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Transparent Restrictions on Beliefs and Forward Induction Reasoning in Games with Asymmetric Information

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  • Pierpaolo Battigalli
  • Andrea Prestipino

Abstract

We analyze forward-induction reasoning in games with asymmetric information assuming some commonly understood restrictions on beliefs. Specifically, we assume that some given restrictions ? on players' initial or conditional first-order beliefs are transparent, that is, not only the restrictions ? hold, but there is common belief in ? at every node. Most applied models of asymmetric information are covered as special cases whereby ? pins down the probabilities initially assigned to states of nature. But the abstract analysis also allows for transparent restrictions on beliefs about behavior, e.g. independence restrictions or restrictions induced by the context behind the game. Our contribution is twofold. First, we use dynamic interactive epistemology to formalize assumptions that capture foward-induction reasoning given the transparency of ?, and show that the behavioral implications of these assumptions are characterized by the ?-rationalizability solution procedure of Battigalli (1999, 2003). Second, we study the differences and similarities between this solution concept and a simpler solution procedure put forward by Battigalli and Siniscalchi (2003). We show that the two procedures are equivalent if ? is "closed under compositions", a property that holds in all the applications considered by Battigalli and Siniscalchi (2003). We also show that when ? is not closed under compositions the simpler solution procedure may fail to characterize the behavioral implications of forward induction reasoning. J.E.L. Classification Numbers: C72, C73, D82. KEYWORDS: Epistemic game theory, Rationalizability, Forward induction, Transparent restrictions on beliefs.

Suggested Citation

  • Pierpaolo Battigalli & Andrea Prestipino, 2011. "Transparent Restrictions on Beliefs and Forward Induction Reasoning in Games with Asymmetric Information," Working Papers 376, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  • Handle: RePEc:igi:igierp:376
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    References listed on IDEAS

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    1. Battigalli, Pierpaolo & Friedenberg, Amanda, 2012. "Forward induction reasoning revisited," Theoretical Economics, Econometric Society, vol. 7(1), January.
    2. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    5. Cappelletti Giuseppe, 2010. "A Note on Rationalizability and Restrictions on Beliefs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-13, September.
    6. Pierpaolo Battigalli & Amanda Friedenberg, 2009. "Context-Dependent Forward Induction Reasoning," Working Papers 351, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
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    Cited by:

    1. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    2. Pierpaolo Battigalli & Gabriele Beneduci & Pietro Tebaldi, 2017. "Interactive Epistemology in Simple Dynamic Games with a Continuum of Strategies," Working Papers 602, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Harrington, Joseph E., 2017. "A theory of collusion with partial mutual understanding," Research in Economics, Elsevier, vol. 71(1), pages 140-158.

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