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Closed-Loop Equilibrium in a Multi-Stage Innovation Race

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  • Kenneth L. Judd

Abstract

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
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  • Kenneth L. Judd, 1985. "Closed-Loop Equilibrium in a Multi-Stage Innovation Race," Discussion Papers 647, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:647
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    Cited by:

    1. Bondarev, Anton & Greiner, Alfred, 2018. "Catching-up and falling behind: Effects of learning in an R&D differential game with spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 134-156.
    2. Alastair Smith, 1998. "Fighting Battles, Winning Wars," Journal of Conflict Resolution, Peace Science Society (International), vol. 42(3), pages 301-320, June.
    3. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    4. Nisvan Erkal & Deborah Minehart, 2007. "Optimal Sharing Strategies in Dynamic Games of Research and Development," EAG Discussions Papers 200707, Department of Justice, Antitrust Division.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. David Gill, 2008. "Strategic Disclosure of Intermediate Research Results," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(3), pages 733-758, September.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Grossman, Gene M & Shapiro, Carl, 1987. "Dynamic R&D Competition," Economic Journal, Royal Economic Society, vol. 97(386), pages 372-387, June.
    18. 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.
    19. Nisvan Erkal & Deborah Minehart, 2013. "Optimal Sharing Strategies in Dynamic," Department of Economics - Working Papers Series 1174, The University of Melbourne.
    20. Christian Ewerhart & Julian Teichgräber, 2019. "Multi-battle contests, finite automata, and the tug-of-war," ECON - Working Papers 318, Department of Economics - University of Zurich.
    21. 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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