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Strategic complementarity in multi-stage games

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  • Xavier Vives

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Abstract

We provide sufficient conditions in finite-horizon multi-stage games for the value function of each player, associated to extremal Markov perfect equilibria, to display strategic complementarities and for the contemporaneous equilibrium to be increasing in the state variables.
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Suggested Citation

  • Xavier Vives, 2009. "Strategic complementarity in multi-stage games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 151-171, July.
  • Handle: RePEc:spr:joecth:v:40:y:2009:i:1:p:151-171 DOI: 10.1007/s00199-008-0354-8
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    References listed on IDEAS

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    1. Cooper, Russell W. & Johri, Alok, 1997. "Dynamic complementarities: A quantitative analysis," Journal of Monetary Economics, Elsevier, vol. 40(1), pages 97-119, September.
    2. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    3. Kydland, Finn, 1975. "Noncooperative and Dominant Player Solutions in Discrete Dynamic Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 321-335, June.
    4. Vives, Xavier, 1990. "Information and competitive advantage," International Journal of Industrial Organization, Elsevier, pages 17-35.
    5. Amir, Rabah & Wooders, John, 2000. "One-Way Spillovers, Endogenous Innovator/Imitator Roles, and Research Joint Ventures," Games and Economic Behavior, Elsevier, vol. 31(1), pages 1-25, April.
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    7. Katz, Michael L & Shapiro, Carl, 1986. "Technology Adoption in the Presence of Network Externalities," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 822-841, August.
    8. Paul Heidhues & Nicolas Melissas, 2006. "Equilibria in a dynamic global game: the role of cohort effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 531-557.
    9. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, pages 111-131.
    10. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
    11. Baldursson, Fridrik M & von der Fehr, Nils-Henrik M, 2004. "A Whiter Shade of Pale: on the Political Economy of Regulatory Instruments," Memorandum 29/2004, Oslo University, Department of Economics.
    12. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    13. Dasgupta, Partha & Stiglitz, Joseph E, 1988. "Learning-by-Doing, Market Structure and Industrial and Trade Policies," Oxford Economic Papers, Oxford University Press, vol. 40(2), pages 246-268, June.
    14. Drew Fudenberg & Jean Tirole, 1983. "Learning-by-Doing and Market Performance," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 522-530, Autumn.
    15. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, pages 546-554.
    16. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    17. Athey, Susan & Schmutzler, Armin, 2001. "Investment and Market Dominance," RAND Journal of Economics, The RAND Corporation, pages 1-26.
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    19. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
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    22. Jun, Byoung & Vives, Xavier, 2004. "Strategic incentives in dynamic duopoly," Journal of Economic Theory, Elsevier, vol. 116(2), pages 249-281, June.
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    Citations

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    Cited by:

    1. Mathevet, Laurent & Steiner, Jakub, 2013. "Tractable dynamic global games and applications," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2583-2619.
    2. Ruiz-Aliseda, Francisco, 2009. "Misinformative advertising," IESE Research Papers D/809, IESE Business School.
    3. Laurent Mathevet & Jakub Steiner, 2012. "Sand in the Wheels: A Dynamic Global-Game Approach," CERGE-EI Working Papers wp459, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    4. repec:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0194-2 is not listed on IDEAS
    5. repec:eee:jetheo:v:169:y:2017:i:c:p:35-61 is not listed on IDEAS
    6. repec:eee:indorg:v:52:y:2017:i:c:p:427-449 is not listed on IDEAS
    7. Sverre Grepperud, 2015. "Optimal safety standards when accident prevention depends upon both firm and worker effort," European Journal of Law and Economics, Springer, vol. 39(3), pages 505-521, June.

    More about this item

    Keywords

    Markov game; Supermodularity; Two-stage game; Linear-quadatric game; Adjustment costs; Learning curve; Network effects; C73;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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