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Closed-loop equilibrium in a multi-stage innovation race


  • Kenneth L. Judd


We examine a multistage model of an R&D race where players have multiple projects. We also develop perturbation methods for general dynamic games that can be expressed as analytic operators in a Banach space. We apply these perturbation methods to solve races with a small prize. We compute second-order asymptotically valid solutions for equilibrium and socially optimal decisions to determine qualitative properties of equilibrium. We find that innovators invest relatively too much on risky projects. Strategic reactions are ambiguous in general; in particular, a player may increase expenditures as his opponent moves ahead of him. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Kenneth L. Judd, 2003. "Closed-loop equilibrium in a multi-stage innovation race," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 673-695, March.
  • Handle: RePEc:spr:joecth:v:21:y:2003:i:2:p:673-695 DOI: 10.1007/s00199-002-0310-y

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    References listed on IDEAS

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    4. BLOISE, Gaetano & DRÈZE, Jacques & POLEMARCHAKIS, Heracles, 2002. "Money and indeterminacy over an infinite horizon," CORE Discussion Papers 2002021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Nisvan Erkal & Deborah Minehart, 2007. "Optimal Sharing Strategies in Dynamic Games of Research and Development," EAG Discussions Papers 200707, Department of Justice, Antitrust Division.
    2. Economides, Nicholas & Mitchell, Matthew & Skrzypacz, Andrzej, 2004. "Dynamic Oligopoly with Network Effects," Santa Cruz Department of Economics, Working Paper Series qt3z59c4p7, Department of Economics, UC Santa Cruz.
    3. By Kenneth L. Judd & Karl Schmedders & Şevin Yeltekin, 2012. "Optimal Rules For Patent Races," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 23-52, February.
    4. Liad Wagman & Vincent Conitzer, 2012. "Choosing fair lotteries to defeat the competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 91-129, February.
    5. Meng, Rujing, 2008. "A patent race in a real options setting: Investment strategy, valuation, CAPM beta, and return volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(10), pages 3192-3217, October.
    6. Fershtman, Chaim & Markovich, Sarit, 2010. "Patents, imitation and licensing in an asymmetric dynamic R&D race," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 113-126, March.
    7. Anton Bondarev, 2016. "Intensity of R&D competition and the generation of innovations in heterogeneous setting," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 621-653, July.
    8. Judd, Kenneth L., 1997. "Computational economics and economic theory: Substitutes or complements?," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 907-942, June.
    9. Aldieri, Luigi & Aprile, Maria Carmela & Vinci, Concetto Paolo, 2015. "R&D Spillovers Effects on strategic behaviour of Large International Firms," MPRA Paper 63402, University Library of Munich, Germany.
    10. Grossman, Gene M & Shapiro, Carl, 1987. "Dynamic R&D Competition," Economic Journal, Royal Economic Society, vol. 97(386), pages 372-387, June.
    11. Gene M. Grossman & Carl Shapiro, 1986. "Optimal Dynamic R&D Programs," RAND Journal of Economics, The RAND Corporation, vol. 17(4), pages 581-593, Winter.
    12. Fabiano Schivardi & Martin Schneider, 2008. "Strategic Experimentation and Disruptive Technological Change," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(2), pages 386-412, April.
    13. Nisvan Erkal & Deborah Minehart, 2013. "Optimal Sharing Strategies in Dynamic," Department of Economics - Working Papers Series 1174, The University of Melbourne.
    14. David Gill, 2008. "Strategic Disclosure of Intermediate Research Results," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(3), pages 733-758, September.
    15. Bondarev, Anton, 2014. "Endogenous specialization of heterogeneous innovative activities of firms under the technological spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 235-249.
    16. Axel Anderson & Luís M. B. Cabral, 2007. "Go for broke or play it safe? Dynamic competition with choice of variance," RAND Journal of Economics, RAND Corporation, vol. 38(3), pages 593-609, September.
    17. Ludkovski, Michael & Sircar, Ronnie, 2016. "Technology ladders and R&D in dynamic Cournot markets," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 127-151.


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