Compare the endings of two films by Quentin Tarantino - Pulp Fiction and Reservoir Dogs. Each film ends in a "truel" - three characters pointing guns at each other. In Reservoir Dogs, all three die. In Pulp Fiction, they resolve their problem peacefully. Why?
In Reservoir Dogs...
Joe is pointing a gun at Mr Orange. His position (column J) is that he should shoot Mr Orange (whom he rightly suspects of being a police spy) and no one else should shoot anyone. Mr White, however, has pulled a gun on Joe and threatened to shoot him if he shoots Mr Orange. At this, Eddie has pulled a gun on Mr White and threatened to shoot him if he shoots Joe.
It's clear, then, that Joe has another option, apart from shooting Mr Orange; it is to shoot Mr White first. He doesn't, however, threaten this or do it.
Mr White, if he carries out his threat to start shooting, will obviously try to shoot Eddie as well as Joe, since Eddie is threatening him. His position, however, is that no one should shoot anyone - Joe should lower his gun, Eddie his, then he will lower his and they should all leave their hide-out together. His threat is that if this isn't agreed, he'll shoot.
Eddie's position, before anyone pulled a gun, was the same as Joe's. After guns are pulled his position becomes unclear - he wants everyone to put guns down and talk. He states that if Mr White doesn't put his gun down (which would merely be a signal of intention not to take his option) he'll shoot him.
What actually happens is that Joe assumes Mr White is bluffing and therefore shoots Mr Orange. He must be assuming this, or he would take his second option first - i.e. he'd leave shooting Mr Orange till later, first shooting the one whose gun is pointed at him.
Mr White, however, isn't bluffing. He is, it transpires, an honorable character who, moved by moral indignation, has come momentarily to prefer the threatened shoot-out (column t, which does give him a chance of survival unhurt) to Joe's position (column J). Hence he triggers the shoot-out.
The shoot-out therefore happens because - (a) Joe can't believe (see the question-mark in column t) that Mr White is so honorable he will actually carry out his threat; (b) so Joe implements his postion by shooting Mr Orange, not believing it will trigger a shoot-out; (c) Mr White is momentarily so moved by honorable indignation that he prefers the shoot-out to letting Mr Orange be shot (the t-pointing arrow in Mr White's row); (d) Eddie obviously prefers to shoot Mr White if he starts shooting, since he's bound to shoot at him as well as Joe; (e) crucially, Joe doesn't attempt to sway Mr White with adequate rational arguments or do anything else to weaken his resolve, he simply goes ahead and puts it to the test.
Note: In the film, the shooting does occur in this order - Joe shoots Mr Orange; Mr White thereupon shoots Joe, then quickly shoots Eddie too; Eddie shoots Mr White at the same time as he himself is shot.
In Pulp Fiction...
Three characters again point guns. Jules is pointing at a young man who has just taken his wallet and a briefcase full of money. A young woman, the young man's accomplice, is pointing a gun at Jules while Vincent, Jules' colleague, is pointing a gun at her.
In this case, anyone who starts shooting will inevitably trigger the shoot-out (column t). When Jules shoots, he'll obviously try to shoot the young woman who has a gun pointing at him before shooting the young man, who has no gun. So it's two shooters (Jules & Vincent) against one (the young woman). She must try to shoot both of them - but will shoot Jules first, since she's pointing her gun at him. Thus, Vincent has a better chance of emerging unhurt than Jules. But as in Reservoir Dogs, no-one can be sure of emerging unhurt from the shoot-out.
Jules' position is a compromise: the young man should take the money ($1500) from Jules' wallet, together with all he has garnered from other people in the restaurant; he should leave the briefcase. Jules' tactics are excellent. He establishes psychological dominance, gives rational arguments for his position and makes it credible (even though it's untrue) that he would prefer a shoot-out to giving up the case by pointing out that the case belongs to a top gangster (whereas no one would believe that he'd prefer the shoot-out to losing his cash). By offering an attractive compromise he shakes the credibility of the young woman's threat. He is so successful that he wins the young man over to his position (column YM is the same as J), though the young man obviously started out at the young woman's position (column YW).
Note that the t-pointing arrow at J/YW represents the young woman's beliefs about Jules' preferences, not his actual ones.
The young woman's emotional tactic (hysteria) is also excellent, making her threat - the shoot-out if they don't get everything - extremely credible, despite the fact that she is out-gunned. She seems oblivious to rational arguments and offers of compromise. This is extremely effective, and would prevail against Jules (who is first in line to be shot by her) were it not that the young man, far from backing her up, switches over to Jules' position, obeys Jules' advice to tell her to calm down (the last thing she should do to maintain her position) and proceeds slowly to implement Jules' position, leaving her with a stark choice between this and the shoot-out and causing the first two arrows in her row to become double-headed (meaning a preference that's unclear).
Vincent's position is that the young man should get nothing, but he is put in the shade by Jules' arguments, so is finally willing to let him take the money (the arrow at Vincent/YW becomes double-headed).
The credibility of the young man's conversion to Jules' position (even though he must obviously prefer the young woman's) is enhanced by his showing fear. The young man has all the initiative in this situation. Whatever he does, they prefer to let him do it rather than risk the shoot-out.
The episode ends peaceably because the young man, instructed by Jules, implements Jules' position so slowly that neither Vincent nor the young woman are sufficiently carried away by emotion to prefer the shoot-out. Both, moreover, are influenced by Jules and the young man's soothing talk and rational, moralistic arguments (of the two, the young woman is the more emotional, Vincent the more morally outraged; neither emotion nor outrage suffices, however). Note, though, that the episode might have had a better chance of a peaceful ending if the young man had supported the young woman and slowly implemented her position (column YW) instead of Jules'. Her hysteria would surely have prevailed, since neither Jules nor Vincent would have wanted to risk their lives for the brief case. A peaceful ending would then have depended upon their rationality rather than hers - surely a more dependable foundation.
She and Jules are the strong ones; Vincent and the young man are weak. On the other hand, the young man commands the initiative; it is left to him to decide whose position is tried out.