This work was funded in part by a grant from the National Science Foundation of the United States. We are grateful for superb insights and suggestions from a referee.
On Forward Induction
Version of Record online: 15 DEC 2008
© 2009 The Econometric Society
Volume 77, Issue 1, pages 1–28, January 2009
How to Cite
Govindan, S. and Wilson, R. (2009), On Forward Induction. Econometrica, 77: 1–28. doi: 10.3982/ECTA6956
- Issue online: 15 DEC 2008
- Version of Record online: 15 DEC 2008
- Manuscript received February, 2007; final revision received May, 2008.
- Game theory;
- equilibrium refinement;
- forward induction;
- backward induction
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.