  L\'evy walks are found in the migratory behaviour patterns of various
organisms, and the reason for this phenomenon has been much discussed. We use
simulations to demonstrate that learning causes the changes in confidence level
during decision-making in non-stationary environments, and results in
L\'evy-walk-like patterns. One inference algorithm involving confidence is
Bayesian inference. We propose an algorithm that introduces the effects of
learning and forgetting into Bayesian inference, and simulate an imitation game
in which two decision-making agents incorporating the algorithm estimate each
other's internal models from their opponent's observational data. For
forgetting without learning, agent confidence levels remained low due to a lack
of information on the counterpart and Brownian walks occurred for a wide range
of forgetting rates. Conversely, when learning was introduced, high confidence
levels occasionally occurred even at high forgetting rates, and Brownian walks
universally became L\'evy walks through a mixture of high- and low-confidence
states.
