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All-Pay Oligopolies: Price Competition With Unobservable Inventory Choices

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  • Joao Montez
  • Nicolas Schutz

Abstract

We study a class of games where stores source unobservable inventories in advance, and then simultaneously set prices. Our framework allows for firm asymmetries, heterogeneous consumer tastes, endogenous consumer information through advertising, and salvage values for unsold units. The payoff structure relates to a complete-information all-pay contest with outside options, non-monotonic winning and losing functions, and conditional investments. In the generically unique equilibrium, stores randomize their price choice and, conditional on that choice, serve all their targeted demand—thus, some inventories may remain unsold. As inventory costs become fully recoverable, the equilibrium price distribution converges to an equilibrium of the associated Bertrand game (where firms first choose prices and then produce to order). This suggests that with production in advance, the choice between a Cournot analysis and a Bertrand-type analysis, as properly generalized in this paper, should depend on whether or not stores observe rivals’ inventories before setting prices.

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  • Joao Montez & Nicolas Schutz, 2018. "All-Pay Oligopolies: Price Competition With Unobservable Inventory Choices," CRC TR 224 Discussion Paper Series crctr224_2018_020, University of Bonn and University of Mannheim, Germany.
  • Handle: RePEc:bon:boncrc:crctr224_2018_020
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    1. Kaplan, Todd, et al, 2002. "All-Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    2. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    3. Kartik, Navin, 2011. "A note on undominated Bertrand equilibria," Economics Letters, Elsevier, vol. 111(2), pages 125-126, May.
    4. Romain de Nijs, 2012. "Further results on the Bertrand game with different marginal costs," PSE-Ecole d'économie de Paris (Postprint) halshs-00916558, HAL.
    5. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    6. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 434-451, June.
    7. Fernando Bernstein & Awi Federgruen, 2004. "A General Equilibrium Model for Industries with Price and Service Competition," Operations Research, INFORMS, vol. 52(6), pages 868-886, December.
    8. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    9. Plum, M, 1992. "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 393-418.
    10. Narasimhan, Chakravarthi, 1988. "Competitive Promotional Strategies," The Journal of Business, University of Chicago Press, vol. 61(4), pages 427-449, October.
    11. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 1992. "It takes two to tango: Equilibria in a model of sales," Games and Economic Behavior, Elsevier, vol. 4(4), pages 493-510, October.
    12. Shelegia, Sandro & Wilson, Chris, 2016. "A Generalized Model of Sales," EconStor Preprints 147411, ZBW - Leibniz Information Centre for Economics.
    13. Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-386, May.
    14. Che, Yeon-Koo & Gale, Ian L, 1998. "Caps on Political Lobbying," American Economic Review, American Economic Association, vol. 88(3), pages 643-651, June.
    15. De Nijs, Romain, 2012. "Further results on the Bertrand game with different marginal costs," Economics Letters, Elsevier, vol. 116(3), pages 502-503.
    16. Ramey, Valerie A, 1991. "Nonconvex Costs and the Behavior of Inventories," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 306-334, April.
    17. Thomas, Charles J., 2002. "The effect of asymmetric entry costs on Bertrand competition," International Journal of Industrial Organization, Elsevier, vol. 20(5), pages 589-609, May.
    18. Marquez, Robert, 1997. "A note on Bertrand competition with asymmetric fixed costs," Economics Letters, Elsevier, vol. 57(1), pages 87-96, November.
    19. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
    20. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    21. Tasnadi, Attila, 2004. "Production in advance versus production to order," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 191-204, June.
    22. Raymond Deneckere & James Peck, 1995. "Competition Over Price and Service Rate When Demand is Stochastic: A Strategic Analysis," RAND Journal of Economics, The RAND Corporation, vol. 26(1), pages 148-162, Spring.
    23. Michael R. Baye & John Morgan, 2001. "Information Gatekeepers on the Internet and the Competitiveness of Homogeneous Product Markets," American Economic Review, American Economic Association, vol. 91(3), pages 454-474, June.
    24. Romain de Nijs, 2012. "Further results on the Bertrand game with different marginal costs," Post-Print halshs-00916558, HAL.
    25. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    26. Xuan Zhao & Derek R. Atkins, 2008. "Newsvendors Under Simultaneous Price and Inventory Competition," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 539-546, September.
    27. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-142, February.
