We're all prisoners of game theoryPublication date: 21 February 2009
Originally published 2008 in Atomic: Maximum Power Computing
Last modified 03-Dec-2011.
"Game theory" is a branch of applied mathematics. And it is, as its name suggests, actually rather fun.
And useful, too. Grasp some basic game-theory concepts, and you've got a short-cut to improved comprehension of all sorts of tricky everyday situations.
Suppose, for instance, that you are a video-game reviewer.
The nice people at SuperExcellentSoft have sent you their newest game, Orphanage Burner IV, which obviously promised to be a lot of fun but is, in your opinion, actually not very good.
But SuperExcellentSoft have bought a great big ad in your magazine for many thousands of dollars. And will surely buy more, not to mention invite you to "release parties" at "corporate entertainment venues" where there will be "hookers" and "blow".
If, that is, you say nice things about OB IV.
Let us further suppose that you live in the frictionless Land of Game Theory, where the concept of professional ethics is as nonexistent as... well, as professional ethics usually actually is, among used-car salesmen, lawyers and journalists.
You now have a choice to make. That choice is one of the many permutations of the "Prisoner's Dilemma", which is one of game theory's Greatest Hits.
In the pure version of the Prisoner's Dilemma, two guys being separately interrogated by the police each have the option of clamming up, or of snitching on the other guy.
If they both keep quiet, they'll each get three months in jail. If they both snitch, they'll get five years each. But if one snitches and the other doesn't, the police will let the snitch go free and put the silent "patsy" away for ten years.
This sort of logical structure - where you can "cooperate" or "betray", and where there's a big reward for you if you betray and the other guy cooperates - is repeated over and over again, in all sorts of real-world situations. It seldom maps perfectly to the pure Game Theory Land version, but the basic concepts hold.
In the game-reviewer situation, you (the reviewer) can tell the truth about OB IV, in which case SuperExcellentSoft will pull their ads from the magazine and demand that you return that BMW M5 they "lent" you.
So you, the reviewer, lose.
But the readers of the review will win, because they won't waste their money on a crappy game. And, multiplied by the number of readers whose buying you may influence, that can be a pretty big aggregate win.
Or you can lie through your teeth, say OB IV is fantastic, and thereby reap great rewards... at the cost of a great big aggregate loss for all of your readers, who'll rush out to buy a crappy game.
To take a more everyday example, let's say you buy a new laptop on eBay from some dude in Hong Kong. He has the option of betraying you, by sending you a box with a brick in it in return for your money. You, in turn, have the option of taking delivery of a real laptop and then just saying that you got a brick in a box, and reversing your payment.
Or let's say you're playing a two-versus-two match in your favourite RTS. If you stick by your ally through thick and thin, you will get, at best, your share of the victory. But if you wait until your enemies are definitely going to lose and then stab your ally in the back, the glory (and online leaderboard points) will be yours alone!
The biggest way in which real-world situations usually differ from the basic game-theory Prisoner's Dilemma is repetition. In the real world, people do repeat business.
So if you skip out on the bill from a restaurant, you're unlikely to be welcome there again. And if you send your eBay customer a brick in a box, his feedback will affect your business. And persistent loot ninjas have a (slightly) harder time getting into MMORPG groups.
And, of course, reviewers who always profess unbounded adoration for anything that crosses their desk are likely to find that their recommendation becomes less and less valuable, as disaffected readers refuse to be fooled twice. (But, in the real world, it seems that there's often a healthy enough supply of fresh readers, TV viewers or stock-market investors to compensate.)
The game-reviewer situation displays one of the many ways in which real-world situations don't map perfectly to the classic Prisoner's Dilemma, because it makes another situation possible, in which the reviewer says the crummy game is great, but the readers, out of native cynicism or because this reviewer has lied to them before, don't believe a word of it and so don't buy the game. In this case, everybody (who matters) wins! The readers get the win of not buying one of those awful games the reviewer keeps saying are excellent, and the reviewer gets his reward from SuperExcellentSoft... until, at least, they realise they're not selling any games and bring the gravy-train to a halt.
All of the above examples illustrate the best strategy for sequential Prisoner's Dilemmas: Cooperate until you're betrayed, then betray.
(But don't make the mistake of betraying someone just because the last couple of times you dealt with someone else, you were betrayed. If people start betraying automatically, as they actually do in some games and unregulated markets, it spreads like a disease until the game's unplayable and the market's completely useless. Everyone's writing cheques that bounce to pay for bricks in laptop boxes.)
Philosophically, this is a neat example of creating "morality" from first principles, rather than waiting for some prophet to tell you what to do.
But it's also a very handy mental tool.
Especially when you notice your ally's parking an awful lot of artillery behind your base.