Recently, collaborative robots have begun to train humans to achieve complex tasks, and the mutual information exchange between them can lead to successful robot-human collaborations. In this paper we demonstrate the application and effectiveness of a new approach called mutual reinforcement learning (MRL), where both humans and autonomous agents act as reinforcement learners in a skill transfer scenario over continuous communication and feedback. An autonomous agent initially acts as an instructor who can teach a novice human participant complex skills using the MRL strategy. While teaching skills in a physical (block-building) ($n=34$) or simulated (Tetris) environment ($n=31$), the expert tries to identify appropriate reward channels preferred by each individual and adapts itself accordingly using an exploration-exploitation strategy. These reward channel preferences can identify important behaviors of the human participants, because they may well exercise the same behaviors in similar situations later. In this way, skill transfer takes place between an expert system and a novice human operator. We divided the subject population into three groups and observed the skill transfer phenomenon, analyzing it with Simpson"s psychometric model. 5-point Likert scales were also used to identify the cognitive models of the human participants. We obtained a shared cognitive model which not only improves human cognition but enhances the robot's cognitive strategy to understand the mental model of its human partners while building a successful robot-human collaborative framework.