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Decision-Theoretic Forward Induction

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Author Info

  • Govindan, Srihari

    (U of Iowa)

  • Wilson, Robert B.

    (Stanford U)

Abstract

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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Bibliographic Info

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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References

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  1. Srihari Govindan & Robert Wilson, 2008. "On Forward Induction," Levine's Working Paper Archive 122247000000001859, David K. Levine.
  2. 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.
  3. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
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  7. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
  8. 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.
  9. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
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  13. 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.
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  16. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  17. Paul R. Milgrom & John Roberts, 1984. "Price and Advertising Signals of Product Quality," Cowles Foundation Discussion Papers 709, Cowles Foundation for Research in Economics, Yale University.
  18. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  19. 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.
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Cited by:
  1. Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.

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