Betting under Common Beliefs: The Effect of Probability Weighting

TL;DR

This paper explores how probability weighting in a Rank-Dependent Utility model can induce endogenous betting and speculative behavior in a no-uncertainty economy, challenging classical full-insurance predictions.

Contribution

It introduces a behavioral foundation for endogenous betting driven by probability weighting, extending classical economic theory to include risk perception heterogeneity.

Findings

Probability weighting leads to endogenous betting despite common beliefs.

Heterogeneity in risk perception causes uncertainty and speculation.

Social interventions can align RDU behavior closer to classical full-insurance outcomes.

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.