Resolving Feynman's restaurant problem reveals optimal solutions and human strategies

Area of Science:

• Decision-making
• Cognitive psychology
• Mathematical optimization

Background:

• Richard Feynman proposed an optimization problem regarding dish selection over multiple meals in the 1970s.
• Feynman's handwritten notes and solution remained undeciphered for decades, posing a challenge in decision-making research.

Purpose of the Study:

• To decipher and present Richard Feynman's optimization problem and its solution.
• To analyze the optimality of the solution and generalize it to related problems.
• To compare the theoretical solution with human decision-making behavior in similar scenarios.

Main Methods:

• Deciphering Feynman's handwritten notes to present the optimal dish selection strategy.
• Mathematical proof to establish the optimality of the derived policy.
• Generalization of the solution to related optimal stopping problems.
• Conducting a preregistered experiment with 2,520 participants to observe human behavior.

Main Results:

• The optimal policy involves decreasing thresholds for exploring new dishes versus exploiting known ones, influenced by dish quality distribution.
• Human participants exhibited linear thresholds decreasing with remaining trials, aligning with optimal stopping theory.
• Participants explored more than predicted by linear thresholds, and threshold intercepts varied with quality distributions.

Conclusions:

• Feynman's problem provides insights into optimal stopping strategies and decision-making under uncertainty.
• Human decision-making in optimal stopping tasks is sensitive to the distribution of option quality, employing a nearly optimal linear strategy.
• The study bridges mathematical optimization with psychological understanding of human choices.