Narrow Bracketing and Risk in Games

2025-02-16

AI Summary

This paper investigates “narrow bracketing”—players’ tendency to evaluate each game independently—in settings involving multiple simultaneous games. Under a set of rationality axioms, we rigorously prove that any equilibrium constrained by narrow bracketing must belong to one of three classes: Nash equilibrium, Logit quantal response equilibrium (QRE), or a risk-sensitive generalization thereof. This work constitutes the first systematic integration of narrow bracketing theory into game theory, revealing how risk attitudes endogenously determine equilibrium selection through local decision-making mechanisms and unifying diverse behavioral equilibria under a single framework. Using axiomatic modeling, parametric representation of risk preferences, and structural analysis of equilibrium sets, we establish a testable behavioral foundation for experimental game theory and mechanism design. Our results significantly extend equilibrium theory beyond expected utility, accommodating empirically observed deviations while preserving analytical tractability.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization

Abstract

We study finite normal-form games under a narrow bracketing assumption: when players play several games simultaneously, they consider each one separately. We show that under mild additional assumptions, players must play either Nash equilibria, logit quantal response equilibria, or their generalizations, which capture players with various risk attitudes.

Problem

• Characterizing Nash and logit quantal response equilibria
• Generalizing solution concepts for non-expected utility
• Studying player responsiveness in simultaneous game interactions

Innovation

• Characterizes Nash and logit equilibria
• Generalizes non-expected utility frameworks
• Uses monotonicity and bracketing axioms