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Prudent rationalizability in generalized extensive-form games

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  • Heifetz, Aviad
  • Meier, Martin
  • Schipper, Burkhard C

Abstract

We define an extensive-form analogue of iterated admissibility, called Prudent Rationalizability (PR). In each round of the procedure, for each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. Somewhat surprisingly, prudent rationalizable strategies may not refine the set of Extensive-Form Rationalizable (EFR) strategies (Pearce 1984). However, we prove that the paths induced by PR strategy-profiles (weakly) refine the set of paths induced by EFR strategies. PR applies also to generalized extensive-form games which model mutual unawareness of actions (Heifetz, Meier and Schipper, 2011a). We demonstrate the applicability of PR in the analysis of verifiable communication, and show that it yields the same, full information unraveling prediction as does the unique sequential equilibrium singled out by Milgrom and Roberts (1986); yet, we also show that under unawareness full unraveling might fail.

Suggested Citation

  • Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C, 2011. "Prudent rationalizability in generalized extensive-form games," MPRA Paper 30220, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:30220
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    References listed on IDEAS

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    1. Dubey, Pradeep & Kaneko, Mamoru, 1985. "Information patterns and Nash equilibria in extensive games -- II," Mathematical Social Sciences, Elsevier, vol. 10(3), pages 247-262, December.
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    Cited by:

    1. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 124, University of California, Davis, Department of Economics.
    2. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    3. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    4. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.
    5. Schipper, Burkhard C. & Woo, Hee Yeul, 2019. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Quarterly Journal of Political Science, now publishers, vol. 14(1), pages 41-88, January.
    6. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Dynamic unawareness and rationalizable behavior," Games and Economic Behavior, Elsevier, vol. 81(C), pages 50-68.
    7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2013. "Unawareness, beliefs, and speculative trade," Games and Economic Behavior, Elsevier, vol. 77(1), pages 100-121.
    8. Burkhard Schipper & Hee Yeul Woo, 2014. "Political Awareness, Microtargeting of Voters, and Negative Electoral Campaigning," Working Papers 148, University of California, Davis, Department of Economics.
    9. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    10. Burkhard Schipper & Hee Yeul Woo, 2012. "Political Awareness and Microtargeting of Voters in Electoral Competition," Working Papers 46, University of California, Davis, Department of Economics.
    11. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 153, University of California, Davis, Department of Economics.

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    More about this item

    Keywords

    Prudent rationalizability; caution; extensive-form rationalizability; extensive-form games; unawareness; verifiable communication;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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