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Extensive-form games and strategic complementarities

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  • Echenique, Federico

Abstract

I prove the subgame-perfect equivalent of the basic result for Nash equilibria in normal-form games of strategic complements: the set of subgame-perfect equilibria is a non-empty, complete lattice. For this purpose I introduce a device that allows the study of the set of subgame-perfect equilibria as the set of fixed points of a correspondence. The correspondence has a natural interpretation. My results are limited because extensive-form games of strategic complementarities turn out| surprisingly|to be a very restrictive class of games.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 46 (2004)
Issue (Month): 2 (February)
Pages: 348-364

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Handle: RePEc:eee:gamebe:v:46:y:2004:i:2:p:348-364

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," GE, Growth, Math methods 9912002, EconWPA.
  2. Leo K. Simon and Maxwell B. Stinchcombe., 1987. "Extensive Form Games in Continuous Time: Pure Strategies," Economics Working Papers 8746, University of California at Berkeley.
  3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  4. AMIR , Rabah, 1995. "Continuous Stochastic Games of Capital Accumulation with Convex Transition," CORE Discussion Papers 1995009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
  6. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  8. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
  9. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  10. Fudenberg, Drew & Levine, David, 1983. "Subgame-perfect equilibria of finite- and infinite-horizon games," Journal of Economic Theory, Elsevier, vol. 31(2), pages 251-268, December.
  11. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-44, May.
  12. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  13. Hellwig, Martin & Leininger, Wolfgang, 1987. "On the existence of subgame-perfect equilibrium in infinite-action games of perfect information," Journal of Economic Theory, Elsevier, vol. 43(1), pages 55-75, October.
  14. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-28, May.
  15. Harris, Christopher, 1985. "A characterisation of the perfect equilibria of infinite horizon games," Journal of Economic Theory, Elsevier, vol. 37(1), pages 99-125, October.
  16. 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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Cited by:
  1. L. Lambertini & A. Mantovani, 2004. "Identifying Reaction Functions in Differential Oligopoly Games," Working Papers 518, Dipartimento Scienze Economiche, Universita' di Bologna.
  2. Renou, Ludovic, 2009. "Commitment games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 488-505, May.
  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 - Economic Institute, Prague.
  4. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2014. "A constructive study of Markov equilibria in stochastic games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 150(C), pages 815-840.
  5. Vives, Xavier, 2006. "Strategic Complementarities in Multi-Stage Games," CEPR Discussion Papers 5583, C.E.P.R. Discussion Papers.
  6. Mathevet, Laurent & Steiner, Jakub, 2013. "Tractable dynamic global games and applications," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2583-2619.
  7. Vives, Xavier, 2006. "Strategic complementarity in multi-stage games," IESE Research Papers D/619, IESE Business School.

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