Pierpaolo Battigalli, Fabrizio Panebianco, Paolo Pin
Consider a set of agents who play a network game repeatedly. Agents may not know the network. They may even be unaware that they are interacting with other agents in a network. Possibly, they just understand that their optimal action depends on an unknown state that is, actually, an aggregate of the actions of their neighbors. Each time, every agent chooses an action that maximizes her instantaneous subjective expected payoff, and then updates her beliefs according to what she observes. In particular, we assume that each agent only observes her realized payoff. A steady state of the resulting dynamic is a selfconfirming equilibrium given the assumed feedback. We characterize the structure of the set of selfconfirming equilibria in the given class of network games, we relate selfconfirming and Nash equilibria, and we analyze simple conjectural best-reply paths whose limit points are selfconfirming equilibria.
Higher Order Beliefs and Emotions in Games
Presented at at the Summer School on "Behavioral Game Theory: Psychological Games," University of East Anglia, Norwich, July 2017.
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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
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
- How Much to Pay for Opacity and How? (1.009 Kb)
Slides on Maxims for Epistemic Game Theory
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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Disclosure of Belief-Dependent Preferences in a Trust Game
Pierpaolo Battigalli, Giuseppe Attanasi, Elena Manzoni, Rosemarie Nagel
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.
Context Dependent Forward Induction Reasoning
Pierpaolo Battigalli, Amanda Friedenberg
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 on Guilt and Shame
Presented at the workshop on "Understanding Moral Emotions, Perspectives From Cognitive Sciences and Economics", Rome, May 2008.
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Slides on Reciprocity
Presented at the conference on "Reciprocity: Theory and Facts", Verbania, February 2007
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Slides on Guilt in Games
Presented at the ASSA meeting, Chicago, January 2007. It contains material omitted from "Guilt in Games" "AER-P&P (2007)
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Comportamento Razionale ed equilibrio nei giochi e nelle situazioni sociali
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)