War in a dystopian setting
In a world where there is ever-declining population due to a phenomenon that has no satisfactory explanation, what could cause war or large-scale armed confrontations between countries or sections of the society?
Assumptions:
* No births have happened for a while. No new pregnancies are happening.
* The cause for this population decline is unknown and there is no apparent cure/solution.
* The decline is unstoppable; humanity will soon be extinct.
Given that humans realize they will soon be gone for good, what could create a situation where human lives are intentionally harmed?
EDIT:
I noticed that I need to word my question better, so I'll add here what I posted in a comment.
Most of the answers so far assume the worst of humanity; stuff like "Might as well do anything I want, since I'll die one day". The thing is, that is true for all humans even now. Why would the possibility of there being zero humans a few decades from now foment conflict today?
For additional clarity, consider the following:
* The realization that there are more humans dying that those being born sinks in slowly. 934
This isn't a T-virus/asteroid/alien invasion scenario, where humanity is given a few weeks till extinction.
* For most people, news about economic indicators like labor costs or population decline isn't worth a lot of attention. So it's conceivable they carry on with their lives (for what I assume will be quite a while) until this starts affecting them personally. By then, governments & society are likely to grasp the fact that every human life is "precious", much like tigers or pandas today.
So, I guess my question is, when governments are actively engaged in (however futile) efforts directed towards conservation of human life, what would cause war or any armed conflict between humans?
EDIT 2:
A lot of excellent answers. I'm going to have to pick out elements from each answer and cook up a cascading series of events that form the basis for some bitter resentment between the principal actors and a spark that starts the fire.
If only I could accept more than one answer... 934