If there is a Mexican standoff in which three gunslingers are arranged so that everyone has a gun pointed at them at point blank range, the situation becomes very tricky, in that the most likely situation in the event that someone fires is that the only person who survives is the second person who shoots. This is a problem for anyone involved who might want to take initiative to resolve the situation by shooting his hostage. Ask anyone if they would do something that resulted in them almost assuredly getting shot in the head, and I bet you they would answer in the negative.
The reason that you can't be the first person to shoot and still survive usually is that the person you'd be shooting is the one pointing a gun at the person who's pointing a gun at your head and insuring that he doesn't fire. As soon as you shoot, he has a brief period of time where he can safely shoot you without getting killed himself. There are several ways to work around this problem, though.
First of all, the nice solution to this problem, if there's enough open space, would be for everyone to reach an agreement where all involved agree to disagree, then slowly back away in opposite directions until they are so far away from each other that they are no longer a threat, or are at least able to engage in a gun battle with a less certain outcome. However, the kind of people who get into Mexican standoffs are probably not that nice.
A meaner way to deal with this problem, if it's feasible, is to convince the guy pointing a gun at your head that the correct person he should be aiming for is the fucking asshole who's pointing a gun at his head, and not you, who's on his side (after all, are YOU the fucker pointing a gun at his head? NO.) Of course, he'll be reluctant to do this, because the guy is pointing a gun at his head, but explain to him that you'll just shoot the guy, it can all be over with, and life can go on (well, except for the guy whose brains are all over the ground.) You also risk the person you're pointing the gun at successfully arguing that YOU in fact are the asshole, in which case he thought up the absolute meanest solution, which is to just say to the guy you're pointing a gun at "I don't care. Shoot him. See if I give a fuck!" Bonus points for total depravity are given if you proceed to shoot the person who tries to see if you do, in fact, give a fuck. Note that, of course, using these ideas could backfire and get you shot, but getting shot could happen at any time anyways, obviously.
Of course, you could try shooting the guy and really quickly shooting the other guy. Don't do this. You aren't fast enough. You will die.
One good option is to wait around until some outside person encounters the standoff. Hopefully, this is a friend with huge muscles and a couple bullet belts attached to two state-of-the-art fully automatic machine guns, but you should take what you can get. Police arrival might be deterimental to all involved if you're the kind of people who shoot other people, so perhaps their arrival could break the tension and convince everyone to just split.
All in all, I try to avoid Mexican standoffs in life.