Bounded arbitrage and nearly rational behavior

TL;DR

This paper links the concept of limited arbitrage opportunities to nearly rational decision-making, providing bounds on collective assessments and stochastic choice deviations, thus bridging arbitrage principles with behavioral models.

Contribution

It introduces a principle of almost absence of arbitrage as equivalent to nearly rational behavior, connecting arbitrage bounds with opinion aggregation and stochastic choice models.

Findings

Bound the difference between collective and individual probabilistic assessments.

Translate arbitrage limitations into bounds on stochastic choice deviations.

Show equivalence between arbitrage principles and nearly rational decision-making.

Abstract

We establish the equivalence between a principle of almost absence of arbitrage opportunities and nearly rational decision-making. The implications of such principle are considered in the context of the aggregation of probabilistic opinions and of stochastic choice functions. In the former a bounded arbitrage principle and its equivalent form as an approximately Pareto condition are shown to bound the difference between the collective probabilistic assessment of a set of states and a linear aggregation rule on the individual assessments. In the latter we show that our general principle of limited arbitrage opportunities translates into a weakening of the McFadden-Richter axiom of stochastic rationality, and gives an upper bound for the minimum distance of a stochastic choice function to another in the class of random utility maximization models.