//------------------------------// // Chapter 1: A Ghost of the Past // Story: A Robust Solution // by Jordan179 //------------------------------// "So you see," Fluttershy said to Rarity as they walked along the lane, "in a Prisoner's Dilemma each one of the ponies can gain an advantage by betraying the other, and if one betrays and the other stays loyal, then the one who betrays gets the most gain, and the one who is betrayed gets the most loss. But if both betray, they both suffer much loss, while if both stay loyal, they both suffer a small loss." Rarity mulled the notion over as they continued down the lane, reaching the main road that led out of Ponyville toward Canterlot. The two mares had no intention of going that far, of course; if they had, they would have taken a train. All they were doing was walking together in the late afternoon, two friends taking in the brisk air of early October and talking about life. Which in Fluttershy's case, meant animals, and the relationships between species in the wild. This was not a topic of great interest to Rarity, but she was happy to see her friend waxing voluble on any topic. Fluttershy was normally too withdrawn from the world, as if it had frightened her long ago and she'd never quite gotten over the start. So, if Fluttershy was willing to talk; Rarity was willing to listen. "So do you see why it's a 'dilemma?'," asked Fluttershy.. "Yes," said Rarity slowly, "I suppose I do. Because each one of the ponies is tempted to take advantage of the other pony, but if they both give way, they both lose." They took a left turn and were now walking northeast along the main road to Canterlot, staying on the shoulder to avoid the deep wagon ruts. The river was to the right; to their left at some distance ran the railroad on its embankment. "So what do you think they do?" Fluttershy was grinning, as if she was sitting on some deep secret. "Well," said Rarity, "I would be loyal. I don't believe that it's right to betray a friend." "Yes," said Fluttershy, "and I'd be loyal too. So if we played the game, then we'd both be loyal and suffer the small loss. Or, in some versions of the game, get a small gain. The important point is the order of the outcomes, not the amounts." "Then I've solved your dilemma," smiled Rarity. "Ah," said Fluttershy, "but that's for you and I. Suppose that you were playing with, say, Cloud Kicker." "Eww," said Rarity. "I wouldn't trust her farther than I could throw her. In fact I wouldn't trust her that far -- she's pretty light." "Hollow bones," said Fluttershy with a hint of smugness, briefly flexing her wings. "And telekinesis," said Rarity, her horn faintly glowing as she lifted a nearby pebble, tossing it into the river, watching it splash "Well, you get the idea. So I -- hmm -- I guess she'd betray me, so suppose I'd want to betray her right back." "She hasn't betrayed you yet," pointed out Fluttershy.. "True," said Rarity. pursing her lips. "But I know her -- I know she can't be trusted." "So it's as if you've played the game with her before," said Fluttershy. "Yes," said Rarity. "Well, in real life, you do play the game more than once, don't you? You meet ponies and see how they behave towards oneself, and then you behave toward them based in part on how they've acted before. Their reputations, so to speak." "Uh-huh," nodded Fluttershy. "That's called an iterated game. Meaning that you play round after round with the same ponies. And that's the key to solving the dilemma." "How so?" asked Rarity, not sure how much of this she was really following, but convinced that there was some significant revelation somewhere at the end of it all. "Well, you see," said Fluttershy, "if you play the game only once there is no good solution, because you have no idea which strategy the other player is going to pick. It's 50-50, but you don't even know that, because the other player has a preference -- you just don't know which preference." They were at the edge of town now, and the houses were growing thin. Far up ahead was some kind of public house -- the Carrot and Stick, Rarity recalled, a place with a somewhat unsavory reputation. There was a chuffing noise far away in the direction of Canterlot -- a train, still miles away. Fluttershy had eyes only for Rarity, attention only for the idea that she was developing. "But if you know the player," said Fluttershy, "know what strategies she likes to pick, you can decide what to pick yourself based on her repuation. And you can also take your own reputation -- both past and intended future -- into account when picking your strategy. So if her reputation is for betrayal, you pick betrayal. If it's for loyalty, you pick loyalty. And -- even better -- there's a general solution to the problem -- assuming you don't know how many rounds you are playing." "What would that be?" Rarity asked. She heard a wagon behind her -- her ears swiveled automatically and she could roughly tell the distance. The friends moved a bit higher on the shoulder of the road to let the vehicle pass them. It was a big fruit wagon, drawn by two burly teamster stallions, who looked and whistled appreciatevely at the two mares as they went by. Rarity lifted her chin, looked away from the stallions and smirked to herself. Fluttershy blushed and twisted her head behind her own pink mane. It was not until the stallions were well down the road that Fluttershy recovered from her embarassment. "About the solution?" Rarity prompted her friend. "Oh, right," replied Fluttershy. "It's called 'Nice Tit-For-Tat.' The way it works, the first