Betting under Common Beliefs: The Effect of Probability Weighting

Paper: arXiv 2602.24194

Authors: Patrick Beissner, Tim Boonen, Mario Ghossoub

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical exploration of how rank-dependent utility and probability weighting generate endogenous betting in an economy with common beliefs. While the mathematical derivations and axiomatic concepts are advanced and complete, it is purely a theoretical paper with no empirical data or backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain speculative betting under common beliefs without aggregate uncertainty] --> B[Data/Inputs: Pure-exchange economy with baseline vNM agents and one RDU agent]
    B --> C[Methodology: Introduce Rank-Dependent Utility with nonlinear probability weighting]
    C --> D[Computational Analysis: Evaluate Pareto-optimal allocations and equilibrium states]
    D --> E[Key Outcome 1: Probability weighting creates endogenous belief heterogeneity and speculative bets]
    D --> F[Key Outcome 2: Social planner nudges RDU agent via costly education to restore full-insurance optima]

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0 of 45 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.