Betting under Common Beliefs: The Effect of Probability Weighting

2026-02-27

AI Summary

This study addresses why endogenous speculation—manifested as Pareto optimal allocations without full insurance—persists even in pure exchange economies characterized by common beliefs and no aggregate uncertainty. Introducing rank-dependent utility (RDU) agents with probability weighting preferences, the paper demonstrates that heterogeneity in risk perception can serve as an endogenous source of belief dispersion, thereby motivating betting behavior. Through general equilibrium analysis and social welfare optimization, it establishes that probability weighting indeed leads RDU agents to Pareto optimal outcomes lacking full insurance. The work further proposes that a social planner can implement costly educational interventions to correct agents’ distorted risk perceptions, nudging their behavior toward von Neumann–Morgenstern rationality and partially restoring full insurance. This provides a novel behavioral explanation for market speculation and lays theoretical groundwork for policy interventions targeting cognitive biases.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

This paper examines the impact of introducing a Rank-Dependent Utility (RDU) agent into a von Neumann-Morgenstern (vNM) pure-exchange economy with no aggregate uncertainty. In the absence of the RDU agent, the classical theory predicts that Pareto-optimal allocations are full-insurance, or no-betting, allocations. We show how the probability weighting function of the RDU agent, seen as a proxy for probabilistic risk aversion that is not captured by marginal utility of wealth, can lead to Pareto optima characterized by endogenous betting, despite common baseline beliefs. Such endogenous betting at an optimum leads to uncertainty-generating trade arising purely from heterogeneity in the perception of risk, rather than in beliefs. Our results formalize the intuitive understanding that probability weighting can act as an endogenous source of belief heterogeneity, and provide a new behavioral foundation for the coexistence of common beliefs and speculative behavior, in an environment with no initial aggregate uncertainty. Interpreting the RDU agent's nonlinear weighting function as an ``internality''prompts the question of whether a social planner should intervene. We show how a benevolent social planner can nudge the RDU agent to behave closer to a vNM agent, through costly statistical or financial education, thereby (partially) restoring the optimality of full-insurance allocations.

Problem

• probability weighting
• common beliefs
• endogenous betting
• Rank-Dependent Utility
• speculative behavior

Innovation

• Rank-Dependent Utility
• probability weighting
• endogenous betting
• common beliefs
• behavioral foundation