纠正了睡美人问题中关于理性决策的常见误解
Sleeping Kelly
- 区分了事前与自我指涉最优下注策略并证明其一致
- 渐近最优策略下三分之一派可避免时间悖论，二分之一派仍会陷入
- 为信念更新与决策合理性提供了新视角，适合哲学与概率学习者
睡美人问题是一个关于不完全记忆的经典难题，长期引发关注。以往研究常假设睡美人应最大化赌注的期望价值来判断决策是否理性，但这一假设存在错误。本文证明：(1) 睡美人的事前最优下注策略与自我指涉最优策略完全一致；(2) 在渐近最优下注策略下，作为三分之一体派的她可免于时间性荷兰赌，而作为二分之一派则仍易受困。研究揭示了信念更新与理性决策之间的深层联系。
原文摘要 · Abstract (English)
The Sleeping Beauty problem is a problem of imperfect recall that has received considerable attention. One approach to resolving the Sleeping Beauty problem has been to allow Sleeping Beauty to make decisions based on her beliefs, and then characterize what it takes for her decisions to be "rational". In particular, she can be allowed to make monetary bets based on her beliefs, with the assumption that she wants to gain wealth rather than lose it. However, this approach is often coupled with the erroneous assumption that Sleeping Beauty should maximize the expected value of her bets. Here, we show that (1) Sleeping Beauty's ex ante optimal betting strategy and de se optimal betting strategy are identical, and (2) under an asymptotically optimal betting strategy Sleeping Beauty is invulnerable to diachronic Dutch Books as a Thirder but remains vulnerable as a Halfer.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。