Optimizing Sequential Decisions: Enhancements to the Brickman Principle with Cumulative Punishment and Probability Adjustments

Introduction Determining the optimal stopping point in sequential decision-making scenarios is crucial for maximizing rewards and minimizing costs. Traditional models like the original Brickman Principle often simplify this process by assuming fixed critical values and equal probabilities at each decision stage. These assumptions may not accurately reflect real-world complexities, where costs can be cumulative and probabilities variable. Objective This work seeks to enhance the Brickman Principle by including cumulative punishment elements and non-uniform probability distributions, therefore improving its capacity to accurately represent the intricacies of real-world decision-making. Methods Through a rigorous experimental study, we evaluate the impact of these modifications on optimal stopping rules and expected profits. Results In line with Prospect Theory's emphasis on loss aversion, the results reveal a distinct pattern of risk-averse behavior, with most participants choosing to stop sooner in the sequence to avoid growing fines. Furthermore, we saw substantial variation in both the termination points and anticipated earnings across participants, suggesting that individual disparities in risk tolerance and decision-making approaches are crucial in influencing results