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.

翻译：重复博弈序列为刻画人类或人工决策主体的风险偏好提供了一种实验工具。这种推断的难度取决于博弈的具体细节以及游戏迭代次数等因素。本文深入探讨了从有限重复博弈序列中观察人工主体选择行为来推断其风险偏好的实际挑战。我们开展研究的动机在于：对于重复加性博弈（其中收益与损失独立于当前财富）序列，最大化长期财富的策略与重复乘性博弈（其中收益与损失与当前财富成比例）的策略存在本质差异。要判断主体是否采用最优策略，需要对风险偏好进行精确测量。为泛化主体所面临的博弈类型，我们引入源于时序分析特征工程的约-约翰逊变换，构建了在加性与乘性情形之间平滑插值的博弈族。随后我们通过解析与数值方法分析了该博弈族的最优策略。研究发现：随着主体财富增加，区分其风险偏好的难度逐渐增大——这是因为当财富达到足够高水平时，不同风险偏好的主体最终会做出相同决策。我们认为这些发现对有效设计人类风险偏好测量实验具有指导意义。