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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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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 647.

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Date of creation: Feb 1985
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Handle: RePEc:nwu:cmsems:647

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Cited by:
  1. 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.
  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 & ┼×evin 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, 02.
  4. Wagman, Liad & Conitzer, Vincent, 2008. "Choosing Fair Lotteries to Defeat the Competition," MPRA Paper 10375, University Library of Munich, Germany.
  5. Schivardi, Fabiano & Schneider, Martin, 2005. "Strategic Experimentation and Disruptive Technological Change," CEPR Discussion Papers 4925, C.E.P.R. Discussion Papers.
  6. David Gill, 2004. "Strategic Disclosure of Intermediate Research Results," Economics Series Working Papers 211, University of Oxford, Department of Economics.
  7. 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.
  8. Nisvan Erkal & Deborah Minehart, 2008. "Optimal Sharing Strategies in Dynamic Games of Research and Development," EAG Discussions Papers 200806, Department of Justice, Antitrust Division.
  9. 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.
  10. 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.
  11. Bondarev, Anton A., 2011. "Endogenous specialization of heterogeneous innovative activities of firms under technological spillovers," MPRA Paper 35424, University Library of Munich, Germany, revised 15 Dec 2011.
  12. Grossman, Gene M & Shapiro, Carl, 1987. "Dynamic R&D Competition," Economic Journal, Royal Economic Society, vol. 97(386), pages 372-87, June.

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