With China and the US MAD applies to virtually any movement. Traditional warfare is out of the question, nuclear weapons are so prevalent in their armed forces that it would quite literally be a world ending conflict (at least from the non-aquatic species over view, as even a minor nuclear conflict is considered capable of seriously disrupting modern civilization).

However non-traditional warfare like the Cold War is similarly completely out of the question. The Cold War dragged on for so long because the USA and USSR were economically independent of each other, they both had mega-quantities of resources and production in their respective regions of control. They couldn't fight outright, but they had enough resources to supply everyone else to do the fighting.

Yet the US-Chinese economies are so intrinsically connected that a war would cause immediate trade embargoes between the countries and would cause an all-out collapse of the respective economies. US desperately relies on Chinese manufacturing for everything from what we wipe our arses with to our knives, computers and even a large part of our ship production (civilian and military production both reside squarely within China's region of control). Similarly China relies wholly on US and European dollars to even have a sustainable economy.

We're not talking $1 trillion in cold hard cash likes some uber-lottery, we're talking a likely payout over the next 50-100+ years. It would be more advantageous for China and the US to team up to extract the resources than to even think about arguing over them.