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Game theory isn't mathematics it is economics and like all economic theory it focuses on mathematical models that ignore the foundational underlying philosophical assumptions.
Game theory is a branch of mathematics.
It is often dubiously applied to economics, political science, foreign policy, etc.
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In your second sentence you include not only assumptions about human behavior and reasoning but assumptions concerning the mechanismism of natural selection, assumptions about the necessity of competition and assumptions about scarcity of resources. All fairly significant assumptions.
It does not contain assumptions about human behaviour. It is trying to argue a point on human behaviour using certain premises, which are arguable but not strictly assumptive because there are very good reasons to think they are true. Some justification was provided in an earlier post.
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As I have consistently stated there is a distinct diffe3rence in stating that humanity is naturally violent and humans have the capacity to behave in a violnet manner, the first statement is deterministic the second is probabalistic.
I think this is wrong, but is a mistake being made by a lot of people in this thread. Natural tendencies are not deterministic. Most people, when they meet an attractive member of the opposite sex, have a natural tendency to want to mate with that person. That inclination is overridden in almost all cases by social and moral rules we have accepted.
If humans contain an inherited instinct to be tribal, as I suggested above, including an instinct to be hostile toward people who are not members of one's tribe, then it doesn't mean violence is inevitable, nor excuse it when it happens. It does, however, have implications in how the problem can be dealt with.