A novel learning model from play-mode to learning-mode as broken symmetry of play states

The objective of this study is to construct a model based on the idea, "the mode transition from child\´s playful state (thereinafter "play-mode") to learning state (thereinafter "learning-mode")" and analyzes it by using the mean field approximation. To accomplish our objective, we introduce an agent-model with several parameters such as reward by play and interaction with other agents, which can choose one out of three play states with certain probability. The key results of our study are as follows; (1) The result of critical point analysis showed that there existed the solution of mode transition from play-mode to learning-mode. (2) The result of numerical calculation indicated that there existed two solutions of learning-mode in a certain regime of interaction with each play state. (3) The detailed analysis of the critical point suggested that the magnitude of interaction with other agents promoted the mode transition.