scholarly journals Opportunity Costs in the Game of Best Choice

10.37236/8322 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Madeline Crews ◽  
Brant Jones ◽  
Kaitlyn Myers ◽  
Laura Taalman ◽  
Michael Urbanski ◽  
...  
Keyword(s):  
Decision Making ◽  
Classical Case ◽  
Secretary Problem ◽  
Sequential Decision Making ◽  
Opportunity Costs ◽  
Sequential Decision ◽  
Probability Of Success ◽  
Uniform Model ◽  
Weighted Model ◽  
Over Time

The game of best choice, also known as the secretary problem, is a model for sequential decision making with many variations in the literature. Notably, the classical setup assumes that the sequence of candidate rankings is uniformly distributed over time and that there is no expense associated with the candidate interviews. Here, we weight each ranking permutation according to the position of the best candidate in order to model costs incurred from conducting interviews with candidates that are ultimately not hired. We compare our weighted model with the classical (uniform) model via a limiting process. It turns out that imposing even infinitesimal costs on the interviews results in a probability of success that is about 28%, as opposed to 1/e (about 37%) in the classical case.

scholarly journals Subjective optimality in finite sequential decision-making

2021 ◽  
Vol 17 (12) ◽  
pp. e1009633
Author(s):  
Yeonju Sin ◽  
HeeYoung Seon ◽  
Yun Kyoung Shin ◽  
Oh-Sang Kwon ◽  
Dongil Chung
Keyword(s):  
Decision Making ◽  
Time Window ◽  
Programming Model ◽  
Secretary Problem ◽  
Optimal Decision ◽  
Sequential Decision Making ◽  
Sequential Decision ◽  
Model Based ◽  
Subjective Valuation ◽  
Optimal Decision Making

Many decisions in life are sequential and constrained by a time window. Although mathematically derived optimal solutions exist, it has been reported that humans often deviate from making optimal choices. Here, we used a secretary problem, a classic example of finite sequential decision-making, and investigated the mechanisms underlying individuals’ suboptimal choices. Across three independent experiments, we found that a dynamic programming model comprising subjective value function explains individuals’ deviations from optimality and predicts the choice behaviors under fewer and more opportunities. We further identified that pupil dilation reflected the levels of decision difficulty and subsequent choices to accept or reject the stimulus at each opportunity. The value sensitivity, a model-based estimate that characterizes each individual’s subjective valuation, correlated with the extent to which individuals’ physiological responses tracked stimuli information. Our results provide model-based and physiological evidence for subjective valuation in finite sequential decision-making, rediscovering human suboptimality in subjectively optimal decision-making processes.

scholarly journals Subjective optimality in finite sequential decision-making

2020 ◽  
Author(s):  
Yeonju Shin ◽  
HeeYoung Seon ◽  
Yun Kyoung Shin ◽  
Oh-Sang Kwon ◽  
Dongil Chung
Keyword(s):  
Decision Making ◽  
Time Window ◽  
Programming Model ◽  
Secretary Problem ◽  
Optimal Decision ◽  
Sequential Decision Making ◽  
Sequential Decision ◽  
Model Based ◽  
Subjective Valuation ◽  
Optimal Decision Making

AbstractMany decisions in life are sequential and constrained by a time window. Although mathematically derived optimal solutions exist, it has been reported that humans often deviate from making optimal choices. Here, we used a secretary problem, a classic example of finite sequential decision-making, and investigated the mechanisms underlying individuals’ suboptimal choices. Across three independent experiments, we found that a dynamic programming model comprising subjective value function explains individuals’ deviations from optimality and predicts the choice behaviors under fewer opportunities. We further identified that pupil dilation reflected the levels of decision difficulty and subsequent choices to accept or reject the stimulus at each opportunity. The value sensitivity, a model-based estimate that characterizes each individual’s subjective valuation, correlated with the extent to which individuals’ physiological responses tracked stimuli information. Our results provide model-based and physiological evidence for subjective valuation in finite sequential decision-making, rediscovering human suboptimality in subjectively optimal decision-making processes.

scholarly journals Optimal Policies for Quantum Markov Decision Processes

2021 ◽  
Author(s):  
Ming-Sheng Ying ◽  
Yuan Feng ◽  
Sheng-Gang Ying
Keyword(s):  
Decision Making ◽  
Reinforcement Learning ◽  
Quantum Systems ◽  
Sequential Decision Making ◽  
Mathematical Framework ◽  
Sequential Decision ◽  
Learning Techniques ◽  
Optimal Policies ◽  
Markov Decision ◽  
Programming Algorithms

AbstractMarkov decision process (MDP) offers a general framework for modelling sequential decision making where outcomes are random. In particular, it serves as a mathematical framework for reinforcement learning. This paper introduces an extension of MDP, namely quantum MDP (qMDP), that can serve as a mathematical model of decision making about quantum systems. We develop dynamic programming algorithms for policy evaluation and finding optimal policies for qMDPs in the case of finite-horizon. The results obtained in this paper provide some useful mathematical tools for reinforcement learning techniques applied to the quantum world.

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