Game Theory (2 page)

CHAPTER 1

‘Tell me again.'

‘I've told you ten gazillion times.'

‘Ten gazillion and sixty.'

‘So why do you want to hear it again?'

‘To make it ten gazillion and sixty-one.'

‘That's not a reason.'

‘It is too.'

‘Not.'

‘Is.'

Phoebe wore the pyjamas I'd bought for her sixth birthday, nearly two years before. They had mathematical equations all over them. E=mc
²
. The Drake theorem. I'd gone crazy. I had a Fourier series:
and quadratics:
She had no idea what most of them were. Seven years old, okay? But she loved them. I'd bought some plain PJs and taken them to a custom print company, the kind that does
corporate logos on work shirts. Each equation was done in a different colour. They'd cost a fortune, but I didn't care. Now she refused to wear anything else at bedtime. Mum had to wash and dry them during the day, so she never missed a night. Phoebe had grown and the material had shrunk, so the sleeves were only just below the elbows and the legs halfway down her calves. It looked like she was preparing for a flood. Some of the equations had faded and the material was pilled, but she still didn't care. Phoebe wasn't interested in mathematics. She liked stories. But she
was
interested in me, her brother, which was why she loved the pyjamas.

She knelt on the bed, her skinny butt on her ankles, and bounced up and down. I loved it when she did that.

‘There's this gorgeous princess and her name is Phoebe.'

‘Why is she gorgeous?'

‘Because she has long, straight hair all down her back.'

‘None on her head, just all down her back.'

She liked to beat me to the punchline.

‘Am I telling this, princess, or are you?'

‘You are.'

‘You bet your skinny butt I am.'

‘Go on, then.'

‘She is so drop-dead gorgeous, so fantastically pulchritudinous, so “oh-my-god-I-can't-believe-she-is-not-bursting-into-flames-she-is-so-hot” that suitors come from far and wide to beg for her hand.'

‘It must be a great hand.'

‘It is a fabulous hand, but they want her other bits as well.'

‘But mainly the hand.'

‘Indeed.' I really wanted to tickle her in the side until she curled into a foetal position and begged for mercy, but I couldn't until I'd finished the story. Phoebe had standards and she had rules. Tickling came later. I folded my legs into a lotus position and rested my chin on interlocked fingers. ‘The suitors are reduced to three. Their names are . . .'

‘Luke, Alex and Corey.'

The names changed according to Phoebe's whims. Corey was always there because he was Phoebe's best friend in Grade Three – a strange looking kid with thin hair and a big nose; but there's no accounting for taste. Luke sometimes made an appearance, but Alex was new to me. He must have been nasty to Phoebe at school recently. I filed the information away.

‘They decide they'll have a fight and the winner will win Phoebe's hand.'

‘And her other bits.'

‘Indeed. So they choose their weapons . . .'

‘Rats.'

‘What?'

‘Rats.'

Phoebe changed the weapons when she felt like it, as well. We'd had guns, bows and arrows, even purses filled with explosives. But rats were new. She wanted a pet for her eighth birthday, which
was a couple of months off, so she had become a little obsessed. Mum wasn't keen on the idea, on the reasonable grounds that she didn't want to share the house with a rodent whose sole notion of social skills was to run around a wheel while shitting prodigiously. Phoebe thought this was an entirely
un
reasonable position to take, and often made her views plain.

‘Ninja rats,' I agreed. ‘When you threw them they latched onto the jugulars of their targets and bit them to death. The thing was, Luke was an expert ninja-rat thrower. He never missed. If he threw a rat three times, it hit three times. Alex was pretty good as well. He hit . . .'

‘Two times out of three.'

‘Correct. But poor old Corey. Well, he wasn't great at rat-chucking. He only hit one time out of three. So, the suitors stand at the points of an imaginary equilateral triangle, rats in hand. They are, as a result, an equal distance from each other. Fair's fair. And then Princess Phoebe . . .'

‘The gorgeous Princess Phoebe.'

‘The exceptionally gorgeous Princess Phoebe says: “In order to be
really
fair, the suitors must take turns in throwing their rats until only one person remains standing. But they
have
to throw in turn. And, what's more, it's only fair that the worst ninja-rat chucker gets first go.”'

‘That
is
fair.'

‘Indeed. So Corey will go first, followed by Alex, followed by
Luke. If there are still two standing, then they will continue to take turns in that order until only one suitor remains to claim Princess Phoebe's hand. And her other bits.'

‘So who should Corey aim at first?'

‘That, dear sis, is the question.'

Phoebe bounced up and down on her bed and ran her hands through her hair. This was so cute, I didn't know whether to shit or pick my nose. I didn't do either, just fixed my eyes on hers. She scrunched up her brow in concentration.

‘For his first go he should aim at Luke because Luke never ever misses, so if he could get rid of him then that would be brilliant and give him the best chance of claiming the gorgeous Phoebe's hand.'

Phoebe knew the answer because we had been over this on ten gazillion and sixty occasions, but we had to go through the same routine every time.

‘Wrong, bozo,' I said. ‘Spectacularly wrong. Corey has only one chance in three of killing Luke. Even if he gets super lucky, that leaves Alex to go next and he only has Corey to target. And that means there's a two in three chance of Corey being cactus.'

‘I know, I know.' She bounced up and down on the bed again. ‘He should aim at Alex.'

