A/N muchos props for this go to garretelliot for beta'ing it, and to John Nash, while I've only seen the guy in passing once, he's cool, and I wouldn't have half this story without him. If you still haven't, I suggest checking out because while I try my best to explain it here, it's a lot easier to understand if you get game theory.
He sprawled out on the decrepit bed, rolling over his options. To go out there and say he wanted to die, or to go out there and say he didn't. What was it the psycho had said? Trust. Trust was the key. Did he trust Woody with his life, or not? Was he willing to risk his life? Probably. But was he willing to risk her life for his?
She was one of the few people that he could say he loved, she was a sister to him, one of his best friends, his closest confidante. He couldn't be responsible for her death, if she died, he couldn't handle it, because he would have had to say that he had chosen his life over hers.
And while he liked Woody well enough, he wasn't going to risk laying down his life while the detective would be free. Which left him in a bit of a trap. It either was lay down his life and risk Woody walking away unharmed, or risk killing her. But even if the three of them lived, an innocent man would die.
The only real question was Woody's decision, if he could figure out which one Woody was going to pick, it made his decision so much easier. The detective loved Jordan, he knew that, so he wouldn't want to see her dead. Which would mean that Woody would sacrifice himself. Unless of course, Woody thought that he would do the same.
But Woody, he didn't think, would plan for that. Woody would only have one thought, and that was keeping Jordan alive. He'd seen Woody play the self-preservationist before, but never before had those cases involved Jordan, everyone when it came down to it wanted to see themselves live and be the hero.
That's what the game was. Pitting the basic human need to survive against higher thought and emotion. Pitting his desire to survive against the what he felt for his friends and against the guilt of having an innocent man die because of his choice. Would he be an animal, devolved into his most basic instinct, or would he be a creature of higher thought?
He hadn't remembered why all this sounded so familiar until he had been locked into the room. He had seen this before, the whole game theory as the prisoner's dilemma. And the only thing he remembered was that the point of equilibrium for that one problem was that the prisoners both chose some jail time. It was the outcome that was the worst for both players but the one that a logical person would come to. The logical folks would choose to confess as it would mean that they would either get a free ride or five years where not confessing would risk life or a single year.
But for him the stakes were raised considerably. This wasn't a game put down on paper. This was his life. He could go out there and say he wanted to die, it would either be his life or the life of the innocent. If he went out there and said he wanted to live, it would either be Woody's life or Jordan's.
Was Jordan worth dying for? She was, but what about Woody's choice? Woody would pick to die, for sure, he was a cop, and all the cops he met, if they had to pick a way to go, would pick for a good cause, and saving someone else was certainly a good cause. So that left him with a choice, Woody or the innocent man.
Woody's death would break Jordan. She would be primed for Stiles if he died. And it would be Woody's death at his choice, he would kill Woody, and it would be just as bad as pulling the trigger himself because he knew how the other man was going to react. And he didn't want the guilt of not only killing a good friend, but seeing his best friend shattered by the death that he had caused.
No, if there was going to be blood shed, it was going to be that of the stranger's. His stomach rolled at the thought. This was what the killer wanted, to see him pick the rational choice of seeing the one he didn't know die. The killer wanted to see him become ruthless and cold, choosing to sacrifice the one that meant the least to him. The thought was sickening and he didn't want to see the killer win, but it was the only option, wasn't it? The best option given the circumstances, given an idea of another player and what they would pick. The Nash Equilibrium.