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Endogenous rationing, price dispersion and collusion in capacity constrained supergames

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  • Emmanuel Dechenaux
  • Dan Kovenock

Abstract

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion.
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  • Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
    • Handle: RePEc:spr:joecth:v:47:y:2011:i:1:p:29-74
    DOI: 10.1007/s00199-010-0527-0
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    Cited by:

    1. de Frutos, María-Ángeles & Fabra, Natalia, 2011. "Endogenous capacities and price competition: The role of demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 399-411, July.
    2. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    3. Heikki Peura & Derek W. Bunn, 2015. "Dynamic Pricing of Peak Production," Operations Research, INFORMS, vol. 63(6), pages 1262-1279, December.
    4. Emmanuel Dechenaux & Dan Kovenock, 2007. "Tacit collusion and capacity withholding in repeated uniform price auctions," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1044-1069, December.
    5. Puzzello, Daniela, 2008. "Tie-breaking rules and divisibility in experimental duopoly markets," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 164-179, July.
    6. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    7. Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
    8. Daniel Cracau & Benjamin Franz, 2012. "An experimental study of mixed strategy equilibria in simultaneous price-quantity games," FEMM Working Papers 120017, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    9. Zoltán Rácz & Attila Tasnádi, 2016. "A Bertrand–Edgeworth oligopoly with a public firm," Journal of Economics, Springer, vol. 119(3), pages 253-266, November.
    10. SANIN, Maria Eugenia, 2006. "Market design in wholesale electricity markets," LIDAM Discussion Papers CORE 2006100, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    12. Liu, Xuyuan & Lu, Jingfeng, 2017. "Optimal prize-rationing strategy in all-pay contests with incomplete information," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 57-90.

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    More about this item

    Keywords

    Bertrand–Edgeworth; Supergame; Collusion; Capacity; C73; D43; L13; L41;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices

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