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On Forward Induction

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  • Wilson, Robert B.

    (Stanford U)

  • Govindan, Srihari

    (U of Iowa)

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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Bibliographic Info

Paper provided by Stanford University, Graduate School of Business in its series Research Papers with number 1955.

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Date of creation: Jan 2007
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Handle: RePEc:ecl:stabus:1955

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Postal: Stanford University, Stanford, CA 94305-5015
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Web page: http://gsbapps.stanford.edu/researchpapers/
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Cited by:
  1. Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.
  2. Srihari Govindan & Robert Wilson, 2007. "On Forward Induction," Levine's Bibliography 321307000000000788, UCLA Department of Economics.
  3. Roman Inderst & Sebastian Pfeil, 2013. "Securitization and Compensation in Financial Institutions," Review of Finance, European Finance Association, vol. 17(4), pages 1323-1364.
  4. Govindan, Srihari & Wilson, Robert B., 2005. "Justification of Stable Equilibria," Research Papers 1896, Stanford University, Graduate School of Business.
  5. 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.
  6. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, Stanford University, Graduate School of Business.
  7. Govindan, Srihari & Wilson, Robert, 2009. "Axiomatic Equilibrium Selection for Generic Two-Player Games," Research Papers 2021, Stanford University, Graduate School of Business.
  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.

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