TY - JOUR

T1 - Optimal Stopping with Behaviorally Biased Agents: The Role of Loss Aversion and Changing Reference Points

AU - Kleinberg, Jon

AU - Kleinberg, Robert

AU - Oren, Sigal

PY - 2021/6/1

Y1 - 2021/6/1

N2 - 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.

AB - 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.

KW - Computer Science - Computer Science and Game Theory

KW - Computer Science - Data Structures and Algorithms

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JO - arxiv cs.GT

JF - arxiv cs.GT

ER -