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Strategies and interactive beliefs in dynamic games

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  • Pierpaolo Battigalli
  • Alfredo Di Tillio
  • Dov Samet

Abstract

Interactive epistemology in dynamic games studies forms of strategic reasoning like backward induction and forward induction by formally representing the players' beliefs about each other, conditional on each history. Work on this topic typically relies on epistemic models where states of the world specify both strategies and beliefs. In this literature, strategies are interpreted as objective descriptions of what the players would choose at each history. But the intuitive interpretation of strategy is that of (subjective) contingent plan of action. As players do not delegate their moves to devices that mechanically execute a strategy, plans cannot be anything but beliefs of players about their own behavior. In this paper we analyze strategic reasoning in dynamic games with perfect information by means of epistemic models where behavior is described only by the play path, and players' beliefs include their contingent plans. We define rational planning, a property of beliefs only, and material consistency, which connects plans with choices on the play path. Material rationality is the conjunction of rational planning and material consistency. In perfect information games of depth two, the simplest dynamic games, correct belief in material rationality only implies a Nash outcome, not the backward-induction one. We have to consider stronger assumptions of persistence of belief in material rationality in order to obtain backward induction and forward induction. We relate our work to the existing literature, and we discuss the extension of our analysis to games with imperfect information.

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Bibliographic Info

Paper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 375.

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Date of creation: 2011
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Handle: RePEc:igi:igierp:375

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  1. Battigalli, Pierpaolo & Bonanno, Giacomo, 1999. "Recent results on belief, knowledge and the epistemic foundations of game theory," Research in Economics, Elsevier, vol. 53(2), pages 149-225, June.
  2. Battigalli, Pierpaolo & Friedenberg, Amanda, 2012. "Forward induction reasoning revisited," Theoretical Economics, Econometric Society, vol. 7(1), January.
  3. Samet, Dov, 2000. "Quantified Beliefs and Believed Quantities," Journal of Economic Theory, Elsevier, vol. 95(2), pages 169-185, December.
  4. Pierpaolo Battigalli & Martin Dufwenberg, 2005. "Dynamic Psychological Games," Levine's Bibliography 784828000000000046, UCLA Department of Economics.
  5. Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
  6. Battigalli, Pierpaolo & Siniscalchi, Marciano, 2002. "Strong Belief and Forward Induction Reasoning," Journal of Economic Theory, Elsevier, vol. 106(2), pages 356-391, October.
  7. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
  8. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
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Cited by:
  1. Giacomo Bonanno, 2010. "AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties," Working Papers 1017, University of California, Davis, Department of Economics.
  2. Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 122, University of California, Davis, Department of Economics.
  3. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
  4. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 132, University of California, Davis, Department of Economics.
  5. Giacomo Bonanno, 2011. "Perfect Bayesian equilibrium. Part II: epistemic foundations," Working Papers 111, University of California, Davis, Department of Economics.

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