Abstract-In this paper, we propose a role adaptation method for human-robot shared control. Game theory is employed for fundamental analysis of this two-agent system. An adaptation law is developed such that the robot is able to adjust its own role according to the human's intention to lead or follow, which is inferred through the measured interaction force. In the absence of human interaction forces, the adaptive scheme allows the robot to take the lead and complete the task by itself. On the other hand, when the human persistently exerts strong forces that signal an unambiguous intent to lead, the robot yields and becomes the follower. Additionally, the full spectrum of mixed roles between these extreme scenarios is afforded by continuous online update of the control that is shared between both agents. Theoretical analysis shows that the resulting shared control is optimal with respect to a two-agent coordination game. Experimental results illustrate better overall performance, in terms of both error and effort, compared to fixed-role interactions.