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Beliefs, Plans, and Perceived Intentions in Games
Battigalli Pierpaolo


Presented at the XVI Conference on "Theoretical Aspects of Rationality and Knowledge," Liverpool, July 2017



  • Slides (365 Kb)
  • Last change 28/07/2017

    Interactive Epistemology in Simple Dynamic Games with a Continuum of Strategies
    Pierpaolo Battigalli, Gabriele Beneduci, Pietro Tebaldi


    Abstract

    We extend the epistemic analysis of dynamic games of Battigalli and Siniscalchi (1999, 2002, 2007) from finite dynamic games to all simple games, that is, finite and infinite-horizon games with finite action sets at non-terminal stages and compact action sets at terminal stages. We prove a generalization of Lubin's (1974) extension result to deal with conditional probability systems and strong belief. With this, we can provide a short proof of the following result: in every simple dynamic game, strong rationalizability characterizes the behavioral implications of rationality and common strong belief in rationality.

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    Last change 28/07/2017

    Ambiguity Attitudes and Self-Confirming Equilibrium in Sequential Games
    Pierpaolo Battigalli, Emiliano Catonini, Giacomo Lanzani, Massimo Marinacci


    Abstract

    We consider a game with sequential moves played by agents who are randomly drawn from large populations and matched. We assume that when players are uncertain about the strategy distributions of the opponents, preferences over actions at any information set admit a smooth-ambiguity representation in the sense of Klibanoff, Marinacci, and Mukerji (Econometrica, 2005). This may induce dynamically inconsistent preferences and calls for an appropriate definition of sequential best response. With this, we define and analyze self-confirming equilibrium (SCE) and rationalizable SCE in sequential games with feedback played by agents with non-neutral ambiguity attitudes. Battigalli, Cerreia-Vioglio, Maccheroni, and Marinacci (Amer. Econ. Rev., 2015) show that the set of SCE's of a simultaneous-move game with feedback expands as ambiguity aversion increases. We show by example that SCE in a sequential game is not equivalent to SCE applied to the strategic form of such game, and that the previous monotonicity result does not extend to general sequential games. Still, we provide sufficient conditions under which the monotonicity result holds for (rationalizable) SCE.

    Keywords: Sequential games with feedback, smooth ambiguity, self-confirming equilibrium, rationalizable self-confirming equilibrium.



  • Poster (197 Kb)
  • Last change 17/05/2017

    Higher Order Beliefs and Emotions in Games
    Pierpaolo Battigalli


    Presented at at the Summer School on "Behavioral Game Theory: Psychological Games," University of East Anglia, Norwich, July 2017.



  • Slides (359 Kb)
  • Last change 28/07/2017

    How Much to Pay for Opacity and How? Negotiating Premiums and the Method of Payment in M&As
    Pierpaolo Battigalli, Carlo Chiarella, Stefano Gatti, Tommaso Orlando


    Abstract

    We model theoretically and quantify empirically the impact of informational frictions on managerial decisions in the context of mergers and acquisitions. In particular, we focus on how bid premiums and methods of payment are affected by the bidder and target firms' degrees of opacity. To this end, we model the negotiation between bidder and target as a signaling game with two-sided private information. We then empirically test the model's predictions concerning the effects of target and bidder opacity on the simultaneous determination of the method of payment and the bid premium, by conditioning cross-sectionally on the basis of firms' stock trading properties, which we interpret as representative of individual firm opacity. Consistently with the predictions of our model, we find, by studying a sample of bids by and for U.S. publicly listed firms over the period 1985-2014, that both the likelihood of a stock bid and the bid premium increase with the opacity of the target, while the opacity of the bidder is related to lower bid premiums. 

    Keywords: Asymmetric information, mergers and acquisitions, method of payment, bid premium

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    Last change 28/07/2017

    Learning and Self-confirming Long-Run Biases
    Pierpaolo Battigalli, Alejandro Francethich, Giacomo Lanzani, Massimo Marinacci


    Abstract

    We consider an uncertainty averse, sophisticated decision maker facing a recurrent decision problem where information is generated endogenously. In this context, we study self-con…firming strategies as the outcomes of a process of active experimentation. We provide inter alia a learning foundation for self-con…firming equilibrium with model uncertainty (Battigalli et al., 2015). We also argue that ambiguity aversion tends to sti‡fle experimentation, increasing the likelihood that decision maker get stuck into suboptimal "certainty traps." 

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  • Slides (244 Kb)
  • Last change 28/07/2017

    A Framework for the Analysis of Self-Confirming Policies
    Pierpaolo Battigalli, Simone Cerreia Vioglio, Fabio Maccheroni, Massimo Marinacci, Thomas Sargent


    Abstract

    This paper provides a general framework for the analysis of self-confirming policies. We first study self-confirming equilibria in recurrent decision problems with incomplete information about the true stochastic model. Next we illustrate the theory with a characterization of stationary monetary policies in a linear-quadratic setting. Finally we provide a more general discussion of self-confirming policies.

    Key words: Self-confirming equilibrium, partial identification, law of large numbers, Keynesian, new classical.

