PIERPAOLO BATTIGALLI

Abstract

This research investigates the motivations in sharing decisions in a dictator game, trying to distinguish the role of guilt aversion from other social preferences, such as altruism and inequity aversion. Using an experimental design that incorporates exogenous variations in beliefs and endowments, we manipulate probabilities to generate scenarios with varying expected sharing costs. This approach allows for an in-depth examination of how sharing behaviors correlate with second-order beliefs across different cost conditions. Focusing on the guilt and inequity aversion channels, the study also explores how gender influences behavior.

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Abstract

We examine the interplay between guilt aversion and inequality in decision-making, specifically in the context of a dictator game. Considering different initial allocations of the surplus, we investigate how the material opportunity cost of reducing inequality influences sharing behavior, revealing complex relationship among guilt-driven choices and opportunity costs.

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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.

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Abstract

It is well known that, in sequential games, the set of paths consistent with rationality and forward-induction reasoning may change non-monotonically with respect to transparent restrictions on players' beliefs (see Battigalli & Siniscalchi J. Econ. Theory 2002, and Battigalli & Friedenberg, Theor. Econ. 2012). Yet, we prove that—in an incomplete-information environment—predictions become sharper when the restrictions only concern initial beliefs about types. This monotonicity theorem implies that strong rationalizability for games with payoff uncertainty characterizes the path-predictions of forward-induction reasoning across all possible restrictions to players' initial hierarchies of beliefs on the exogenous uncertainty. The latter result allows us to solve an open problem in implementation theory: The implementation of social choice functions through sequential mechanisms under forward-induction reasoning—which considerably expands the realm of implementable functions compared with simultaneous-move mechanisms (Mueller, J. Econ. Theory 2016)—is robust in the sense of Bergemann and Morris (Theor. Econ. 2009).

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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.

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

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

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

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Annotated Extended Abstract in English (March 2012)

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• 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)