IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

On Forward Induction

  • Srihari Govindan
  • Robert Wilson

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. Copyright 2009 The Econometric Society.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://hdl.handle.net/10.3982/ECTA6956
File Function: link to full text
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 77 (2009)
Issue (Month): 1 (01)
Pages: 1-28

as
in new window

Handle: RePEc:ecm:emetrp:v:77:y:2009:i:1:p:1-28
Contact details of provider: Phone: 1 212 998 3820
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/
Email:


More information through EDIRC

Order Information: Web: https://www.econometricsociety.org/publications/econometrica/access/ordering-back-issues Email:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Ben-Porath, Elchanan & Dekel, Eddie, 1992. "Signaling future actions and the potential for sacrifice," Journal of Economic Theory, Elsevier, vol. 57(1), pages 36-51.
  2. 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.
  3. van Damme, Eric, 1989. "Stable equilibria and forward induction," Journal of Economic Theory, Elsevier, vol. 48(2), pages 476-496, August.
  4. David Kreps & Robert Wilson, 1998. "Sequential Equilibria," Levine's Working Paper Archive 237, David K. Levine.
  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.
  6. Grossman, Sanford J. & Perry, Motty, 1986. "Sequential bargaining under asymmetric information," Journal of Economic Theory, Elsevier, vol. 39(1), pages 120-154, June.
  7. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  8. Paul Milgrom & John Roberts, 1998. "Limit Pricing and Entry Under Incomplete Information: An Equilibrium Analysis," Levine's Working Paper Archive 245, David K. Levine.
  9. Srihari Govindan & Robert Wilson, 2008. "On Forward Induction," Levine's Working Paper Archive 122247000000001859, David K. Levine.
  10. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
  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.
  12. Ying Chen & Navin Kartik & Joel Sobel, 2008. "Selecting Cheap-Talk Equilibria," Econometrica, Econometric Society, vol. 76(1), pages 117-136, 01.
  13. 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.
  14. Kyle Bagwell & Garey Ramey, 1988. "Advertising and Limit Pricing," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 59-71, Spring.
  15. Esther Hauk & Sjaak Hurkens, 1999. "On forward induction and evolutionary and strategic stability," Economics Working Papers 408, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 1999.
  16. George J. Mailath, 1996. "How Proper is Sequential Equilibrium?," Discussion Papers 1161, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  17. 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.
  18. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  19. 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.
  20. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May.
  21. Yossi Feinberg & Andrzej Skrzypacz, 2005. "Uncertainty about Uncertainty and Delay in Bargaining," Econometrica, Econometric Society, vol. 73(1), pages 69-91, 01.
  22. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  23. 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.
  24. 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.
  25. Anat R. Admati & Motty Perry, 1987. "Strategic Delay in Bargaining," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 345-364.
  26. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
  27. Wilson, Robert B. & Govindan, Srihari, 2006. "Sufficient conditions for stable equilibria," Theoretical Economics, Econometric Society, vol. 1(2), pages 167-206, June.
  28. Gul, Faruk & Sonnenschein, Hugo, 1988. "On Delay in Bargaining with One-Sided Uncertainty," Econometrica, Econometric Society, vol. 56(3), pages 601-11, May.
  29. John Hillas, 1996. "On the Relation Between Perfect Equilibria in Extensive Form Games and Proper Equilibria in Normal Form Games," Game Theory and Information 9605002, EconWPA, revised 14 May 1996.
  30. McLennan, Andrew, 1985. "Justifiable Beliefs in Sequential Equilibrium," Econometrica, Econometric Society, vol. 53(4), pages 889-904, July.
  31. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  32. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:77:y:2009:i:1:p:1-28. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)

or (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.