People are often reluctant to sell a house, or shares of stock, below the price at which they originally bought it. While this is generally not consistent with rational utility maximization, it does reflect two strong empirical regularities that are central to the behavioral science of human decision-making: a tendency to evaluate outcomes relative to a reference point determined by context (in this case the original purchase price), and the phenomenon of loss aversion in which people are particularly prone to avoid outcomes below the reference point. Here we explore the implications of reference points and loss aversion in optimal stopping problems, where people evaluate a sequence of options in one pass, either accepting the option and stopping the search or giving up on the option forever. The best option seen so far sets a reference point that shifts as the search progresses, and a biased decision-maker's utility incurs an additional penalty when they accept a later option that is below this reference point. We formulate and study a behaviorally well-motivated version of the optimal stopping problem that incorporates these notions of reference dependence and loss aversion. We obtain tight bounds on the performance of a biased agent in this model relative to the best option obtainable in retrospect (a type of prophet inequality for biased agents), as well as tight bounds on the ratio between the performance of a biased agent and the performance of a rational one. We further establish basic monotonicity results, and show an exponential gap between the performance of a biased agent in a stopping problem with respect to a worst-case versus a random order. As part of this, we establish fundamental differences between optimal stopping problems for rational versus biased agents, and these differences inform our analysis.
翻译:通常人们不愿意出售房屋或股票,低于他们最初购买房屋或股票的价格。虽然这通常不符合理性的效用最大化,但确实反映了两种强有力的经验规律,对于人类决策的行为科学至关重要:相对于背景确定的参考点(在本案中是原始购买价格)评价结果的倾向,以及人们特别容易避免低于参考点的结果的损失厌恶现象。我们在这里探讨参考点和损失厌恶对最佳制止问题的最佳弥补作用的影响,在这种情况下,人们评价一种选择的顺序,要么接受选择,停止搜索,要么永远放弃基本选择。迄今为止,最好的选择设定了一个参照点,随着搜索的进展而变化,偏向决策者的效用在后来接受低于这一参考点的一个选择时将受到额外的惩罚。我们制定并研究一种具有良好动机的最佳解决办法,即最佳制止问题,包括参考依赖和损失对立概念。我们从这一模型中评估一个有偏见的代理人的表现,相对于最佳选择,要么停止搜索,要么永远放弃基本选择,要么永远放弃基本选择。我们所看到的最佳选择,一个有偏向的代理人的性表现,一种我们先行,一种先行,先行,先行,先行,先行,先行,先行,先行,先行,先行,先行,先行,先行,先行,先行,后行,先行,先行,后行,先行,先行,先行,后行,先行,后行,然后行,先行,先行,先行,后行,后行,先行,后行,先行,后行,然后行,然后行,后行,后行,后行,后行,后行,后行,后行,先行,后行,后行,后行,后行,先行,先行,后行,先行,后行,后行,后行,先行,后行,后行,后行,先行,后行,后行,后行,后行,后行,先行,先行,后行,后行,先行,后行,后行,后行,后行。,后行。,后行。,后行。。。。。,先行,先行,先行,后行,后行。,先行,后行,后行,先行,后行,先行,先行,后行,