fixed capacities, homogeneous products and price sensitive customer purchase decision are primary distinguishing characteristics of numerous revenue management systems. Even with two or three rivals, competition is still highly fierce. This paper studies sub-game perfect Nash equilibrium of a price competition in an oligopoly market with perishable assets. Sellers each has one unit of a good that cannot be replenished, and they compete in setting prices to sell their good over a finite sales horizon. Each period, buyers desire one unit of the good and the number of buyers coming to the market in each period is random. All sellers' prices are accessible for buyers, and search is costless. Using stochastic dynamic programming methods, the best response of sellers can be obtained from a one-shot price competition game regarding remained periods and the current-time demand structure. Assuming a binary demand model, we demonstrate that the duopoly model has a unique Nash equilibrium and the oligopoly model does not reveal price dispersion with respect to a particular metric. We illustrate that, when considering a generalized demand model, the duopoly model has a unique mixed strategy Nash equilibrium while the oligopoly model has a unique symmetric mixed strategy Nash equilibrium.

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  • Niloofar Fadavi, 2022. "Subgame perfect Nash equilibrium for dynamic pricing competition with finite planning horizon," Papers 2208.02842, arXiv.org.
    • Handle: RePEc:arx:papers:2208.02842
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    1. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    2. Marc Dudey, 1992. "Dynamic Edgeworth-Bertrand Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(4), pages 1461-1477.
    3. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 175-204.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    5. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    6. Michael R. Baye & John Morgan, 2004. "Price Dispersion in the Lab and on the Internet: Theory and Evidence," RAND Journal of Economics, The RAND Corporation, vol. 35(3), pages 448-466, Autumn.
    7. Raymond Deneckere & James Peck, 2012. "Dynamic Competition With Random Demand and Costless Search: A Theory of Price Posting," Econometrica, Econometric Society, vol. 80(3), pages 1185-1247, May.
    8. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    9. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    10. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    11. Ching-jen Sun, 2017. "Dynamic price dispersion in Bertrand–Edgeworth competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 235-261, March.
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