I'm game if you are

Honey.

Uh-huh.

You're not going to believe what I learnt in class today.

What?

You know how we're always arguing over what to do over the weekends? Like last week, when I wanted to catch that special Antonioni retrospective and you wanted me to take you shopping?

I DID NOT argue. You promised that we would go to the sale, and then backed out at the last minute. I mean, you don't even like Antonioni for god's sake, and....

Ya, ya, okay. It was a once in a lifetime event and I didn't know about it when I promised, but okay, so it was my fault. The point is you know how we always have trouble deciding? Well, I discovered in class today that there's this game called the Battle of the Sexes which looks at exactly that problem. It's really cool.

You were sitting around in class playing games?

No, no, it's Game Theory. It's like this uber-cool branch of economics. So listen. It turns out that there's something called a mixed strategy equilibrium that provides a better answer to the problem than just having one person give in to the other.

Really? That's interesting. How does it work?

Well, for starters, you take a dice.

A dice? What kind of dice?

A normal dice. Like the one that comes with our snakes and ladders game.

So this mastermind solution has something to do with snakes and ladders?

No, no. Look, it could be any dice. It just has to be unbiased, that's all.

Hmmm...I'm not sure that snakes and ladders thing is unbiased actually. The way you kept getting all those sixes last time was really suspicious. If we're going to need a dice for this method of yours I think we should get a new one.

Yes, yes, all right, we'll get a new dice. But listen. So once you have this dice, one of us, say I, throws it, and if it comes up 1 or 2 then I do what you want, otherwise I do what I want.

Huh? Wait. So basically you're saying there's twice as high a chance of you getting what you want than of me getting what I want. That's convenient, isn't it? Why don't we just split the bloody dice equally - if it comes up 1, 2 or 3 we do what I want, and we do what you want otherwise. I'm okay with that. I don't see why I should be at a disadvantage just because it's your game.

Ah, but you won't be at a disadvantage. You see, after I throw the dice, you throw it too and the same rules apply. If it comes up 1 or 2 then you do what I want otherwise you do what you want. So you see, there's a two-in-three chance that you'll end up doing what you want as well.

So basically you're saying there's a two-thirds chance that you'll do what you want AND there's a two-thirds chance that I'll do what I want?

Yes, exactly.

Not very strong on fractions, are they, these game theorists of yours. It feels like one of us has a third of a chance too many.

No, no, obviously we don't always do the same thing you see. We can separate and each do our own thing.

So now you don't want us to spend weekends together? You want us to separate and do things by ourselves? Why don't you just come out and say that you don't want to spend time with me, instead of trying to blame it on some vague model that you made up?

No, look, it's not that I don't want to spend time with you. You know I do. It's just that that's the way the rules are set up. You do what the dice tells you to do and I do what the dice tells me to do. The rest is just up to chance. That's the whole point of it. Besides, it's not like we would be spending all our weekends separately. In fact, there's a 4/9th chance that we'd be together - either doing what you want or what I want (2/9th chance of each). It all depends on what the dice comes up with.

So basically we spend more than half our weekends apart. What joy. And wait. What happens if we both throw a 1? Then you'd have to do what I want and I'd have to do what you want, wouldn't we?

Yes, exactly.

What? You mean I'd have to go to an Antonioni retrospective while you went shopping for dresses? That doesn't make any sense. Why wouldn't one of us just go with the other?

Because you have to stick with the rules. Start switching decisions opportunistically and the whole thing will break down. Look, anyway, it's not like that's going to happen all the time. The probability of getting that outcome is just 1/9.

So basically your master strategy to keep us from arguing is to say that 5 times a year we each go do something that we don't want to, without the person we're doing it for?

Well, it wouldn't be 5 times a year exactly, of course. It could be more. It could be less. It's all probabilistic, you see.

I see. So we could end up doing this every weekend for an entire year.

We could. But it'd be really, really unlikely. A total freak chance.

But still, it could happen. If we were going to do this at all (and I'm NOT saying I agree, mind you) why wouldn't we just schedule it? Set aside the weekends that we were both going to be miserable? That way at least we wouldn't run the risk of it happening more often.

No, no, then it wouldn't be random anymore would it? That doesn't work.

Right. So not only should we be doing something neither of us wants to do, but we should also do it completely at random. Sort of like a weekly surprise.

Yes, exactly. Look, I know it sounds a little daft when you put it like that, but it really works. Honest. You can show mathematically that there's no way that either of us could do better by ourselves.

Really? We couldn't just talk about it like grown-ups, for instance? Instead of playing games with dice like we were five years old.

No, no, that's where the arguing starts. It's precisely to avoid having to talk about it that you need the algorithm in the first place.

So you're basically admitting that you'd rather leave your weekend plans up to chance than talk to me about them. Do you really hate talking to me that much? Has it really come to this?

No. Look, it's just a game, all right.

Our relationship is just a game to you?

No. This decision rule thing is just a game I learnt at school. I just thought it might be fun to try it.

I don't think so. Why are you spending your time doing stuff like this anyway? I thought your PhD was in Corporate Strategy. What are you doing trying to solve husband-wife conflicts?

No, no. I mean, the whole husband-wife thing is a metaphor, obviously. This stuff has tons of applications to other business problems.

Really? Like what exactly?

I don't know. Tons. Mergers and Acquisitions stuff. Systems integration. Competitive Dynamics. Lots of great stuff like that. You wouldn't understand.

I'm sure. So now you want our lives to be determined by a metaphor? What else can this Game Theory of yours do for us? Is there anything in it about sharing the TV remote, for example? I think I could use some innovative solutions there.

Well, actually, there is this game that kind of has the same structure. The way it works is...

I DON'T CARE!! Don't think I can't see what you're trying to do with this. Trying to weasel your way out of things you don't want to do. Well it won't work. That sale you didn't take me to last week is still on this weekend, and we're going. And no amount of manipulation with dice is going to get you out of that. So there.

Um...right. Okay. No need to get all hot and bothered about it, darling. I was just saying...


Notes:

I sometimes wonder why game theorists don't get divorced more. Don't get me wrong. I love the stuff. I watched A Beautiful Mind three times. Once I even cried. I'm just unconvinced that Game Theory has anything to do with real life.

Before people who love Game Theory start jumping down my neck, though - let me say two things. First, I'm well aware that the 'husband''s understanding of the Battle of the Sexes game above is woefully inadequate. There's a lot more nuance to the solution (and to Nash equilibria more generally), which he completely misses. And second, that I'm not saying that my criticism of being unconnected to the real world is true only of Game Theory. I actually think it holds for much of academia, I just think the Game Theory disconnect is the most amusing, and the description of the Battle of Sexes game simply lends itself to being made fun of.

Categories: Fiction, Humour