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game theory.’ ”

“Well, Webmind certainly needs to understand human behavior better.”

So everyone keeps saying, Webmind sent to her eye.

“Okay,” said her mom. “Let’s go downstairs.”

Her mother got a clipboard, some pens, and some paper, and the two of them went to the dining room, which had a big table. There was normally one chair on each side of the table, but Caitlin’s mom moved hers to be next to Caitlin’s.

“Webmind is listening, right?” asked her mom.

The word Yes flashed in Caitlin’s vision, and she repeated it.

“Okay,” her mom said. “Do you know what the prisoner’s dilemma is?”

Caitlin thought, How to pick up the soap in the shower? But what she said was, “No.”

Her mother seemed to consider for a moment, then: “Okay, let’s do it like this: say you and Bashira both get in trouble at school. Say Principal Auerbach has said that he thinks you guys have hacked into the school’s computer and changed your grades—just like in WarGames, right? And he talks to each of you separately. He says to you, ‘Okay, look, Caitlin, I admit I haven’t got enough evidence to actually prove you did this, but I can suspend each of you for a week just because, well, because I’m the principal.’ ”

Caitlin nodded, and her mother went on. “But the principal’s real interest is in making sure this never happens again, so he adds that if you’ll say Bashira did it and explain how it was done, you get off scot-free—no suspension at all—and he’ll suspend Bashira for three weeks. Oh, except for this: if you say Bashira did it, and Bashira says you did—that is, if you each blame the other—then you’ll both get suspended for two weeks. Got that? You can end up with no suspension, one week’s worth, two weeks’ worth, or three weeks’ worth. And you know he’s going to make the same offer in private to Bashira. What do you do?”

Caitlin didn’t hesitate. “I clam up; I don’t say a word.”

“But if Bashira fingers you, you’ll get three weeks of suspension.”

“But she won’t,” Caitlin said firmly.

Her mother seemed to consider this. “Okay, okay, let’s say it’s not you and Bashira for the moment. Let’s say it’s just two random guys—um, Frank and Dale. What should you do if you’re Frank?”

Caitlin suppressed a smile. Frank was the name of her mother’s first husband, who had come and gone long before she’d been born, and Dale, she knew, was the former head of the Economics Department at the University of Houston—someone her mother had famously not gotten along with. Picking truly random people was as hard as generating really random numbers, it seemed.

Still, the math was easy. “I rat out Dale,” Caitlin said.

“Why?”

“Because it’s the best thing for me. If he doesn’t rat me out, I get away without any punishment, instead of having a one-week suspension. And if he does rat me out, then I’m still better off, because then I only get a two-week suspension, instead of the three weeks I’d have gotten by keeping my mouth shut. No matter what he does, I cut a week off my punishment by ratting him out.”

“And what about Dale? What should he do?”

Caitlin frowned. “Well, I guess he should rat me out, too.”

“Why?”

“The same reasons: no matter what I do, he gets one week less suspension by turning me in.”

Her mother smiled—but whether at Caitlin’s brilliance or at the thought of both Frank and Dale being punished, she couldn’t say. “Exactly,” her mom said, and she started to draw on the paper. “If we make a chart with Frank’s possible moves—we call them ‘defecting’ or ‘cooperating’—on the x-axis and Dale’s possible moves— the same things, defect or cooperate—on the y-axis, we get what’s called the payoff matrix: a table with a score for each possible outcome, see?” She pointed at one of the squares in the matrix. “Even though the best possible outcome—one week’s punishment—occurs when you both cooperate, the math says you should both defect. Granted it doesn’t give you personally the best possible outcome, but it does give you the best outcome you can reasonably expect given that the other player will selfishly act in his or her own interests.”

Caitlin frowned again. If game theory was all about people being selfish, it wasn’t going to help her accomplish what she wished with Webmind; she needed a way to make it want to act altruistically.

“Now,” her mom went on, “that’s a simple game: each player only got to make one move. But most games involve a series of turns. Consider a dollar bill—”

“We’re in Canada now, Mom,” Caitlin said, teasing. “They don’t have dollar bills.” She knew the Canadian one-dollar coin was called a loonie, because it had a picture of a loon—a kind of waterfowl—on the tails side. She also knew that the two-dollar coin was called a toonie. She thought a much more clever name would have been “doubloon,” but nobody had asked her.

“Fine,” her mother said, smiling. “Consider a dollar coin, then—and consider a bunch of people at a party. Now, I’ve actually tried this myself, and it really works. Announce to the group at the party that you’re going to auction off the dollar—highest bidder gets to keep it. But, unlike normal auctions, there’s one special condition: the second-highest bidder also has to pay up whatever his or her highest bid was—but gets nothing for it. Got that?”

Caitlin nodded.

“How much, on average, do you think the dollar sells for?”

She lifted her shoulders. “Fifty cents?”

“Nope. The average is $3.40.”

“That’s crazy!” said Caitlin.

“Loony, even,” her mother replied. “But it’s true.”

“Why do people bid so high?”

“Well, remember, the second-highest bidder has to pay the auctioneer, too, so…” She trailed off, clearly wanting Caitlin to figure it out for herself.

She tried to do so. The first bidder presumably bid a penny to start—which would net him a ninety-nine-cent profit. But then as soon as a second bidder offered two cents, the first bidder probably figured that offering three cents was still a good deal: he’d net ninety-seven cents in profit.

And so it would continue, until—

Ah!

Until one bidder bid ninety-nine cents—which would still give him a one-cent profit. But the previous bidder, whose bid might have been, say, ninety-eight cents, was now looking at losing that much and getting nothing in return. And so he would bid a dollar—thereby breaking even, at least. But then the guy who had bid ninety-nine cents faced a dilemma: he either walked away and lost ninety-nine cents, or he bid, say, $1.01—which would cut his losses to just a penny.

And so, indeed, it would escalate, with bids going higher and higher, until the utter ridiculousness of the situation finally caused all but one of the bidders to drop out.

Caitlin said as much to her mom, who smiled encouragingly. “That’s right, dear. Now, can you think of what the optimal strategy would be—and no cheating by having Webmind tell you.”

Caitlin considered for a second then: “Make an opening bid of ninety-nine cents. No one else would have any motive to bid against you, because the best they could do, if they outbid you by one cent, is break even, and if they bid more, they’d lose money. You’d end up being the only bidder, and you’d still make a profit, even if it’s only a penny.”

“That’s right,” her mother said again, “assuming all the potential bidders were rational and that their only motive was profit. But here’s where simple math fails to account for reality—there’s a psychological element that Webmind will need to understand.”

“Yes?”

“Suppose it was your worst enemy who had just bid ninety-nine cents. You might bid, say, $1.98, just so he’d be out almost a buck—and you’d still be out less than he was.”

“Wow,” Caitlin said. “That’s nasty.”

“I’ve seen this game get very ugly at parties,” her mom said. “I’ve seen couples who arrived together leave