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Decision-Theoretic Forward Induction

  • Govindan, Srihari

    (U of Iowa)

  • Wilson, Robert B.

    (Stanford U)

A player's pure strategy is called relevant for an outcome of a game in extensive form with perfect recall if there exists a weakly sequential equilibrium with that outcome for which the strategy is an optimal reply at every information set it does not exclude. The outcome satisfies forward induction if it results from a weakly sequential equilibrium in which players' beliefs assign positive probability only to relevant strategies at each information set reached by a profile of relevant strategies. We prove that if there are two players and payoffs are generic then an outcome satisfies forward induction if every game with the same reduced normal form after eliminating redundant pure strategies has a sequential equilibrium with an equivalent outcome. Thus in this case forward induction is implied by decision-theoretic criteria.

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Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 1986.

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Date of creation: Jan 2008
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Handle: RePEc:ecl:stabus:1986
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  8. McLennan, Andrew, 1985. "Justifiable Beliefs in Sequential Equilibrium," Econometrica, Econometric Society, vol. 53(4), pages 889-904, July.
  9. Cho, In-Koo & Sobel, Joel, 1990. "Strategic stability and uniqueness in signaling games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 381-413, April.
  10. van Damme, E.E.C., 2002. "Strategic equilibrium," Other publications TiSEM aac2f01c-517a-488c-93cd-a, School of Economics and Management.
  11. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
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  14. Kyle Bagwell & Garey Ramey, 1988. "Advertising and Limit Pricing," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 59-71, Spring.
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  16. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May.
  17. Milgrom, Paul & Roberts, John, 1986. "Price and Advertising Signals of Product Quality," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 796-821, August.
  18. Banks, Jeffrey S. & Sobel, Joel., 1985. "Equilibrium Selection in Signaling Games," Working Papers 565, California Institute of Technology, Division of the Humanities and Social Sciences.
  19. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  20. Ausubel, Lawrence M. & Cramton, Peter & Deneckere, Raymond J., 2002. "Bargaining with incomplete information," 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 50, pages 1897-1945 Elsevier.
  21. Kyle Bagwell, 1987. "Introductory Price as a Signal of Cost in a Model of Repeat Business," Discussion Papers 722, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  22. Ponssard, Jean-Pierre, 1991. "Forward induction and sunk costs give average cost pricing," Games and Economic Behavior, Elsevier, vol. 3(2), pages 221-236, May.
  23. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  24. Gul, Faruk & Sonnenschein, Hugo, 1988. "On Delay in Bargaining with One-Sided Uncertainty," Econometrica, Econometric Society, vol. 56(3), pages 601-11, May.
  25. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  26. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  27. Peter Cramton & Joseph S. Tracy, 1994. "Wage Bargaining with Time-Varying Threats," Papers of Peter Cramton 94jolew, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
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