The Worst Good Trade

The teacher had taped the rules to the wall and then gone to deal with the buses, because everything outside was white and nobody was going home soon.

"It's a trading game," Maya said, reading. "Two players. Each one holds up a card. Cooperate or Defect. You don't show until the same second."

Soren read the payoff square out loud. "Both cooperate, you each get three points. Both defect, you each get one. But if I defect and you cooperate, I get five and you get zero."

"So defecting is greedy."

"Defecting is winning," Soren said. "Look. Whatever you do, I do better by defecting. If you cooperate, I get five instead of three. If you defect, I get one instead of zero. There's no situation where cooperating is better for me."

Maya tipped her head. "That's annoying."

"It's just true."

They played. Both slapped down Defect. One point each. They played again. Defect, Defect. One each.

"This is the worst game ever invented," Maya said. "We keep doing the smart thing and we keep getting one stupid point."

Soren stopped with his card halfway up. "Say that again."

"We keep doing the smart thing," Maya said, "and we keep losing."

He wrote the four numbers in a square in his notebook and looked at them. "There's a three sitting right there. Three and three. We could both have a three."

"So let's both cooperate."

"We can't," Soren said. "The second I trust you to cooperate, the best move for me is to defect and take the five. And you know that, so the best move for you is to defect first. So we both defect."

"We both defect," Maya repeated. She sat back. "To protect ourselves from the thing we're both doing."

Other kids drifted over, bored of the snow. Maya turned the game into a tournament. Bracket on a napkin. Everybody played everybody, ten rounds a match, points piling up.

And a strange thing started happening in the cafeteria.

"Everyone's getting ones," Soren said. He was tracking scores. "Almost everybody. It's a room full of people losing on purpose by being smart."

"Not Priya," Maya said.

Priya was up by a lot. They watched her play Dev. First round, Priya cooperated. Dev defected and grinned, five to zero. Second round, Priya defected. Then she cooperated again.

"She's giving away points," Soren said. "She cooperated and he stabbed her. Why would she do it again?"

Maya leaned in close. Watched four more rounds. Then she said, "She's not playing the round. She's playing Dev."

"What does that mean."

"It's not one game," Maya said slowly. "It's ten in a row with the same person. So you remember. You can find out who they are." She pointed. "Watch. She copies him. He defects, next round she defects. He cooperates, next round she cooperates. She's holding up a mirror."

Soren wrote it down. Watched. It was exactly true. Priya did whatever Dev had just done.

"That's a trap," he said. "If Dev keeps defecting, she punishes him every time, and they both crawl along at one point. He can't get ahead. The only way he ever gets a three is to be nice to her first."

Dev figured it out around round seven. They watched him figure it out. He cooperated, looking suspicious about it. Priya cooperated back. He did it again. So did she. Three, three, three, three.

"They're getting threes," Maya breathed. "Look at them. They're getting the threes that were always sitting there."

Soren stared at his square of four numbers like it had moved. "In one round, defecting always wins. That's still true. I didn't make a mistake before."

"You didn't."

"But the game isn't one round." He said it carefully, the way he said things he was still climbing into. "When it's the same people again and again, and they remember, the math changes. Being trustworthy is the winning move. Not the nice move. The winning move."

"It pays better," Maya said.

"It pays better," Soren said, "because you'll see them tomorrow."

Maya went very quiet, and then she laughed, because something had clicked all the way through. "Soren. That's everything. That's why anyone keeps a promise. Not because they're good. Because there's a round eight."

They ran the numbers on the napkin. A player who always defected cleaned up against strangers, against people they'd never meet again, and got buried by anybody who remembered them. A player who copied, who started kind and answered each move with the same move, never won a single match but never lost badly either, and ended up with more points than anyone in the room.

"It never wins," Soren said. "The copying strategy. It can't. The most it can ever do is tie, because it never defects first."

"And it's winning the whole tournament," Maya said.

He checked the scores twice. It was.

Maya was looking around the cafeteria now, at all of it, the trays and the line for milk and two teachers who shared bus duty and a kid lending another kid a pencil he might not get back.

"It's not just the game," she said. "It's the whole room. The whole everything. Everybody walking around with a card behind their back. Cooperate, or take the five and run."

"And the only thing that makes anybody cooperate," Soren said, "is that it's not one round."

"There's always a round eight."

"There's always a round eight," he said.

The two kids sharing a pencil were arguing now, and then they weren't, and the pencil went back across the table.

Maya pointed at it. "See."

The snow kept coming down outside, sealing them all in together, nobody going anywhere, everybody about to see everybody again tomorrow. Soren slid the napkin into the back of his notebook and the bracket lines showed faint through the paper.

Across the cafeteria, Priya held out her hand to Dev, palm up, and Dev put down a card without looking at it, and they both flipped at the same second, and both cards said Cooperate.