Game Theory (19 page)

‘You reckon the kidnapper knows you?' said Dixon.

The question startled me. I'd said as much to the guy on the phone not half an hour earlier. Why would Dixon say that? If he was the person behind the voice, then why would he bring it up now? And wouldn't something that coincidental indicate his innocence? I was so tired. My thoughts wouldn't assume any shape.

‘Maybe,' I replied. ‘He knows a lot about us, that's for sure. My mobile number, for one thing.'

Dixon waved a hand and then ran it across his brow. It wasn't particularly hot, but he was sweating anyway.

‘Easily found,' he said. ‘Phoebe might have given it to him. More interesting is that he wants to talk to you and not your sister.'

‘He said she's stupid and a slut,' I replied.

‘You believe that?'

‘That she's stupid and a slut? No comment.' I watched Dixon's face but it was impassive.

‘No, do you believe that's the reason he wants to deal with you.'

I gave that some thought. We walked for probably two or three minutes in silence and Dixon didn't try to make conversation. He let me process his question. Out of the corner of my eye I saw him hitch his trousers a couple more times. I went through
the possibilities. I had been with Phoebe in that supermarket, so maybe the kidnapper was tapping into my sense of guilt. I was the one who had lost her, therefore I was the one most emotionally qualified to move heaven and earth to get her back. The redemption motive. Plus, Summerlee was nothing more than a bank account to him. Did it really matter if he talked to her directly or used me as a go-between? Perhaps all of this was simple common sense. Maybe, logically, I was the ideal candidate for negotiation. Dad couldn't cope, Mum was wired, Summer was fucked up on drugs and alcohol most of the time. I was the mathematician. I was more likely to respond in a controlled and rational fashion. But something in my gut rebelled against the argument. It was all that, but it was something more.

‘I think he wants to play games,' I said. Still no decipherable reaction, though he took out a handkerchief and mopped his brow. It really
wasn't
that hot.

‘Meaning?' he said.

I held up my hands. What did I mean? What evidence could I put forward in support of that assertion? Was I elevating myself to a position of importance that couldn't be justified
? I'm at the centre here. It's all about
me. But the feeling persisted. What I had said on the phone was true. I felt sure this was a game and the kidnapper knew it, was in some way relying on it.

‘I get the impression,' I said, ‘that he wants me to understand that he knows my thoughts, my feelings, my motivations, and that he is one step ahead of me all the way. Almost like he wants us to
be friends, for fuck's sake.' I stopped on the pavement and Dixon turned towards me. ‘No. Not friends. He wants me to
admire
him. You know, two minds in battle, two chess players moving towards an endgame and he is the one with the skill to see it through. He wants my applause.'

Dixon stroked his moustache and examined his shoes, which were old, scuffed and dull. A small strip of the sole was coming loose and one lace had broken at some stage and he'd had to shorten it to make it fit. He sucked at his teeth.

‘You think I'm full of shit,' I said. ‘Over-complicating.'

He looked up at me then and seemed genuinely surprised.

‘No. Not at all,' he replied. ‘Seriously.' He kicked at one shoe with the other. No wonder they looked like crap. ‘You're the one he's been talking to, Jamie. You're the one qualified to make judgements based on your conversations. Certainly not me. If that's what your instincts tell you, then that's good enough for me. The real point, though, is does it help? Assuming you're right.'

I shrugged. Dixon hoisted his pants and moved on. I think he needed shade.

‘What about you, Jamie?' he said a moment later. ‘Are you a game player?'

‘Not when it comes to Phoebe's life,' I replied. Then I thought again. What about that first phone call when I told the kidnapper I was busy? What was that about if it wasn't game playing? And did it really matter if that was an instinctive reaction? Christ, how much did I have in common with this guy?

I was so tired. My suspicions of Monkhouse and Abbott, and Dixon himself, were starting to appear absurd. Why not anyone who had ever known me, passed a casual word in the street? Fuck, I might as well work on the telephone directory as a list of potential suspects. Mum and Dad? Christ, what was I thinking? Suddenly I felt the urge to just answer honestly, without worrying about what was going on in the head of the person I was talking to. I was tired of games, especially my own.

‘Game theory,' I said.

‘Game theory?'

