[Siegmund]

Fools rush in, etc etc... I'll take a stab at those two questions:

[ QUOTE ]

1) Does your decision affect the decisions of others playing the game. That is, if you choose to contribute rather than defect, does it have any affect on what the other 99 do.

2) Is it possible for the players in the game to play different strategies. For example, 80 choose to contribute and 20 choose to be a parasite.

[/ QUOTE ]

1) No. However, I have an awareness that whatever decision I am facing, the other players in the game are facing the same decision. My opponents have the same awareness. That is, if I am considering defecting, I know others are also considering defecting (and hoping for 99 people to cooperate while I defect is unrealistic.)

2) Ill-posed question: the first and second sentences use "strategy" differently. Here are three sub-answers:

2a) Trivially, yes, real-world players might make all sorts of stupid plays; but our interest is in sensible plays (where 'sensible' has not been firmly defined.)

2b) No; to answer your first sentence, for all sensible definitions of 'sensible', symmetric games have symmetric solutions. That is, everyone will play the same, possibly mixed, strategy.

2c) But 'playing the same (mixed) strategy' does not mean 'making the same move.' It's perfectly possible, for instance, for everyone to randomly choose parasite with probability .25 and cooperate with probability .75, and for this to result in 80 cooperators and 20 parasites.

The only dispute, really, is whether you are imagining each player optimizing only by partial derivatives, or imagining one big optimization where all the players' defection probabilities move at once. As we've seen, we arrive at different answers, both symmetric - a Nash solution of defection 31% of the time, or the superrational / "diagonally optimal" solution of defection 0% of the time.