  This paper focuses on investigating the optimal actuator location for
achieving minimum norm controls in the context of approximate controllability
for degenerate parabolic equations. We propose a formulation of the
optimization problem that encompasses both the actuator location and its
associated minimum norm control. Specifically, we transform the problem into a
two-person zero-sum game problem, resulting in the development of four
equivalent formulations. Finally, we establish the crucial result that the
solution to the relaxed optimization problem serves as an optimal actuator
location for the classical problem.