I gave Dixon the potted version, the establishment of game theory as a respected branch of mathematics and economics. ‘Essentially, it's the analysis of decisions made between at least two independent and rational players and how outcomes are influenced by those decisions.' Dixon scratched his head and sucked his teeth. He gave me a shucks-I'm-just-a-humble-cop smile.

‘I'll give you an example,' I said. ‘One that should appeal to you as a police officer. Answer this: is it true to say that if we all became better people, the world would be a better place?'

Dixon looked at me as if I was a bit simple.

‘Sounds to me,' he said, ‘like that goes without saying. I suppose you're going to tell me it's not true.'

‘You're right. It isn't true. It's absolutely false and I could prove it to you with mathematics.'

Dixon held up a hand.

‘Spare me,' he said. ‘I always sucked at maths.'

‘The fallacy of composition,' I continued. ‘What applies to an individual doesn't necessarily apply to the group.' I looked at Dixon's face and decided to press on quickly. ‘Let's say that one definition of being ‘better' is that we think more about other people's feelings and do things specifically to make them feel good. Yes?'

Dixon nodded.

‘Okay,' I continued. ‘So criminals behave better, but we also behave better in response to criminals. Punishment is less harsh, which means that there's a greater incentive for criminals to behave badly. That would make the world a worse place, wouldn't it?'

Dixon screwed up his eyes and sucked his teeth. He opened his mouth and closed it again.

‘Whatever,' he said finally. ‘You think this game theory is useful as far as the kidnapping goes?'

‘Possibly,' I replied. ‘It has applications in most areas where there are winners and losers.'

He chewed on that for a while. We had circled the block and he shambled over to his car, an old Ford that looked as battered as his shoes. I thought he might be overdoing the down-at-heel persona, the gritty cop with no formal education but high on street-smarts. Did it work to lull suspects into a false sense of security? Did Dixon, in his own way, employ game theory to maximise his chances of success in the game of good versus
evil? He motioned me to the passenger seat and then turned on the engine, which coughed for a moment before catching. Almost immediately a blast of cold air poured from the vents. He might not spend money on the car's bodywork, but he hadn't stinted on the air conditioning. Dixon mopped his face with his handkerchief and lay back in the seat.

‘So,' he said. ‘Two possibilities. One, your interest in this game theory is clouding your judgement of the crim's motivations. In other words, you're finding an interest in game-playing because that's what
you're
interested in.' He took a pack of cigarettes from his jacket pocket, tapped one loose and put it into his mouth. He glanced over at me. ‘You mind?' he asked.

‘It's your car and your lungs,' I said.

‘Well, your lungs as well, in this instance.'

‘Go ahead,' I said. He lit up and gave a sigh of satisfaction. ‘You were saying?' I added.

‘Two, the kidnapper knows about your interest in game-playing. He has, you say, considerable information about your family. It might be reasonable to assume he also knows about your personal interests.'

‘And how does that help?'

‘It makes it more likely you know the kidnapper. Phoebe left the supermarket with him, after all, which suggests it was someone she might have reason to trust.'

‘He explained that.'

Dixon took a long drag and flicked ash out of his window.

‘Yeah,' he said. ‘But that doesn't mean we have to believe him, does it? Pulled your strings, I reckon. Worked on your guilt. Maybe he was making a calculated move to get just that reaction. To gain an advantage in the battle between the two of you. Am I getting the hang of this game theory of yours?'

I thought it over. Bad shoes, poor diet, as witnessed by the waistline and the fast-food wrappers in the car's footwell, but an intellect that was sharp and well-maintained. Yes. Dixon might well be spot on.

‘Not just getting the hang,' I replied. ‘I think you might be an expert player but aren't aware of it. You've been using game theory all your professional life but just didn't know the term.'

‘I called it police work,' said Dixon. ‘But then I'm just a dumb cop.'

‘Oh, please,' I said. ‘Don't play
me
.' He smiled at that and I tried to smile back but it turned into a yawn. ‘I've got to get some sleep,' I said. ‘I'm on the point of dropping.'

