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twenty-five

Caitlin had heard her mom use the phrase “nonzero-sum” from time to time. She knew it was a term from her mother’s field of expertise, game theory. Webmind had already read everything on Wikipedia about game theory, but that didn’t mean he actually understood what “nonzero-sum” meant. Nor, if she was really honest with herself, did Caitlin, and yet this notion of nonzero-sum games was stuck in her mind: win-win situations in which everything could be made better.

Her mother had been having her own conversations with Webmind all day long while Caitlin was at school. Once Caitlin got home and had checked her email and so forth, she went across the hall to her mother’s office and told her about that poor Australian girl who had committed suicide, and about how she’d told Webmind that he should intervene in nonzero-sum situations.

Her mom looked horrified. “It just… just watched her kill herself? It didn’t try to stop her?”

“He, Mom. He didn’t know what to do, what to think. We need him to understand what to do the next time, and not just with teen suicides, but in any nonzero-sum situations. Can you help us?”

Her mother’s face moved through several expressions but then settled on one that Caitlin had seen before: the take-charge, supermotherscan-do-everything face. “Yes, I’ll help it—help him—learn to help the rest of us. That’s something I definitely want in on.”

“Thanks,” replied Caitlin. “But, I mean, I know—we know—what nonzero-sum is; we get that. But there must be a lot more to game theory than just that.”

“Oh… a bit,” said her mother. Caitlin realized she was still coming to grips with the magnitude—the importance—of what she was about to do.

“So, could you explain it to us? I remember hearing you say once that game theory really isn’t just about mathematics, but about human psychology.”

“That’s right,” her mother said. “In fact, the hottest branch of game theory right now is called ‘behavioral 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 separately after playing it.”

“Ah, okay, then I’ve got a question for you, Mom. What would you wish for if you knew that your worst enemy would get double what you got?”

“Hmmm. A million—no. Um, I don’t know.”

“To be blind in one eye,” Caitlin replied.

“God!” said her mother. “But, um, yes, that’s an example of what I’m trying to get at: it’s possible for people to value outcomes differently. Do you remember when your father taught you how to play chess?”

They had a special chessboard with Braille characters on the heads of each piece. “Sure.”

“And remember how he used to let you win?”

Caitlin raised her eyebrows. “Say what?”

“Um, dear, he—”

“I’m just kidding, Mom.”

She smiled. “Well, why did he let you win?”

“I dunno. I guess, ’cause if he didn’t, I wouldn’t have wanted to play anymore. I wouldn’t have come back for another game.”

“That’s right. What he valued most was not him winning, but rather you winning. In other words, you both wanted the same thing, and even though it cost him—in the sense of losing the game—to let you win, he was happy when you did.”

“I get it,” Caitlin said. “But, in the dollar auction, people don’t want to play anymore after a certain point, too, right? And I bet it’s not just that it’s ridiculous that causes them to finally stop bidding. It’s also boredom: I mean, even if you were bidding in ten-cent increments, instead of penny increments, it would still take thirty-four bids to get the $3.40 you mentioned. But if I was writing a pair of computer programs to play that game, they’d keep playing forever—because the only way you lose money is if you stop bidding.”

She paused, and then a big smile came to her face. “Or, to put it in terms like in that movie Dad and I watched, the only losing move is not to go on playing.”

“Good point,” her mom said. “Now, can you think of any real-life examples of things like the dollar game?”

Caitlin was trying to do just that when Schrödinger crossed her field of view, moving absolutely silently. “Evolution,” she said.

“Yes, exactly!” said her mom. “But why?”

“Evolution is an arms race, right?” said Caitlin. They’d talked about this in biology class. “Predators keep getting faster and stronger, so prey keeps getting faster and better able to defend itself. Gazelles evolved the ability to run fast in response to lions doing the same thing. The game goes on and on forever—because whoever stops upping the ante dies. Again, the only losing move in evolution is not to play.”

“Bingo,” said her mom.

Caitlin nodded. “Mr. Lockery—my biology teacher—says if dinosaurs were magically brought forward in time today, we’d have nothing to worry about. Dogs, wolves, and bears would make short work of tyrannosaurs.” She nodded at Schrödinger, who was now padding across the floor in the opposite direction. “Big cats, too. They’re faster, tougher, and brighter than anything that existed seventy million years ago. Everything is always ramping up, always escalating.”

