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L\'evy walks are found in the migratory behaviour patterns of variousorganisms, and the reason for this phenomenon has been much discussed. We usesimulations to demonstrate that learning causes the changes in confidence levelduring decision-making in non-stationary environments, and results inL\'evy-walk-like patterns. One inference algorithm involving confidence isBayesian inference. We propose an algorithm that introduces the effects oflearning and forgetting into Bayesian inference, and simulate an imitation gamein which two decision-making agents incorporating the algorithm estimate eachother's internal models from their opponent's observational data. Forforgetting without learning, agent confidence levels remained low due to a lackof information on the counterpart and Brownian walks occurred for a wide rangeof forgetting rates. Conversely, when learning was introduced, high confidencelevels occasionally occurred even at high forgetting rates, and Brownian walksuniversally became L\'evy walks through a mixture of high- and low-confidencestates.

L\'evy walks derived from a Bayesian decision-making model in non-stationary environments