序贯渐近学习的速度
The speed of sequential asymptotic learning
摘要：
在经典的羊群文学中，代理人收到一个关于二元自然状态的私人信号，并在观察其前任的行为后依次选择一个行为。当私人信号的信息量是无限的，它是已知的，代理收敛到正确的行动和正确的信念。我们研究如何快速收敛发生，并表明，它发生得更慢，比代理观察信号时。然而，我们还表明，从动作中学习的速度可以任意接近从信号中学习的速度。特别是，直到代理停止采取错误行动的预期时间可以是有限的或无限的，这取决于私人信号分布。在高斯私人信号的典型情况下，我们精确地计算了收敛速度，并明确表明，在这种情况下，从动作中学习比从信号中学习要慢得多。
英文摘要：
In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more slowly than it does when agents observe signals. However, we also show that the speed of learning from actions can be arbitrarily close to the speed of learning from signals. In particular, the expected time until the agents stop taking the wrong action can be either finite or infinite, depending on the private signal distribution. In the canonical case of Gaussian private signals we calculate the speed of convergence precisely, and show explicitly that, in this case, learning from actions is significantly slower than learning from signals.
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