‘Sure,' said Dixon.' He flicked the butt of his cigarette out onto the road, then reached into his pocket and took out a business card. ‘I have no jurisdiction in this, you understand. But if you want to talk – if anything else occurs to you and you'd like to bounce it off someone, then call. I like to think I still have my uses sometimes.'

I took it. ‘Day or night?' I asked.

‘Hell, no. I need my sleep. But up to ten in the evening is good and I'm generally out of bed by five in the morning. One of the lifestyle changes that comes with age.'

I opened the car door.

‘One other thing,' said Dixon. ‘This business about disguising his voice, so you can't tell if it's a man or a woman. You think he'd bother doing that if he was a stranger to you?'

I put the card into the top pocket of my shirt.

‘Yes. If the cops might recognise his voice,' I said.

‘True,' said Dixon. ‘Worth thinking about, though.'

I got out and closed the door. His car took off trailing a plume of smoke from its exhaust. I watched until it disappeared around the bend at the end of our street, then I went back inside the house. Summer was where I had left her, though she'd slumped over the side of the couch and was snoring gently. Spider was leaning forward and rolling a joint on the coffee table.

‘If you're smoking that, you can go into the backyard,' I said.

‘Sure, man,' said Spider. ‘No worries.' He stuck the end of the roach into his mouth, twirled it round to wet it, then put it behind his ear.

I went into my bedroom and fell onto the bed. I wasn't sure if I would manage to sleep, and anyway, I was too tired to undress. Adrenaline was surging, as it had for the last twenty-four hours. It was as if every corpuscle of blood, every firing neuron, was jumping in its own electrical dance. But I had barely closed my eyes before I fell asleep.

I dreamed.
I was in the supermarket, carrying a basket, and putting carrots into it, one by one. The woman with the tattoo was there, as was the guy on the mobile phone. This time, though, he wasn't saying, ‘Sure, yeah, sure'. He was saying, ‘He's here with me. In the veg section. The coast is clear.' I met his eyes and they had no whites to them, just black holes containing the dim reflections of the fluorescent lights. I glanced from side to side. Where was Phoebe? She'd been here a moment ago.

I spotted her: a glimpse of the back of her head as she disappeared round a display of baked beans. Her dark hair swayed and was gone. I saw the red denim material of one of her sneakers, its heel tilted. ‘Hey, Phoebe!' I called, but she didn't come back. I went to the aisle and looked along it. Phoebe was turning right at the end. This time I thought there was a man with her. The flap of trousers, a flash of a dark shoe. I ran to the end, looked left and right. Nothing. I went to the next aisle. She was at the far end, turning left. I ran. There was no way Phoebe could outrun me. I was only two metres behind her. At the end I looked right and left. Nothing. Then I saw the back of her head, the tilt of red denim sneaker, as she turned the corner. Was she holding someone's hand? ‘PHOEBE!' I yelled. ‘YOU CAN'T RUN THAT FAST.' She didn't come back.

I moved as if in a maze. Now the supermarket was deserted, except for Phoebe and me and the faintest hint of another presence. Someone, something dark. The aisles stretched and twisted and went on forever. I ran headlong through each one, and each
time caught a glimpse of hair, the tilt of a sneaker. I never got closer.

And then a sound. I stopped halfway down one aisle. Baked beans were on all of the shelves. Thousands, millions of cans, stretching to infinity. The sound coalesced. A hum. It made my heart leap in my chest.

I jolted upright in bed. My phone was buzzing. Not a call. A text message notification. I fumbled with the screen. Unknown caller. I pressed to bring up the message, but there was no message as such to bring up.

I had received a video.

CHAPTER 19

Phoebe sat in front of a completely blank wall.
It was obviously brickwork – I could see the classical outline of staggered individual bricks – but it had been painted an off-white. She wasn't wearing her school uniform, but something I'd never seen before. A kind of green smock with a bright bow at the neckline. Definitely not something she would have chosen to wear. It was too girly for her taste. Clearly, the person who'd taken her had picked this. It was exactly the kind of dress that someone who didn't know kids would have chosen. It spoke of conventional fashion, a sense of what little girls
should
look like. Questions rose like bile in my throat. Had she been forced to change into this from her school uniform? Most importantly, had she been given privacy while she struggled into this monstrosity? I wanted to shut my eyes to keep the appalling alternative at bay.