Application of an Iterated Function System with Dynamic Selection Probability to Deliberative Decision-Making

A simple model of learning that describes changes in an animal’s behavior based on its actions and rewards from the environment was analyzed by Karlin in 1953. The model can be formulated as an iterated function system with state-dependent probability. To develop a simple mathematical model of learning in which animals repeatedly alternate strategies between exploitation and exploration, we extend the Karlin model by introducing time- and state-dependent selection probabilities. The fractal nature shown in the probability measure is discussed.