    28. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    29. Fudenberg, Drew & Tirole, Jean, 1987. "Understanding Rent Dissipation: On the Use of Game Theory in Industrial Organization," American Economic Review, American Economic Association, vol. 77(2), pages 176-183, May.
    30. Blume, Andreas, 2003. "Bertrand without fudge," Economics Letters, Elsevier, vol. 78(2), pages 167-168, February.
    31. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 439-454.
    32. Alan S. Blinder, 1986. "Can the Production Smoothing Model of Inventory Behavior be Saved?," The Quarterly Journal of Economics, Oxford University Press, vol. 101(3), pages 431-453.
    33. Gene M. Grossman & Carl Shapiro, 1984. "Informative Advertising with Differentiated Products," Review of Economic Studies, Oxford University Press, vol. 51(1), pages 63-81.
    34. Todd R. Kaplan & David Wettstein, 2006. "Caps on Political Lobbying: Comment," American Economic Review, American Economic Association, vol. 96(4), pages 1351-1354, September.
    35. Anderson, Simon & Baik, Alicia & Larson, Nathan, 2015. "Personalized pricing and advertising: An asymmetric equilibrium analysis," Games and Economic Behavior, Elsevier, vol. 92(C), pages 53-73.
    36. Blanchard, Olivier J, 1983. "The Production and Inventory Behavior of the American Automobile Industry," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 365-400, June.
    37. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
    38. Robert G. Hansen, 1988. "Auctions with Endogenous Quantity," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 44-58, Spring.
    39. Spulber, Daniel F, 1995. "Bertrand Competition When Rivals' Costs Are Unknown," Journal of Industrial Economics, Wiley Blackwell, vol. 43(1), pages 1-11, March.
    40. Michael Arnold & Chenguang Li & Christine Saliba & Lan Zhang, 2011. "Asymmetric Market Shares, Advertising And Pricing: Equilibrium With An Information Gatekeeper," Journal of Industrial Economics, Wiley Blackwell, vol. 59(1), pages 63-84, March.
    41. Kahn, James A, 1987. "Inventories and the Volatility of Production," American Economic Review, American Economic Association, vol. 77(4), pages 667-679, September.
    42. Romain de Nijs, 2012. "Further results on the Bertrand game with different marginal costs," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00916558, HAL.
    43. Frank Chen & Zvi Drezner & Jennifer K. Ryan & David Simchi-Levi, 2000. "Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information," Management Science, INFORMS, vol. 46(3), pages 436-443, March.
    44. Gerard R. Butters, 1977. "Equilibrium Distributions of Sales and Advertising Prices," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 465-491.
    45. Sharkey, William W. & Sibley, David S., 1993. "A Bertrand model of pricing and entry," Economics Letters, Elsevier, vol. 41(2), pages 199-206.
    46. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
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    2. Tasnádi, Attila, 2020. "Production in advance versus production to order: Equilibrium and social surplus," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 11-18.
    3. Lenhard, Severin, 2022. "Imperfect Competition with Costly Disposal," VfS Annual Conference 2022 (Basel): Big Data in Economics 264038, Verein für Socialpolitik / German Economic Association.
    4. Montez, João & Marxen, Annabelle, 2020. "Licensing at the patent cliff and market entry," CEPR Discussion Papers 14276, C.E.P.R. Discussion Papers.
    5. Iwan Bos & Marco A. Marini, 2022. "Oligopoly Pricing: The Role of Firm Size and Number," Games, MDPI, vol. 14(1), pages 1-16, December.
    6. Severin Lenhard, 2021. "Imperfect Competition with Costly Disposal," Diskussionsschriften dp2105, Universitaet Bern, Departement Volkswirtschaft.
    7. Michele Bisceglia, 2023. "Vertical Contract Disclosure in Three‐Tier Industries," Journal of Industrial Economics, Wiley Blackwell, vol. 71(1), pages 1-46, March.
    8. Ewerhart, Christian & Li, Sheng, 2023. "Imposing Choice on the Uninformed: The Case of Dynamic Currency Conversion," Journal of Banking & Finance, Elsevier, vol. 154(C).
    9. Lenhard, Severin, 2022. "Imperfect competition with costly disposal," International Journal of Industrial Organization, Elsevier, vol. 82(C).
    10. Christian Ewerhart & Sheng Li, 2020. "Imposing choice on the uninformed: the case of dynamic currency conversion," ECON - Working Papers 345, Department of Economics - University of Zurich, revised May 2023.
    11. Shelegia, Sandro & Wilson, Chris M., 2022. "Costly participation and default allocations in all-pay contests," MPRA Paper 115027, University Library of Munich, Germany.
    12. Somogyi, Robert & Vergote, Wouter & Virag, Gabor, 2023. "Price competition with capacity uncertainty - feasting on leftovers," Games and Economic Behavior, Elsevier, vol. 140(C), pages 253-271.

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    More about this item

    Keywords

    Oligopoly; inventories; production in advance; all-pay contests; Bertrand convergence;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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