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On Forward Induction

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  • Srihari Govindan
  • Robert Wilson

Abstract

We examine Hillas and Kohlberg's conjecture that invariance to the addition of payoff-redundant strategies implies that a backward induction outcome survives deletion of strategies that are inferior replies to all equilibria with the same outcome. That is, invariance and backward induction imply forward induction. Although it suffices in simple games to interpret backward induction as a subgame-perfect or sequential equilibrium, to obtain general theorems we use a quasi-perfect equilibrium, viz. a sequential equilibrium in strategies that are admissible continuations from each information set. Using this version of backward induction, we prove the Hillas-Kohlberg conjecture for two-player extensive-form games with perfect recall. We also prove an analogous theorem for general games by interpreting backward induction as a proper equilibrium, since a proper equilibrium is equivalent to a quasi-perfect equilibrium of each extensive form with the same normal form, provided beliefs are justifed by perturbations invariant to inessential transformations of the extensive form. For a two-player game we prove that if a set of equilibria includes a proper equilibrium of every game with the same reduced normal form then it satisfies forward induction, i.e. it includes a proper equilibrium of the game after deleting strategies that are inferior replies to all equilibria in the set. We invoke slightly stronger versions of invariance and properness to handle nonlinearities in an N-player game.
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Suggested Citation

  • Srihari Govindan & Robert Wilson, 2008. "On Forward Induction," Levine's Working Paper Archive 122247000000001859, David K. Levine.
  • Handle: RePEc:cla:levarc:122247000000001859
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    References listed on IDEAS

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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. Evdokimov, Piotr & Rustichini, Aldo, 2016. "Forward induction: Thinking and behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 195-208.
    5. 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.
    6. Roman Inderst & Sebastian Pfeil, 2013. "Securitization and Compensation in Financial Institutions," Review of Finance, European Finance Association, vol. 17(4), pages 1323-1364.
    7. 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.
    8. 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.
    9. 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.
    10. repec:eee:jetheo:v:169:y:2017:i:c:p:489-516 is not listed on IDEAS
    11. Yildiz, Muhamet, 2015. "Invariance to representation of information," Games and Economic Behavior, Elsevier, vol. 94(C), pages 142-156.
    12. 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.
    13. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
    14. 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.
    15. 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.
    16. 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.
    17. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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