Distinguishing Risk Preferences using Repeated Gambles

TL;DR

This paper investigates the challenges of inferring risk preferences from repeated gamble choices, highlighting how difficulty increases with wealth and proposing a generalized gamble model using the Yeo-Johnson transformation.

Contribution

It introduces a flexible family of gambles interpolating between additive and multiplicative cases and analyzes the difficulty of distinguishing risk preferences in these scenarios.

Findings

Distinguishing risk preferences becomes harder as wealth increases.

Agents with different risk preferences make similar decisions at high wealth levels.

The generalized gamble model helps in designing better experiments for measuring risk preferences.

Abstract

Sequences of repeated gambles provide an experimental tool to characterize the risk preferences of humans or artificial decision-making agents. The difficulty of this inference depends on factors including the details of the gambles offered and the number of iterations of the game played. In this paper we explore in detail the practical challenges of inferring risk preferences from the observed choices of artificial agents who are presented with finite sequences of repeated gambles. We are motivated by the fact that the strategy to maximize long-run wealth for sequences of repeated additive gambles (where gains and losses are independent of current wealth) is different to the strategy for repeated multiplicative gambles (where gains and losses are proportional to current wealth.) Accurate measurement of risk preferences would be needed to tell whether an agent is employing the optimal strategy or not. To generalize the types of gambles our agents face we use the Yeo-Johnson transformation, a tool borrowed from feature engineering for time series analysis, to construct a family of gambles that interpolates smoothly between the additive and multiplicative cases. We then analyze the optimal strategy for this family, both analytically and numerically. We find that it becomes increasingly difficult to distinguish the risk preferences of agents as their wealth increases. This is because agents with different risk preferences eventually make the same decisions for sufficiently high wealth. We believe that these findings are informative for the effective design of experiments to measure risk preferences in humans.