What happens if both players resign at the same time?

According to my rule book, it really depends on the type of chocolate... sometimes it is a stalemate, sometimes you even win.

I agree 2 players could see the game differently and want to resign at the same time. (Also one player might want to resign as he is so short of time say less 2 seconds so resigns even if he has an advantage – though I think most people would play until they run out of time.) 

In correspondence chess, there are some players who resign very early say on move 5 for reasons other than because of the game eg want to reduce their points etc. (Some such players even resign on move 1 in several of their games.) So two such players could be playing each other and want to resign on the same move. May be in theory they could resign at exactly the same time and requests to server to resign are reached at exactly the same time?

Depending on the quality of the chocolate? 

The trouble if going back in time is allowed (!) then your opponent could do the same and also go back in time. So both of you would be constantly be going back in time. I don't know if a game then would ever finish.

If I could go back in time, I would be playing lottery instead of chess. 

 I agree and if I were the TD/Arbiter I would score a loss to them both.

I take your point. But if everyone could go back in time, you probably would not win anything on the lottery

I forgot people can calculate couple moves away in chess forums, and blundered. 

Even I know you couldn't force somebody not to resign. Cripes! What could be a possible penalty for resigning against your opponent's will? 

 I was trying to make a question as silly as the one in this thread......

But the player who is actually losing won't want to play on and would prefer it to be called a draw.

i think they both win ....looooool

nah, these things never happen...

http://www.youtube.com/watch?v=fxApKBCUJkg

I'll give you one such scenario.

A beginner had been taught that he/she should always resign one move from a checkmate position.

However, this beginner is winning and is one move away from checkmating his/her opponent and hence resigns :S His/her opponent resigns too because they will lose in one move.

Voila.

would they get 0 points for each player?

double forfeit. this can also happen if both players are really noisy and don't stop after a warning, usually in kids tournaments. i saw it happen once

It happend to me

You can actually resign when it's your opponent's turn

 both sides lose

In Ignatz vs Marco, 1902, we almost had the mutual resignation situation:

In this position, Black decided that he was going to lose his pinned Bishop on d4, and he resigned. If he had spotted it, he had a rather better move, though...