The content presents a lateral-thinking puzzle by Michael Rabin involving a world where poisons have strange properties. In this world, a healthy person who ingests a poison will die within an hour unless they ingest a stronger poison, which will restore their health. There are two types of poisons - magical and medical - that are strictly linearly ordered in strength.
The King wants to find the strongest poison in the land, so he summons the Royal Magician and the Royal Physician and instructs them to each bring their strongest poison to a showdown. The catch is that they must first drink the other's poison before drinking their own. The survivor will be the one with the stronger poison.
The author analyzes several possible strategies the Servants could employ, including:
The author shows that there are three ways, other than the intended "A-versus-A" scenario, in which both Servants could die from poisoning. The author then applies game theory to analyze the optimal strategies, finding that there are multiple Nash equilibria with varying survival probabilities.
The content concludes by noting that the puzzle admits further subtleties and unanswered questions, particularly when more than two poisons are available, and suggests the possibility of an empirical investigation through a tournament-style setup.
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by Timothy Y. C... às arxiv.org 04-09-2024
https://arxiv.org/pdf/2404.05053.pdfPerguntas Mais Profundas