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Decision-Theoretic Forward Induction

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Author Info
Govindan, Srihari (U of Iowa)
Wilson, Robert B. (Stanford U)

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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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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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  1. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October. [Downloadable!] (restricted)
  2. Kyle Bagwell & Garey Ramey, 1988. "Advertising and Limit Pricing," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 59-71, Spring. [Downloadable!] (restricted)
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  3. Admati, Anat R & Perry, Motty, 1987. "Strategic Delay in Bargaining," Review of Economic Studies, Blackwell Publishing, vol. 54(3), pages 345-64, July. [Downloadable!] (restricted)
  4. Bagwell, Kyle, 1987. "Introductory Price as a Signal of Cost in a Model of Repeat Business," Review of Economic Studies, Blackwell Publishing, vol. 54(3), pages 365-84, July. [Downloadable!] (restricted)
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  5. Olivier Compte & Philippe Jehiel, 2002. "On the Role of Outside Options in Bargaining with Obstinate Parties," Econometrica, Econometric Society, vol. 70(4), pages 1477-1517, July. [Downloadable!] (restricted)
  6. McLennan, Andrew, 1985. "Justifiable Beliefs in Sequential Equilibrium," Econometrica, Econometric Society, vol. 53(4), pages 889-904, July. [Downloadable!] (restricted)
  7. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June. [Downloadable!] (restricted)
  8. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May. [Downloadable!] (restricted)
  9. Wilson, Robert B. & Govindan, Srihari, 2006. "Sufficient conditions for stable equilibria," Theoretical Economics, Society for Economic Theory, vol. 1(2), pages 167-206, June. [Downloadable!]
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  10. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  11. Lawrence M. Ausubel & Peter Cramton & Raymond J. Deneckere, 2002. "Bargaining with Incomplete Information," Papers of Peter Cramton 02barg, University of Maryland, Department of Economics - Peter Cramton, revised 12 Mar 2001. [Downloadable!]
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  12. van Damme,Eric, 1987. "Stable equilibria and forward induction," Discussion Paper Serie A 128, University of Bonn, Germany.
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  13. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January. [Downloadable!] (restricted)
  14. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  15. Wilson, Robert B. & Govindan, Srihari, 2007. "On Forward Induction," Research Papers 1955, Stanford University, Graduate School of Business. [Downloadable!]
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  16. 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. [Downloadable!] (restricted)
  17. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May. [Downloadable!] (restricted)
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  18. Sanford J. Grossman & Motty Perry, 1986. "Sequential Bargaining Under Asymmetric Information," NBER Technical Working Papers 0056, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  19. Van Damme, Eric, 2002. "Strategic equilibrium," 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 41, pages 1521-1596 Elsevier. [Downloadable!] (restricted)
  20. Cramton, Peter C & Tracy, Joseph S, 1994. "Wage Bargaining with Time-Varying Threats," Journal of Labor Economics, University of Chicago Press, vol. 12(4), pages 594-617, October. [Downloadable!] (restricted)
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  21. 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. [Downloadable!] (restricted)
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  22. Ying Chen & Navin Kartik & Joel Sobel, 2008. "Selecting Cheap-Talk Equilibria," Econometrica, Econometric Society, vol. 76(1), pages 117-136, 01. [Downloadable!] (restricted)
  23. 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. [Downloadable!] (restricted)
  24. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-94, July. [Downloadable!] (restricted)
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