# PIERPAOLO BATTIGALLI

## Working papers

BATTIGALLI Pierpaolo DUFWENBERG Martin

The mathematical framework of psychological game theory is useful for describing many forms of motivation where preferences depend directly on own or others' beliefs. It allows for incorporating, e.g., emotions, reciprocity, image concerns, and self-esteem in economic analysis. We explain how and why, discussing basic theory, experiments, applied work, and methodology.

Keywords: psychological game theory; belief-dependent motivation; reciprocity; emotions; image concerns; self-esteem

JEL codes: C72; D91

Psychological Game Theory

Pierpaolo Battigalli, Martin Dufwenberg

Abstract

The mathematical framework of psychological game theory is useful for describing many forms of motivation where preferences depend directly on own or others' beliefs. It allows for incorporation of emotions, reciprocity, image concerns, and self-esteem in economic analysis. We explain how and why, discussing basic theory, a variety of sentiments, experiments, and applied work.

Keywords: psychological game theory, belief-dependent motivation, reciprocity, emotions, image concerns, self-esteem.

- Psychological Game Theory (523 Kb)

Learning and Selfconfirming Equilibria in Network Games

Pierpaolo Battigalli, Fabrizio Panebianco, Paolo Pin

Abstract

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 payoffs depend on an unknown state that in reality is an aggregate of the actions of their neighbors. Each time, every agent chooses an action that maximizes her 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 such dynamic is a selfconfirming equilibrium given the assumed feedback. We characterize the structure of the set of selfconfirming equilibria in network games and we relate selfconfirming and Nash equilibria. Thus, we provide conditions on the network under which the Nash equilibrium concept has a learning foundation, despite the fact that agents may have incomplete information. In particular, we show that the choice of being active or inactive in a network is crucial to determine whether agents can make correct inferences about the payoff state and hence play the best reply to the truth in a selfconfirming equilibrium. We also study learning dynamics and show how agents can get stuck in non-Nash selfconfirming equilibria. In such dynamics, the set of inactive agents can only increase in time, because once an agent finds it optimal to be inactive, she gets no feedback about the payoff state, hence she does not change her beliefs and remains inactive.

Beliefs, Plans, and Perceived Intentions in Games

Pierpaolo Battigalli, Nicodemo De Vito

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

Abstract

We adopt the epistemic framework of Battigalli and Siniscalchi (J. Econ. Theory 88:188-230, 1999) to model the distinction between a player's contingent behavior, which is part of the external state, and his plan, which is described by his beliefs about his own behavior. This allows us to distinguish between intentional and unintentional behavior, and to explicitly model how players revise their beliefs about the intentions of others upon observing their actions. We illustrate our approach with detailed examples and with a new derivation of backward induction from epistemic conditions. Specifically, we prove that common full belief in optimal planning and in belief in continuation consistency imply the backward induction strategies and beliefs. We also present within our framework other relevant epistemic assumptions about backward and forward-induction reasoning, and relate them to similar ones studied in the previous literature.

Keywords: Epistemic game theory, plans, perceived intentions, backward induction, forward induction.

- Beliefs, Plans, and Perceived Intentions in Games (480 Kb)
- Slides (529 Kb)

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)

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

- How Much to Pay for Opacity and How? (1.009 Kb)

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.

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

Slides on Maxims for Epistemic Game Theory

Pierpaolo Battigalli

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

- Slides (94 Kb)

Disclosure of Belief-Dependent Preferences in a Trust Game

Pierpaolo Battigalli, Giuseppe Attanasi, Rosemarie Nagel

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.

Context Dependent Forward Induction Reasoning

Pierpaolo Battigalli, Amanda Friedenberg

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"

- Slides (135 Kb)

Slides on Guilt and Shame

Pierpaolo Battigalli

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

- Slides (82 Kb)

Slides on Reciprocity

Pierpaolo Battigalli

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

- Slides (116 Kb)

Slides on Guilt in Games

Pierpaolo Battigalli

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

- Slides (95 Kb)

Comportamento Razionale ed equilibrio nei giochi e nelle situazioni sociali

Pierpaolo Battigalli

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)