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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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File URL: http://hdl.handle.net/10.1007/s00199-002-0310-y
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 21 (2003)
Issue (Month): 2 (03)
Pages: 673-695

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Handle: RePEc:spr:joecth:v:21:y:2003:i:2:p:673-695

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Related research

Keywords: Keywords and Phrases: Multistage races; Perturbation methods; Dynamic games.; JEL Classification Numbers: C630; 0310.;

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Cited by:
  1. 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.
  2. Wagman, Liad & Conitzer, Vincent, 2008. "Choosing Fair Lotteries to Defeat the Competition," MPRA Paper 10375, University Library of Munich, Germany.
  3. Kenneth Judd & Karl Schmedders, 2002. "Optimal Rules for Patent Races," Discussion Papers 1343, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. 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.
  6. 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.
  7. Kenneth L. Judd, 1997. "Computational Economics and Economic Theory: Substitutes or Complements," NBER Technical Working Papers 0208, National Bureau of Economic Research, Inc.
  8. David Gill, 2004. "Strategic Disclosure of Intermediate Research Results," Economics Series Working Papers 211, University of Oxford, Department of Economics.
  9. Nisvan Erkal & Deborah Minehart, 2007. "Optimal Sharing Strategies in Dynamic Games of Research and Development," EAG Discussions Papers 200707, Department of Justice, Antitrust Division.
  10. Grossman, Gene M & Shapiro, Carl, 1987. "Dynamic R&D Competition," Economic Journal, Royal Economic Society, vol. 97(386), pages 372-87, June.
  11. 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.
  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.

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