We propose five original strategies of successively increasing complexity and efficiency that address a novel version of a classical mathematical problem that, in essence, focuses on the determination of an optimal protocol for exchanging limited amounts of information among a group of subjects with various prerogatives. The inherent intricacy of the problem�solving protocols eliminates the possibility to attain an analytical solution. Therefore, we implemented a large-scale simulation study to exhaustively search through an extensive list of competing algorithms associated with the above-mentioned 5 generally defined protocols. Our results show that the consecutive improvements in the average amount of time necessary for the strategy-specific problem-solving completion over the previous simpler and less advantageously structured designs were 18, 30, 12, and 9% respectively. The optimal multi-stage information exchange strategy allows for a successful execution of the task of interest in 1722 days (4.7 years) on average with standard deviation of 385 days. The execution of this protocol took as few as 1004 and as many as 4965 with median of 1616 days.
Barrett, Alexander S. and Rakovski, Cyril
"A Two-Light Version of the Classical Hundred Prisoners and a Light Bulb Problem: Optimizing Experimental Design through Simulations,"
e-Research: A Journal of Undergraduate Work: Vol. 2:
2, Article 5.
Available at: https://digitalcommons.chapman.edu/e-Research/vol2/iss2/5