I wonder if results would be different if cooperation would result in a loss (as opposed to merely smaller reward).

Psychologically, it's much easier to forgo additional reward than to give up what you already have.

People have tendency to strongly prefer avoiding losses to acquiring gains:

http://en.wikipedia.org/wiki/Loss_aversion

That's a very interesting study.

Preachers have known this for years of course, which is why any request to donate is always preceded by a healthy reminder on the benefits of altruism.