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Like several of you, I found that serendip would mimic my last move.  I didn't play particularly systematically, though.  I usually won if I cooperated for several moves and then competed once or twice before reestablishing a pattern of cooperation (lulling serendip into a false sense of security ;) 

I also am not sure how to apply the game to real life.  All this talk of cooperation v. competition makes me think of communism v. capitalism - the former of which works in theory only, the latter of which can be unpalatable, but functional.  Individually, I tend to favor competition over cooperation - I think when people are in competition they try harder and do more interesting things. I don't advocate a cutthroat approach, though.  To me, all of this discussion is contained under the assumption that the players agree and adhere to the terms of the fight (that there is an expectation of fairness).  In which case, as with all interaction, the foundation is one of cooperation (we cooperate in agreeing to play).  Without this, all bets are off.