Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments
Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments
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DOI：
10.3390/sym13040718
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发表时间：
2021-04
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影响因子：
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通讯作者：
Shuji Shinohara;Nobuhito Manome;Y. Nakajima;Y. Gunji;Toru Moriyama;Hiroshi Okamoto;S. Mitsuyoshi;Ung-il Chung
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文献类型：
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作者：
Shuji Shinohara;Nobuhito Manome;Y. Nakajima;Y. Gunji;Toru Moriyama;Hiroshi Okamoto;S. Mitsuyoshi;Ung-il Chung
包括人类在内的各种生物的迁移行为中步长出现的频率的特征在于幂律分布。这种行为模式被称为Lévy walk，这种现象的原因已经被广泛研究。特别是在人类中，一种可能性是这种模式反映了一个人选择行为的自信心的变化。我们用模拟来证明，积极的假设导致的信心水平在一个人的选择缺乏信息的情况下的变化。更具体地说，我们提出了一种算法，引入学习和遗忘的影响贝叶斯推理，并模拟了模仿游戏，其中两个决策代理将算法估计对方的内部模型。对于遗忘而不学习，每个代理人的信心水平在自己的估计仍然很低，由于缺乏信息的对手，和代理人经常改变他们的假设对对手，和频率分布的持续时间的假设遵循指数分布的遗忘率范围很广。相反，当引入学习时，即使在高遗忘率下也偶尔会出现高置信水平，指数分布普遍变成幂律分布。
The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution.