Power laws derived from a bayesian decision-making model in non-stationary environments

Shuji Shinohara*, Nobuhito Manome, Yoshihiro Nakajima, Yukio Pegio Gunji, Toru Moriyama, Hiroshi Okamoto, Shunji Mitsuyoshi, Ung Il Chung

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Article number718
Issue number4
Publication statusPublished - 2021 Apr


  • Active assumption
  • Bayesian inference
  • Decision-making
  • Imitation game
  • Non-stationary environments
  • Power law

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)


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