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Robust Quantitative Comparative Statics for a Multimarket Paradox


  • Tobias Harks
  • Philipp von Falkenhausen


We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually reduce the monopolist's profit. We use our approach to quantify for the first time the worst case profit reduction for multimarket oligopolies exposed to arbitrary positive price shocks. For markets with affine price functions and firms with convex cost technologies, we show that the relative profit loss of any firm is at most 25% no matter how many firms compete in the oligopoly. We further investigate the impact of positive price shocks on total profit of all firms as well as on social welfare. We find tight bounds also for these measures showing that total profit and social welfare decreases by at most 25% and 16.6%, respectively. Finally, we show that in our model, mixed, correlated and coarse correlated equilibria are essentially unique, thus, all our bounds apply to these game solutions as well.

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  • Tobias Harks & Philipp von Falkenhausen, 2013. "Robust Quantitative Comparative Statics for a Multimarket Paradox," Papers 1307.5617,, revised Dec 2015.
  • Handle: RePEc:arx:papers:1307.5617

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    References listed on IDEAS

    1. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
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    3. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    4. Fevrier, Philippe & Linnemer, Laurent, 2004. "Idiosyncratic shocks in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 835-848, June.
    5. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    6. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    7. Gaudet, Gerard & Salant, Stephen W, 1991. "Increasing the Profits of a Subset of Firms in Oligopoly Models with Strategic Substitutes," American Economic Review, American Economic Association, vol. 81(3), pages 658-665, June.
    8. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    9. Brander, James A. & Spencer, Barbara J., 1985. "Export subsidies and international market share rivalry," Journal of International Economics, Elsevier, vol. 18(1-2), pages 83-100, February.
    10. Jonathan Eaton & Gene M. Grossman, 1986. "Optimal Trade and Industrial Policy Under Oligopoly," The Quarterly Journal of Economics, Oxford University Press, vol. 101(2), pages 383-406.
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