Eventually we will run out of resources such as gas and that will lead to World war 3.
Eh, while I'm certainly a strong supporter of conservation and efficiency the threat of "peak oil" and what not isn't nearly as dire as many people make it sound. At the moment technology is being developed that allows gas and oil (or alternatives) to be obtained from algae and similar life. While far less environmentally pleasant the technology also exists to extract oil from oil shale.
Why don't we do this now? Well the first case is still fairly experimental, some of the technology is proven but still several years away from being commercially viable. The second case is potentially viable but at its current state requires mining the rock and then processing it, which basically requires strip mining huge swaths of land. Even the developers of the technology don't like the idea of this so the technology is pretty much being kept on the back burner while they try to develop a way of cooking or processing the oil shale without mining it.
The point of this science lesson? Even if we had a sudden crisis of natural resources right now there exists technology to alleviate it - however without a critical situation its best not to use it. Given another decade or so and far cleaner and greener technologies will likely exist . . . it will probably take longer for them to become commercially viable but if there was a sudden crisis with conventional oil they would give us very solid options.
Being able to produce oil and fuel in this manner wouldn't be able to solve a critical situation by themselves but the energy sector has known for some time that the future would require diversification and this is being pursued. Of course the problem with diversification is it takes longer for any individual technology to prove itself and far more technologies are required to have much impact. But again while this will
likely keep them in the background for some time a resource crisis would certainly expedite their arrival.
As such I don't see a Fallout-esq resource wars situation leading to another World War. This isn't to say there couldn't be some other spark for global war, but even in this case I don't see a Fallout-esq situation deriving from it. The possibility of nuclear armageddon should never be ignored but its wildly unlikely.