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On Forward Induction

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  • Srihari Govindan
  • Robert Wilson

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. Copyright 2009 The Econometric Society.

Suggested Citation

  • Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
  • Handle: RePEc:ecm:emetrp:v:77:y:2009:i:1:p:1-28
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    Cited by:

    1. Govindan, Srihari & Wilson, Robert B., 2005. "Justification of Stable Equilibria," Research Papers 1896, Stanford University, Graduate School of Business.
    2. Srihari Govindan & Robert Wilson, 2009. "On Forward Induction," Econometrica, Econometric Society, vol. 77(1), pages 1-28, January.
    3. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, vol. 80(4), pages 1639-1699, July.
    4. Eguia, Jon X. & Llorente-Saguer, Aniol & Morton, Rebecca & Nicolò, Antonio, 2018. "Equilibrium selection in sequential games with imperfect information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 465-483.
    5. Evdokimov, Piotr & Rustichini, Aldo, 2016. "Forward induction: Thinking and behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 195-208.
    6. Andreas Blume & Peter H. Kriss & Roberto A. Weber, 2017. "Pre-play communication with forgone costly messages: experimental evidence on forward induction," Experimental Economics, Springer;Economic Science Association, vol. 20(2), pages 368-395, June.
    7. Roman Inderst & Sebastian Pfeil, 2013. "Securitization and Compensation in Financial Institutions," Review of Finance, European Finance Association, vol. 17(4), pages 1323-1364.
    8. Kriss, Peter H. & Blume, Andreas & Weber, Roberto A., 2016. "Coordination with decentralized costly communication," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 225-241.
    9. Oikonomou, V.K. & Jost, J, 2013. "Periodic strategies and rationalizability in perfect information 2-Player strategic form games," MPRA Paper 48117, University Library of Munich, Germany.
    10. Dufwenberg, Martin & Köhlin, Gunnar & Martinsson, Peter & Medhin, Haileselassie, 2016. "Thanks but no thanks: A new policy to reduce land conflict," Journal of Environmental Economics and Management, Elsevier, vol. 77(C), pages 31-50.
    11. repec:eee:jetheo:v:169:y:2017:i:c:p:489-516 is not listed on IDEAS
    12. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    13. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 997-1026, August.
    14. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
    15. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2014. "Do Actions Speak Louder Than Words? Auditing, Disclosure, and Verification in Organizations," Working Papers gueconwpa~14-14-04, Georgetown University, Department of Economics, revised 13 Jun 2015.
    16. Srihari Govindan & Robert Wilson, 2008. "Axiomatic Theory of Equilibrium Selection in Signalling Games with Generic Payoffs," Levine's Working Paper Archive 122247000000002381, David K. Levine.
    17. Anderlini, Luca & Gerardi, Dino & Lagunoff, Roger, 2016. "Auditing, disclosure, and verification in decentralized decision problems," Journal of Economic Behavior & Organization, Elsevier, vol. 131(PA), pages 393-408.
    18. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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