in general, higher testosterone in response to the opposite sex means men take higher risks, like doing risky tricks and stunts to impress. Think, a bunch of guys in a skate park in front of a group of girls.

I understand your point, however, my point is that there is a selflessness in the above example. Along the same vein, a man will offer to pay just to show off.

Both paying and stunts are in response to how testosterone promotes risk taking.

Two different things. Testosterone leads to narcicism leads to increased selfishness along a continuum. However testosterone also increases risk taking. Since giving away stuff and offering to pay is high risk, it happens more often in situations where men have increased testosterone due to the presense of the opposite sex.