Tuesday, August 10, 2010

Game Theory for Writers: Part I. Go Ahead and Burn That Bridge!

I had hoped to get this out much earlier, but later is better than never.

I also am going to have to do this in a couple different series since there is SOOOOOO much I could write about and don’t want to overwhelm all at once.

Now first, why do we care about game theory (GT) in writing? Well for one it helps you get a good grasp on what people would do in various situations. For second it will allow you to identify strategies that a smart character would use to win some sort of game (by game I could mean a game of checkers, or the “game” of taking over the world. Basically game just means a situation where there is some sort of competition). So hopefully you will be able to craft out a well thought-out plot that has your evil villain choosing the wrong strategy and going down in defeat because your hero was smart and picked the right one.

If that convinced you, now we need to get you grounded in GT. Basically all you do is write down the different choices the different players could make and the outcomes of those choices. So a real simple model game would be odd/even. This would be where player 1 (Bob) holds either 1 or 2 fingers behind his back. Then player 2 (Meg) tries to guess the number. Real simple.

Now lets say that when Bob chooses a 1 and Meg chooses a 1, then Meg gets $2 and Bob gets $1. If Bob chooses 1 and Meg chooses 2, then Meg gets nothing, and Bob gets $1. Now if Bob chooses 2 and Meg chooses 1, then again Meg gets nothing and Bob gets $1. Now if they both choose 2, then Meg gets $2 and Bob gets nothing. This is shown by the following chart.

Meg/Bob Bob (holds 1) Bob (holds 2)
Meg (guesses 1) 2/1 0/1
Meg (guesses 2) 0/1 2/0

So you can easily see that Bob should always choose 1, since his payoff is always going be be as good or better than if he chooses 2, and Meg, knowing this should also choose 1 every time. And since neither player can do better than this, both choosing 1 is called a Nash Equilibrium. Yes that same John Nash from A Beautiful Mind.

What does this particular game tell us about writing? Not much frankly, but that is notation that you need to know before we get onto the good stuff.

So the first thing I want to show you is why a smart character will eliminate one of their options in certain situations in order to gain an advantage. Yes that’s right, you can gain an advantage if you eliminate an option. So a businessman can gain an advantage over a competitor if he shuts down a factory, or a warrior if they burn their ships. Lets see how.

Lets take a business case. Say Sony and Microsoft are both existing in the business world. Microsoft happily making software, and Sony happily making TVs. Then one day both of them get the idea to make a gaming system, but then the market research folks come in and spoil the day. They conclude that if both companies enter the market, the competition for market share will be a drain on the company and they will both make $0 in profits. If both companies give up plans to make a gaming system, they will both go back to making $2 billion in profits. But if one company retreats, while the other company goes forward; the company making the gaming system will see profits of $5 billion, and the other will suffer from embarrassment and their customers won’t want their products. They will only make $1 billion in profits.

Here is the chart:

Sony/Microsoft Microsoft (retreat) Microsoft (go ahead)
Sony (retreat) 2/2 1/5
Sony (go ahead) 5/1 0/0

After many intense negations, neither company is willing to let the other be the only one with a gaming system, so obviously the best solution is for both of them to retreat. But then Bill Gates out of nowhere guts his software business and declares that from this day forward, Microsoft will focus only on their gaming system. They have essentially removed the option for them to retreat, and only the second column remains. Sony now has to choose between $1 billion in profits, or $0. Unless they want to sacrifice their company too, they will retreat and Microsoft will win.

So a warrior then who burns the bridges behind them and forces themselves to fight will gain this advantage. Same with somebody playing chicken who removes their steering wheel. Same with hostage negotiations when you have a policy where you can’t negotiate. The list goes on.

The one caveat with this is that the other player must know this. If not there could be disastrous results.

Now go out there and show off how smart you can make a character look by having them eliminate the safe option and take victory!


  © Blogger template Brooklyn by Ourblogtemplates.com 2008

Back to TOP