“Exactly,” said her mom. Caitlin saw her glance out toward the living room, at—ah, she was looking at the staircase, the one that led up to the bedrooms, up to where Caitlin’s computer was, up to where they’d been talking to Webmind. His powers were growing, too, and not just generation by generation, as in biological evolution, but moment by moment. Caitlin turned back to her mom and saw something else for the first time: she saw a person shudder.

When Harl Marcuse had found the property that now housed his institute, it had seemed like an ideal location: twenty-five acres of rolling grassland, with a dome-shaped man-made island in the middle of a pond. But that had been based on the assumption that Hobo was going to be a cooperative ape. Hobo’s island wasn’t large, but he could easily keep his distance from anyone who set foot upon it. Of course, if two people went onto the island, one could go left and the other right, but a cornered, angry ape was not a pretty sight.

Shoshana, Dillon, and Dr. Marcuse were discussing the problem in the main room of the bungalow. Dillon was leaning against the wall, Sho was seated in front of a computer, and Marcuse was in the easy chair.

An idea suddenly occurred to her. “If he won’t talk to us,” she said, “maybe he’ll talk to another ape.”

Marcuse’s shaggy eyebrows went up. “Virgil, you mean?”

Virgil was an orangutan; Hobo and Virgil had made history the previous month with the first interspecies webcam call.

“He might indeed speak to Virgil,” Dillon said. “But do we dare risk bringing Hobo into the house now?” He spread his arms, indicating all the breakables.

“Good point,” Marcuse said. “Plus, I doubt he’d come willingly, and I don’t want to drug him. Let’s set up a webcam chat system for him out in the gazebo.” He turned to Shoshana. “I’m still not talking to that shithead at the Feehan. You work out the details.” And the Silverback headed out of the room.

Shoshana exchanged a look with Dillon, then picked up the phone and dialed the number in Miami.

“Feehan Primate Center,” said a male voice with a slight Hispanic accent.

“Hi, Juan. It’s Shoshana Glick, at the Marcuse.”

“Shoshana! Is the old man still pissed at me?” Juan had leaked word of the initial webcam call between Hobo and Virgil to a stringer for New Scientist, and that had triggered the chain of events that had led to the Georgia Zoo filing its custody lawsuit.

She swiveled her chair and looked out the window. “Well, let’s just say it’s a good thing you’re two thousand miles away.”

“I’m so sorry,” Juan said.

It had been a year or so since she’d last seen Juan in the flesh. He was about thirty, had a thin face, high cheekbones, and lustrous long black hair that Sho envied. “Don’t worry,” she said. “I’m not mad at you—and I’ve got a favor to ask.”

“Yes?”

“We’re having lots of trouble with Hobo. He’s become violent and antisocial.”

“Chimps,” said Juan in a “Whatcha gonna do?” tone of voice.

“If it’s just that he’s reaching maturity, there may be nothing that we can do—but he is young for that, and, of course, he is a very special ape, and, well, maybe it’s foolish, but we’re hoping we can get him to cooperate again, at least for a bit. We need him to stand up for himself if we’re going to keep him from… well, you know.”

“Georgia wants to castrate him, right?” said Juan.

“Yes. Barbarians.”

“Well, if they did, Hobo might become a lot more docile.”

“We don’t want him docile, for God’s sake.”

“I’m just saying…”

“Don’t.”

“Sorry,” Juan said. “Um, what can we do for you?”

“We thought if we could get Hobo talking again to someone, we might be able to get him back to talking to us.”

“His old pal Virgil?”

“Exactly. We can’t even get Hobo to come when we call to him anymore, but we thought if we established an open, ongoing webcam link between his hut here and Virgil’s room, maybe they’d start chatting again.”

“Virgil would love that. He was asking about Hobo just today. ‘Where that banana ape?’ he said. ‘Where that talking ape?’ ”

“Good, good,” said Shoshana. “So, can we get this set up?”

“Sure, no problem,” said Juan. “Just tell the old man I helped, okay?”