time you meet a new player, you choose 'loyal.' You're being 'nice' -- giving her the benefit of the doubt, so if she's trustworthy you won't give her the wrong idea about yourself." "That makes sense," Rarity said. "Like making sure to give a new customer good service, so she'll come back for more." "Exactly," Fluttershy continued. "And what do you suppose you do the next round?" "Hmm," said Rarity. "I guess I'd be nice again, if she was nice to me. But if she betrayed me --" A slight stress came into her voice, as she considered the concept of betrayal. "Right!" said Fluttershy happily. "You've got it! You're Nice the first round, and then afterward you do exactly what the other girl did the round before -- including betrayal, or being 'nasty,' if that's what she did to you. Nice Tit-For-Tat." "Wouldn't you want to sometimes try being nice again," Rarity asked. "Just in case you'd misjudged them before?" "That can work too," Fluttershy conceded. "It's called 'Forgiving Nice Tit-For-Tat, and it's better against some specialized strategies. But the important point is always be nice first, and usually do as you are done unto. It's sometimes also called the Silver Rule, to distinguish it from the Golden Rule of the ancient philosophers, which would be just a pure Nice strategy." "I see," said Rarity. They had continued walking, and were now about half of the way to the public house. The teamsters had pulled their wagon up there. What, can't they get a mile out of town without deciding it's time for a drink? Rarity thought to herself with some annoyance -- it meant that they'd have to walk past their perhaps over-appreciative eyes again -- then felt guilty for the sentiment. It's hard work pulling those wagons. They're probably just thirsty. "Can pure Nice work?" She felt it couldn't, but wanted to see what her friend thought. "Sometimes," said Fluttershy. "It works perfectly with other pure Nice players, or Nice Tit-For-Tat. But the problem is that it can be easily exploited by a number of strategies that Betray. It's not 'robust,' in game theory terms. Pure Nice can't survive around others willing to be Nasty." "That's a lot like business," Rarity observed. "I always try to be nice to my customers, my suppliers, everypony I work with -- because if they're nice back to me, we'll both benefit. But I've found that there are some ponies who will just take advantage of me if I let them, so I can't be nice to them. I have to watch them like a hawk, or they'll rob me blind. I prefer not to do business with ponies like that at all, if I can possibly avoid it." "In real life you can choose not to play with those whose reputation is sufficiently bad," said Fluttershy. "This is really a lot like business," Rarity said enthusiastically. "It reminds me of some of the things I was taught in my business courses, when I went away to Fillydelphia. Always make a good impression on your customers from the start, treat them well, and only extend credit to the creditable -- don't waste your time and money chasing after sunk costs and bad debts." "And it is very important to ecology," said Fluttershy. "That's how I got into game theory. You see, in Nature there's something called 'symbiosis,' which ..." "Hey, ladies!" cried one of the teamsters. He was a big, chestnut-coated Earth pony; his team mate a slightly smaller tan; both were black-maned. They were handsome in a rough sort of way, but right now they weren't behaving very handsomely. They were showing off in a crude fashion, prancing in place, swaying their heads, and flicking their ears suggestively. "Did you come here for some of what we've got?" The smaller stallion did the same, though a bit more hesitantly -- he was obviously following his friend's lead. "Well, I never!" said Rarity, huffing and raising her nose, refusing to make direct eye contact with them. She started to trot away, her tail demurely arched down to block them from a direct view of her rump. She trotted a few steps ... ... then suddenly noticed that her friend wasn't following her. "Fluttershy?" Rarity turned around, looking with concern. Fluttershy was not, as Rarity had expected, trying to crawl under her own mane and slink away from there. Instead, she seemed absolutely terrified; her forelegs splayed, hindlegs pushed back, tail under her own belly, ears down, a wide-eyed look of horror on her face as she stared at the two stallions. Not the Stare -- thankfully, as Rarity knew it would be utterly-uncalled for in this minor confrontation -- but simply a stare as if the stallions were the most incredibly threatening thing she'd ever seen in her life. Since, just a month ago, she had seen Fluttershy face down a full-grown Dragon right outside its lair, Rarity found this almost unbelievable. Rarity glanced at the two stallions, to see if they were doing anything beyond mere crudeness to justify such a response from her friend. Instead, the bigger chestnut one had stopped, and was looking at Fluttershy oddly -- as she watched, he motioned his smaller tan buddy to stop -- he was evidently worried by the intensity of Fluttershy's fear. Why was Fluttershy so frightened by them? Rarity instinctively moved forward to put herself between her friend and the perceived threat, and as she did she realized something. Fluttershy was not staring in fear at the two stallions. She was staring in fear at the building. At that moment, Fluttershy bolted, galloping pell-mell back toward Ponyville. Rarity glared accusingly at the two teamsters, who wilted before her gaze. Then she galloped off after her friend.