IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

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.

(This abstract was borrowed from another version of this item.)

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:
Download Restriction: no

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 122247000000001859.

in new window

Date of creation: 04 Feb 2008
Date of revision:
Handle: RePEc:cla:levarc:122247000000001859
Contact details of provider: Web page:

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. 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.
  2. Mailath, G.J. & Samuelson, L., 1996. "How Proper Is Sequential Equilibrium?," Working papers 9611, Wisconsin Madison - Social Systems.
  3. 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.
  4. van Damme, E.E.C., 2002. "Strategic equilibrium," Other publications TiSEM aac2f01c-517a-488c-93cd-a, Tilburg University, School of Economics and Management.
  5. Hauk, Esther & Hurkens, Sjaak, 2002. "On Forward Induction and Evolutionary and Strategic Stability," Journal of Economic Theory, Elsevier, vol. 106(1), pages 66-90, September.
  6. Banks, Jeffrey S & Sobel, Joel, 1987. "Equilibrium Selection in Signaling Games," Econometrica, Econometric Society, vol. 55(3), pages 647-61, May.
  7. 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.
  8. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  9. 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.
  10. David M Kreps & Robert Wilson, 2003. "Sequential Equilibria," Levine's Working Paper Archive 618897000000000813, David K. Levine.
  11. Wilson, Robert B. & Govindan, Srihari, 2006. "Sufficient conditions for stable equilibria," Theoretical Economics, Econometric Society, vol. 1(2), pages 167-206, June.
  12. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  13. repec:oup:restud:v:54:y:1987:i:3:p:365-84 is not listed on IDEAS
  14. Grossman, Sanford J. & Perry, Motty, 1986. "Perfect sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 39(1), pages 97-119, June.
  15. Kyle Bagwell & Garey Ramey, 1988. "Advertising and Limit Pricing," RAND Journal of Economics, The RAND Corporation, vol. 19(1), pages 59-71, Spring.
  16. Ying Chen & Navin Kartik & Joel Sobel, 2008. "Selecting Cheap-Talk Equilibria," Econometrica, Econometric Society, vol. 76(1), pages 117-136, 01.
  17. Srihari Govindan & Robert Wilson, 2006. "On Forward Induction," Levine's Working Paper Archive 321307000000000618, David K. Levine.
  18. Gul, Faruk & Sonnenschein, Hugo, 1988. "On Delay in Bargaining with One-Sided Uncertainty," Econometrica, Econometric Society, vol. 56(3), pages 601-11, May.
  19. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
  20. 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.
  21. McLennan, Andrew, 1985. "Justifiable Beliefs in Sequential Equilibrium," Econometrica, Econometric Society, vol. 53(4), pages 889-904, July.
  22. repec:oup:restud:v:54:y:1987:i:3:p:345-64 is not listed on IDEAS
  23. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
  24. Bagwell, Kyle, 1987. "Introductory Price as a Signal of Cost in a Model of Repeat Business," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 365-84, July.
  25. Grossman, Sanford J. & Perry, Motty, 1986. "Sequential bargaining under asymmetric information," Journal of Economic Theory, Elsevier, vol. 39(1), pages 120-154, June.
  26. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  27. Yossi Feinberg & Andrzej Skrzypacz, 2005. "Uncertainty about Uncertainty and Delay in Bargaining," Econometrica, Econometric Society, vol. 73(1), pages 69-91, 01.
  28. 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.
  29. Milgrom, Paul & Roberts, John, 1982. "Limit Pricing and Entry under Incomplete Information: An Equilibrium Analysis," Econometrica, Econometric Society, vol. 50(2), pages 443-59, March.
  30. van Damme, E.E.C., 1989. "Stable equilibria and forward induction," Other publications TiSEM bd598a8f-f017-4cab-a9ed-8, Tilburg University, School of Economics and Management.
  31. 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.
  32. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
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:cla:levarc:122247000000001859. 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: (David K. Levine)

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.