PIERPAOLO BATTIGALLI

Abstract

We study theoretically and experimentally sharing behavior in a dictator game with asymmetrically observed random initial allocation of a fixed surplus. Our findings are consistent with two other-regarding channels mitigating selfish behavior: a belief-independent desire to comply with an equal-sharing norm, and belief-dependent guilt aversion. The norm-channel allows us to manipulate first and second-order beliefs by changing the commonly known distribution of the initial allocation observed only by the dictator. Comparing behavior for fixed endowment in the high and low-expectations treatments, we test for the presence of guilt aversion.

Keywords: sharing norm, opportunity cost, first and second-order beliefs, guilt aversion.

JEL classification codes: A13; C91; D01; D64.

IGIER Working Paper

Abstract

We formalize a novel framework allowing for the observation of noisy signals about co-players’ emotions, or states of mind. Insofar as the latter are belief-dependent, such feedback allows players to draw inferences informing their strategic thinking. We analyze players’ strategic reasoning adapting the strong rationalizability solution concept, and we give its epistemic justification in terms of players’ rationality and interactive beliefs. The “forward-induction” reasoning entailed by such solution allows players to make inferences about their co-players’ beliefs, private information, and future, or past and unobserved behavior based on the behavioral and emotional feedback they obtain as the game unfolds. We illustrate our framework with a signaling-like example, showing that the possibility of betraying lies, e.g., by blushing, may incentivize truth-telling.

IGIER Working Paper

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Abstract

We develop a general approach to exploring how regret influences strategic interaction and risky choice. Regret is captured by the payoff gap between what a player actually gets and what he believes he would have gotten had he chosen differently. Ex post beliefs are critical to that evaluation, and the modeling therefore draws on tools from psychological game theory. Predictions depend in novel ways on the information structure across end-nodes and assumptions regarding the precise nature of Chance moves. Regret can have a powerful impact in a variety of economic settings including, e.g., investments, delegation, gambling, market entry, and information revelation. 

Keywords: Regret, psychological games, belief-dependent motivation, rumination,information

JEL codes: C72; D91.

IGIER Working Paper

Presented at the workshop on "Behavioral & Experimental Economics", Soleto, Spring 2026

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Abstract

We consider a multistage game where players have reached a pre-play, non-binding agreement on which path to follow. We study the credibility of the agreement, that is, compatibility with forward-induction reasoning, when players are averse to the residual risk and uncertainty that a deviation entails. We show that the set of credible paths expands as risk or ambiguity aversion increase. This is true also when only an upper bound on risk and ambiguity aversion is commonly known. While credibility does not imply necessary compliance with the agreed-upon path, when players perceive sufficient uncertainty and are sufficiently risk or ambiguity averse, compliance with the path is guaranteed. This supports the view that aversion to the uncertainty that deviations entail can be the fundamental reason for staying on the agreed-upon path, rather than precise off-path beliefs imposed by Nash equilibrium and its standard refinements.

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Abstract

In a recent paper, Lin & Palfrey (2024) developed a theory of cognitive hierarchies (CH) in sequential games and observed that this solution concept is not reduced-normal-form invariant. In this note I qualify and explain this observation. I show that the CH model is normal-form invariant, and that the differences arising from the application of the CH model to the reduced normal form depend only on how randomization by level-0 types is modeled. Indeed, while the uniform behavior strategy in the extensive form yields the uniform mixed strategy in the normal form, the latter does not correspond to the uniform randomization in the reduced normal form, because different reduced strategies may correspond to sets of equivalent strategies with different cardinalities. I also comment on (i) the invariance of the CH model to some transformations of the sequential game, and (ii) the independence of conditional beliefs about co-players’ level-types.

Keywords: Cognitive hierarchies, sequential games, extensive form, normal form, structurally reduced normal form, coalescing of moves, independence, observable deviators.

JEL codes: C72; C73; C92; D91.

IGIER Working Paper

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"

IGIER Working Paper

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

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

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

• Slides (95 Kb)

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)