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    Last change 28/07/2017

    A Note on Comparative Ambiguity and Justifiability
    Pierpaolo Battigalli, Simone Cerreia Vioglio, Fabio Maccheroni, Massimo Marinacci


    We consider a decision maker who ranks actions according to the smooth ambiguity criterion of Klibanoff et al. (2005). An action is justifiable if it is a best reply to some belief over probabilistic models. We show that higher ambiguity aversion expands the set of justifiable actions. In turn, this implies that higher ambiguity aversion expands the set of rationalizable actions of a game. Our results follow from a generalization of the duality lemma of Wald (1949) and Pearce (1984).

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    Last change 28/07/2017

    Frustration and Anger in Games
    Pierpaolo Battigalli, Martin Dufwenberg, Alec Smith


    Abstract

    Frustration, anger, and aggression have important consequences for economic and social behavior, concerning for example monopoly pricing, contracting, bargaining, traffic safety, violence, and politics. Drawing on insights from psychology, we develop a formal approach to exploring how frustration and anger, via blame and aggression, shape interaction and outcomes in economic settings.

    Keywords: frustration, anger, blame, belief-dependent preferences, psychological games

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  • Slides (305 Kb)
  • Last change 28/07/2017

    Slides on Maxims for Epistemic Game Theory
    Battigalli Pierpaolo


    Presented at the roundtable on "Knowledge and Rationality" at the Conference "The Constructive in Logic and Applications" - Cuny, May 25th 2012.
     



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  • Last change 16/03/2017

    Disclosure of Belief-Dependent Preferences in a Trust Game
    Battigalli Pierpaolo, Attanasi Giuseppe and Nagel Rosemarie


    Abstract

    Experimental evidence suggests that agents in social dilemmas have belief-dependent, other-regarding preferences. But in experimental games such preferences cannot be common knowledge, because subjects play with anonymous co-players. We address this issue theoretically and experimentally in the context of a trust game, assuming that the trustee’s choice may be affected by a combination of guilt aversion and intention-based reciprocity. We recover trustees’ belief-dependent preferences from their answers to a structured questionnaire. In the main treatment, the answers are disclosed and made common knowledge within each matched pair, while in the control treatment there is no disclosure. Our main auxiliary assumption is that such disclosure approximately implements a psychological game with complete information. To organize the data, we classify subjects according to their elicited preferences, and test predictions for the two treatments using both rationalizability and equilibrium. We find that guilt aversion is the prevalent psychological motivation, and that behavior and elicited beliefs move in the direction predicted by the theory.

    Keywords: Experiments, trust game, guilt, reciprocity, complete and incomplete information. 

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    Last change 28/07/2017

    Context Dependent Forward Induction Reasoning
    Battigalli Pierpaolo, Friedenberg Amanda


    Abstract

    This paper studies the case where a game is played in a particular context. The context influences what beliefs players hold. As such, it may affect forward induction reasoning: If players rule out specific beliefs, they may not be able to rationalize observed behavior. The effects are not obvious. Context-laden forward induction may allow outcomes precluded by context-free forward induction. At the formal level, forward induction and contextual reasoning are defined within an epistemic structure. In particular, we represent contextual forward induction reasoning as rationality and common strong belief of rationality(RCSBR) within an arbitrary type structure. (The concept is due to Battigalli-Siniscalchi [6, 2002].) We ask: What strategies are consistent with RCSBR (across all type structures)? We show that the RCSBR is characterized by a solution concept we call Extensive Form Best Response Sets (EFBRS’s). We go on to study the EFBRS concept in games of interest.

    A new, abridged version of this paper is published in THEORETICAL ECONOMICS (2012) under the title "Forward Induction Reasoning Revisited"
     
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  • Slides (135 Kb)
  • Last change 28/07/2017

    Slides on Guilt and Shame
    Battigalli Pierpaolo


    Presented at the workshop on "Understanding Moral Emotions, Perspectives From Cognitive Sciences and Economics", Rome, May 2008.



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  • Last change 27/01/2009

    Slides on Reciprocity
    Battigalli Pierpaolo


    Presented at the conference on "Reciprocity: Theory and Facts", Verbania, February 2007



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  • Last change 27/01/2009

    Slides on Guilt in Games
    Battigalli Pierpaolo


    Presented at the ASSA meeting, Chicago, January 2007. It contains material omitted from "Guilt in Games" "AER-P&P (2007)



  • download (95 Kb)
  • Last change 27/01/2009

    Comportamento Razionale ed equilibrio nei giochi e nelle situazioni sociali
    Battigalli Pierpaolo


    Battigalli Pierpaolo, Bocconi University

    Annotated Extended Abstract in English (March 2012)

     



  • Download Abstract (138 Kb)
  • Cover and Index (69 Kb)
  • Introduction (590 Kb)
  • Chapter 1 (824 Kb)
  • Chapter 2 (1.792 Kb)
  • Chapter 3 (2.966 Kb)
  • Chapter 4 pp 142-187 (1.970 Kb)
  • Chapter 4 pp 188-229 (1.916 Kb)
  • Chapter 5 + Conclusions (299 Kb)
  • Last change 03/04/2012



    Last updated September 05, 2008