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Open and Closed Loop Nash Equilibria in Games with a Continuum of Players

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  • Agnieszka Wiszniewska-Matyszkiel

    (Warsaw University)

Abstract

In this paper, the problem of relations between closed loop and open loop Nash equilibria is examined in the environment of discrete time dynamic games with a continuum of players and a compound structure encompassing both private and global state variables. An equivalence theorem between these classes of equilibria is proven, important implications for the calculation of these equilibria are derived and the results are presented on models of a common ecosystem exploited by a continuum of players. An example of an analogous game with finitely many players is also presented for comparison.

Suggested Citation

  • Agnieszka Wiszniewska-Matyszkiel, 2014. "Open and Closed Loop Nash Equilibria in Games with a Continuum of Players," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 280-301, January.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0317-5
    DOI: 10.1007/s10957-013-0317-5
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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    3. Reinganum, Jennifer F., 1981. "Dynamic games of innovation," Journal of Economic Theory, Elsevier, vol. 25(1), pages 21-41, August.
    4. Miao, Jianjun, 2006. "Competitive equilibria of economies with a continuum of consumers and aggregate shocks," Journal of Economic Theory, Elsevier, vol. 128(1), pages 274-298, May.
    5. Drew Fudenberg & David K. Levine, 1988. "Open and Closed-Loop Equilibria in Dynamic Games With Many Players," Levine's Working Paper Archive 221, David K. Levine.
    6. Agnieszka Wiszniewska-Matyszkiel, 2002. "Discrete Time Dynamic Games With A Continuum Of Players I: Decomposable Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 331-342.
    7. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    8. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Balder, Erik J, 1995. "A Unifying Approach to Existence of Nash Equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 79-94.
    10. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," 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 46, pages 1761-1808, Elsevier.
    11. Drew Fudenberg & David K. Levine, 2008. "Open-Loop and Closed-Loop Equilibria in Dynamic Games with Many Players," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 3, pages 41-58, World Scientific Publishing Co. Pte. Ltd..
    12. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    13. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    14. Agnieszka Wiszniewska-Matyszkiel, 2003. "Discrete Time Dynamic Games With Continuum Of Players Ii: Semi-Decomposable Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 27-40.
    15. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    16. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    17. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    18. Wiszniewska-Matyszkiel, Agnieszka, 2005. "Stock market as a dynamic game with continuum of players," MPRA Paper 32982, University Library of Munich, Germany, revised 2006.
    19. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1994. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 975-1006, November.
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