OK, assume infinite resources, but the attacker only has one missile, and the defender only has one interceptor.

Optimal strategy for the attacker: Figure out how fast the interceptor can reach your missile, and have it split into a dozen warheads on different trajectories a mile before that. Include the blast radius of the interceptor in the calculation in case the defender decides to set of high-altitude nukes to defend itself against your missile.

The non-proliferation treaties we just pulled out of banned multi-warhead ICBMs decades ago because there's no feasible counter-move. That's bad for the missile business.

Back in reality, the attacker just builds 100,000 conventional drones, and 1 identical looking one with a nuke in it. Eventually, the defender runs out of interceptors, so the intercept probability trends to 0. At that point, the attacker sends the nuke without varying the behavior of the conventional drones.