Zero-Sum Games and Halting Problem

Wikipedia states on the page of the halting problem, “For any program f that might determine if programs halt, a “pathological” program g called with an input can pass its own source and its input to f and then specifically do the opposite of what f predicts g will do.”

Suppose we have 2 neural networks, approximating f and g (allowing infinite size and depth limits). Is it wrong to assume that these two NNs can participate in a zero-sum game against each other, and that the Nash equilibrium (if it exists) of these 2 NNs contains the solution to the halting problem?