Game Theory and Content Copying / 2009-09-26

Since I learned a bit of game theory recently, I thought I’d apply it to the problem of consumers copying digital content, rather than paying the producer for their own copy. The idea is that it’s similar to classic examples in game theory where all individuals acting in their own interest (or “rationally,” according to capitalism) result in the situation being worse for everybody.

We could set up a theoretical example like this: say we have a million players, and each player has to choose independently whether or not to pay $10 for music (think of it as a particular CD if that’s easier, and pretend that it’s music everybody likes). Because of free copying, they will receive the music regardless. The quality (i.e., monetary value) of the music, however, is directly determined by the number of people that pay. For simplification purposes, let’s say that the value of the music is equal to half of what’s payed for it (suspend your disbelief about this for a moment). So if all of the one million people pay, then $10,000,000 has been payed, and music worth $5,000,000 is distributed to everybody. Obviously this is a pretty decent situation: everybody has virtually become $4,999,990 richer because they now have access to some great music.

So let’s say you’re one of these people, and you have to decide whether or not to pay. You may not know what the other people are going to choose, but when you analyze your two choices, it really doesn’t matter. Your $10 will only increase the value of the music by $5, so you’ll be better off by not paying. This is intuitive from several different angles. The only Nash equilibrium in this game is when nobody pays. Nobody pays, and nobody gets any music, so nobody’s net worth has increased at all. Everybody is much worse off, even though they each individually made decisions that were cleary favorable for them.

Of course, anybody who needed to suspend disbelief back when I suggested to will probably also notice that the game was set up this way. If I had said that the value of the music was equal to the amount paid for it, then there would have been no tendency not to pay. In that case, every strategy would be in equilibrium, so behavior would be impossible to predict. On the other hand, if I had said that the value of the music was more than the amount paid, we would have the opposite equilibrium: everybody would want to pay. So now I’m going to see if I can determine the more influential factors that affect this game in real life, so we can predict the future of music as we know it.

To Pay vs. Not To Pay

There are a number of influencing factors in real life. To start with, if nobody pays for music, this does not mean there won’t be music. Plenty of people make music for free, for a variety of reasons. So it’s not entirely clear that we’re worse off if nobody pays (mostly because, if everybody pays, then we’ve collectively spent a lot of money on music).

Second, artists producing music may be able to increase the quality of their product if they’re paid more, but there’s certainly a logical limit to this. I doubt anyone would expect that a musician paid $10,000,000 for an album will necessarily produce an album that’s ten times better than the same musician paid $1,000,000 for the same album. There may even be no discernable difference at all.

Third, musicians usually aren’t paid until after the music has already been produced. So they can really only guess what they’ll be paid for it. This means a person deciding whether or not to pay for music knows for certain that their choice will have no effect whatsoever on the quality of the music in question. It certainly may have an effect on the quality of future music, but that requires a bit of foresight to act on.

Fourth, owning music without paying for it may be illegal. However, this may be very difficult to enforce. For example, I could take a song file and encode it in a series of pictures and post it on flickr for anybody to download and decode. Attempts to enforce this sort of law end up producing complicated actions and reactions that usually make everybody fed up with the content producing industry.

Fifth, many people grew up in an age where musicians were paid by anyone who wanted to own their music, and therefore consider it to be the natural way of things. However, generations in this category will eventually be replaced by generations without the same inclination.

Sixth, many people feel social pressure to pay, because to not do so would be seen as mooching off of those who do. This can influence a lot of non-compulsory behavior, such as tipping, and other examples I can’t think of. However, of all the things in this category, the act of downloading a file in the privacy of one’s own home is least likely to be influenced by social pressure. I suspect this is a major reason why guilting people into paying has such a minor effect.

Seventh, in a global market the effect of any given individual is difficult to detect, so people will be easily able to convince themselves that their actions are inconsequential. Only in very local markets does the opposite become true.


It’s complicated. You figure it out.