‘Even worse, bozo,' I said. ‘Super spectacularly wrong. If he is really lucky, then Alex is dead and that leaves Luke's turn and he never misses. So Corey is
definitely
cactus.'

‘This is dumb.'

‘You're dumb.'

‘Not.'

‘Are too.'

‘Tell me.'

‘I've just told you. You're dumb.'

‘No. Tell me the answer.'

‘Okay.' I made as if I was going to shift my position on the bed, but then grabbed her under the armpits and flipped her onto her back. She squealed and tried to kick out at me but I was too quick. I bounced on top of her so she was pinned, my knees in the crook of her elbows, my butt on her scrawny legs. I put my head down so my fringe tickled her face. She thrashed her head from side to side, but she was laughing so hard stringy bits were coming from her nose. ‘Yeeuk, gross,' I said. ‘You are so gross. You are a gross, dumb bozo.' She was screaming by now but trying to talk at the same time. It came out all strangled.

‘But I'm . . . also . . . gorgeous.'

‘Granted,' I said. ‘A gorgeous, gross, dumb, bozo princess. Listen up, poo for brains. This is game theory and that means you don't just think about what
you
are going to do, but what
others
will do. That's the point of it. If it was Alex's turn first, who would he shoot at?'

‘Luke.'

‘Correct, bozo. Because if he doesn't, he's dead. Luke knows that Alex is his biggest threat, so he will shoot him first. If Alex
kills Luke then Corey gets the next go and he stands a chance. So what Corey should do is shoot his gun in the air.'

‘HIS RAT, poo for brains.'

‘Right,' I said. ‘His rat. By deliberately missing, he's guaranteeing one of the others will die because they will target each other. Either Luke or Alex is dead and it's Corey's turn next. So he will get the first shot in a duel. It is statistically his best option of getting the hand of the gorgeous Phoebe, not to mention her other bits.'

‘And does he?'

‘Does he what?'

‘Win.'

‘I don't know. That's not the point. It's game theory, bozo, not a fairy story.'

‘And you call me dumb! You don't even know how the story ends.'

I hopped off and pulled the bedclothes over her. She instantly snuggled down so that just her nose peeped over the blanket. There was a broad, slimy patch on the material where her nasal discharge had found a glistening home. I ruffled her hair and made for the door. I was halfway through when I turned back.

‘Okay. Corey
does
win. He wins the gorgeous Phoebe but after a week he finds out that she is a dumb bozo with poo for brains, so he throws his own rat at his own neck. That's how bad she is.'

‘He'll miss two times out of three.'

I laughed so hard I nearly got my own nasal discharge.

‘I love you, Jamie,' she said as I went to close the door.

‘Course you do,' I said. ‘You might be dumb but you're not insane.'

CHAPTER 2

Summerlee, Jamie and Phoebe.
Maybe it was a private joke between my parents. Maybe they just liked names that ended in the -ee sound. Whatever the reason, it sucked but there's nothing you can do about it.

Phoebe loves Mum and Dad. I tolerate them. Summerlee despises them. Does it always work that way? Someone once said that you start by loving your parents, then you judge them, and rarely, if ever, do you forgive them. It's clever enough to be true. But it's also sad. I don't want Phoebe to grow up and away from them. Up and away from me, too, I guess. Not because of Mum and Dad's feelings or even mine, but because there's something pure and innocent in her love. It doesn't make conditions and it doesn't expect disappointments. At some point we grow into that and I don't know why.

I am a mathematician and I am not comfortable with stories. I'm at a loss for how to tell this tale because words are not what
I'm best at. And you have to use so many of them just to express a simple truth. Maths isn't like that. Take E=mc
²
, the most famous equation in the world. Five symbols, but they tell a story of the universe and the laws that govern it that would take –
have
taken – volumes and volumes of writing just to scratch its surface. Energy, mass, the speed of light and the relationship between them. It is the story of everything. In five symbols. How concise, how
beautiful
, is that?

There are no symbols to tell Summerlee's story, so I'll have to make do with the clunkiness of words. She is my other sister, eighteen years old. She used to be a stunner, when she was between the ages of about thirteen and sixteen, but in the last couple of years that's changed. She's dyed her hair, for example. It used to be dark and when it caught the sun it would explode with flashes and gleams. Now it is a dull blonde, leached of life. Like straw. Her eyes are like that, too. Not blonde, obviously, but a pale blue that seems to get paler as time passes. Sometimes I think she's being dissolved as a person – all that vibrancy, personality and joy in life has been exposed to some kind of element that's stripped everything away until all that is left is hard, yet brittle. Pale. It is like watching something baking in the sun and dying by degrees.

I can't recall when she changed. It appears a sudden transformation in my memory, but I guess it must have been gradual. I
do
remember one incident that made me realise the sister I knew was somehow lost. She was in Year Ten, about fifteen. I was in Year Eight at the same school. It was breakfast time and I was chowing
down on a bowl of cereal, while Mum was getting Phoebe ready for kindy. It was a routine. Dad had normally gone off to work by then. He sorts out people's mortgages which, apparently, involves long hours at an office desk. So Mum was left with three kids to feed, clothe, make presentable and then take to their respective educational institutions. I guess it was a ritual played out across the entire nation. And I also suppose it was a stressful time for Mum. But I was in Year Eight, when other people's stresses, particularly your parents', fly way below your radar.