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

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Date of creation: 04 Feb 2008
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Handle: RePEc:cla:levarc:122247000000001859

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References

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Citations

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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, 2007. "'On Forward Induction," Levine's Working Paper Archive 321307000000000825, David K. Levine.
  3. Srihari Govindan & Robert Wilson, 2012. "Axiomatic Equilibrium Selection for Generic Two‐Player Games," Econometrica, Econometric Society, Econometric Society, vol. 80(4), pages 1639-1699, 07.
  4. Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.
  5. Govindan, Srihari & Wilson, Robert B., 2008. "Axiomatic Theory of Equilibrium Selection in Signaling Games with Generic Payoffs," Research Papers 2000, Stanford University, Graduate School of Business.
  6. Roman Inderst & Sebastian Pfeil, 2013. "Securitization and Compensation in Financial Institutions," Review of Finance, European Finance Association, European Finance Association, vol. 17(4), pages 1323-1364.
  7. Govindan, Srihari & Wilson, Robert B., 2008. "Decision-Theoretic Forward Induction," Research Papers 1986, 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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