Anonymity in Predicting the Future
Anonymity in Predicting the Future
复制标题
匿名预测未来
DOI：
10.4169/amer.math.monthly.123.08.777
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Daniel J. Velleman
中科院分区：
文献类型：
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作者：
Dvij Bajpai;Daniel J. Velleman
考虑一个任意集合S和一个任意函数f：f → S。我们认为f的定义域代表时间，对于每一个x，我们认为f（x）是某个系统在时间x的状态。想象一下，在每个时刻x，有一个智能体可以看到f在（-∞，x）上的值，并试图猜测f（x）-换句话说，智能体试图从过去的历史中猜测系统的当前状态。在2008年的一篇论文中，克里斯托弗·哈丁和艾伦·泰勒使用选择公理构建了一个策略，智能体可以使用该策略来保证，对于每个函数f，除了可数的许多人之外，他们中的大多数人都会猜对。在2013年的一本专著中，他们介绍了匿名猜测策略的想法，在这种策略中，智能体可以看到过去，但不知道他们在时间上的位置。在本文中，我们考虑了一些匿名的变化。例如，如果除了不知道他们在时间上的位置之外，代理人也不知道时间进展的速率，那该怎么办？如果他们不知道任何两个事件之间的时间流逝了多少呢？我们表明，在某些情况下，代理商仍然可以猜到成功，而在其他情况下，他们表现得很差。
Abstract Consider an arbitrary set S and an arbitrary function f : ℝ → S. We think of the domain of f as representing time, and for each x ∊ ℝ, we think of f(x) as the state of some system at time x. Imagine that, at each time x, there is an agent who can see the values of f on (—∞, x) and is trying to guess f(x)—in other words, the agent is trying to guess the present state of the system from its past history. In a 2008 paper, Christopher Hardin and Alan Taylor use the axiom of choice to construct a strategy that the agents can use to guarantee that, for every function f, all but countably many of them will guess correctly. In a 2013 monograph, they introduce the idea of anonymous guessing strategies, in which the agents can see the past but don't know where they are located in time. In this paper, we consider a number of variations on anonymity. For instance, what if, in addition to not knowing where they are located in time, agents also do not know the rate at which time is progressing? What if they have no sense of how much time elapses between any two events? We show that in some cases agents can still guess successfully, while in others they perform very poorly.