Tuesday, October 21, 2008

A tale of two Cities

Because they are self-contained economies, online games can lead to interesting natural experiments in economics.

Consider 'City of Heroes/City of Villains'. As the name suggests, this single game is divided into two distinct parts: good guys and bad guys. Subscribers to the game pay a monthly fee for the privilege of pretending to be a hero or a villain. The game world is shared by thousands of players, leading to a vibrant artificial economy.

The economy is set up as neatly as an economics instructor could hope for. The 'City of Heroes' and the 'City of Villains' may be thought of as two closed economies. Each produces the same products. Handily enough, these fall into the textbook favourite of two categories: recipes and salvage. For the present discussion, it does not matter what these goods actually are, only that they exist.

As in textbooks, the only input required for the creation of these outputs is time. Heroes 'arrest' bad guys and villains engage in nefarious acts to produce these goods. For various reasons, the City of Heroes has an absolute advantage in the production of recipes. In particular, heroes have easier access to certain rare recipes than villains do. Heroes and villains produce salvage at roughly the same rate, though arguably heroes have an absolute advantage here, as well. Anecdotal evidence suggests that heroes tend to work in teams more than villains, leading to factory work (heroes) vs cottage industry (villains).

One quirk is that salvage and recipes are complementary in production: if you make one, you generally make the other, as well. For heroes, the recipe/salvage production ratio is on the whole larger than for villains. (For those in the know: due to quick Katies, etc.)

Each City has its own currency. Goods are traded for currency anonymously on a consignment market, under a system that is very close to a Vickrey auction. Sellers post their goods along with a reserve price. This reserve price is not visible to buyers. If a buyer places a bid at or above the lowest reserve price, the good is sold at the bidded price to the seller with the lowest reserve price. That is, this system encourages high bidding by buyers and low bidding by sellers. There is no penalty for changing a buyer's bid, but sellers are subject to a transaction fee for each time they change their price.

While the prices at which items are posted by sellers are not visible to other players, buyers have easy access to the prices at which the last five units of the item have actually sold.

Market prices in the City of Heroes are generally much higher than in the City of Villains. The exception is for certain rare recipes, which due to their scarcity and some differences in tastes are far more valuable for villains than for heroes. (For those in the know: Pool C drops and Pet Damage IOs go for a lot more villainside.)

Scarcity is a constant problem in the City of Villains. There are far less producers (that is, there is a lower population) than in the City of Heroes, and so many goods are not available at any price.

There has been some demand for a merging of the two markets - that is, opening them up to trade. Most opposition has come from dedicated merchants on both sides. These are players who spend a considerable fraction of their time in arbitrage, buying low and selling high - essentially ensuring that the market in each city functions like a market.

Salvage traders in the City of Heroes worry that the price of salvage will drop considerably if there is trade between the Cities.

Most dedicated traders in the City of Villains worry that the entry of more producers (and traders) will lower their profits - right now, the villain market functions much like an oligopoly.

What does basic economics tell us about what may happen if the markets are merged?

First, for the easy part: water seeks a level, and so do prices. If the markets are merged, we can expect hero prices to drop and villain prices to rise, with the exception of the rare recipes mentioned above, in which case the effect will be the opposite.

The more interesting question (for me, at least) has to do with the nature of the money supply, and the speed at which currency changes hands.

The minting of money in the game is very different than in the modern real world. There is no central monetary authority. Instead, players mint their own money. Every time heroes 'arrest' a bad guy or villains mug someone, the game creates new currency and deposits it in the player's account. These are the same activities that also generate salvage and recipes.

In other words, in this virtual world, the money supply rises automatically with the production of goods.

There are some money 'sinks', of course, to ensure that inflation does not get out of control. There are transaction fees, luxury and vanity services that may be paid for and so on. Perhaps most importantly, there are no inheritances. When a player stops susbcribing to the game, the currency in their account is taken out of circulation. There are also restrictions on the transfer of currency between players. It is possible, but intentionally cumbersome and potentially risky.

The Fisher equation, beloved of economists, may provide considerable insight into what's going on.

MV = PY, as the saying goes, where 'M' is the money supply, 'V' is the velocity of money - that is, the speed at which money changes hands, 'P' is the price level, and 'Y' is output.

All this equation says is that, all in all, the value of transactions in an economy (the left-hand side) must add up to the value of output (the right-hand side).

For the purposes of our game world, 'Y' is the aggregate of recipes and salvage.

The same process mints money and produces good, so let's suppose that the money supply is some multiple z of output. That is, suppose that whenever salvage or a recipe is produced, so are z units of currency.

Our equation becomes

(zY)V = PY

Dividing both sides by Y,

zV = P

We now have a formula for the price level.

I mentioned that heroes produce recipes more easily than villains. In a half-hour period (the time for a 'quick Katie' task force, an activity which guarantees the produciton of a recipe by each player), heroes can produce more recipes than villains. The amount of currency (and salvage) produced in this time period is much the same for heroes and villains.

Since z represents M/Y, the money supply over output, z should be smaller for heroes than for villains.

If V is the same for heroes and villains, this suggests that heroes should have lower prices, overall... but they don't.

There are two reasons for this.

One is simply due to my simplifying assumptions. I assumed that all recipes are the same, where in fact heroes only have an advantage in producing a particular subset of all possible recipes - and these are, indeed, lower in price for heroes than for villains. The lesson: be very careful in your assumptions when trying to apply textbook economic models.

The second, more interesting reason, is that the velocity of money is drastically different between heroes and villains. The population of the City of Villains is much lower than that of the City of Heroes. Despite the two cities having similar (but not congruent) tastes, the variety of goods available for sale is much greater for heroes than for villains. All in all, this means that the market is far more active for heroes than for villains, and in turn, money changse hands far more frequently among heroes than among villains. There's more stuff to buy, and it's bought more often.

In terms of our equation, V is higher for heroes than for villains.

Let's look back at the original equation:


Rearranging this,

P = V x (M/Y)

What this tells us is that the higher the speed at which money changes hands, the higher you can expect the price level to be.

If the markets in the City of Heroes and the City of Villains were merged, we should expect the speed at which money changes hands to increase overall, due to the larger effective population of each market. This, everything else being equal, WILL lead to a rise in the price level of BOTH cities.

City of Heroes/City of Villains is quite a popular and active game, and new players join all the time.

There is some worry that if prices keep rising, new players, who start with no currency, will be priced out of the market.

This will not necessarily be the case, of course. Since new players automatically become producers of salvage and recipes as they go about their adventures, a high price level means that they receive large amounts of money for the goods they sell, as well as being charged high prices for those they buy. As any self-respecting economics student will tell you, the absolute price level matters very little: it's relative prices that you need to watch.

Still, there are some valid reasons for being worried about the price level. Suppose that the 'government' - the game's developers - wished to step in and keep the price level below a certain threshhold. What can they do?

They could adjust the rate at which money is minted. By lowering z, they may lower the price level.

They could place additional restrictions on transactions, lowering the speed at which money changes hands. For example, they could code in a law that required a cooldown period of an hour (say) after any transaction involving currency, however minor. This would be annoying for players, but certainly has the potential of lowering the price level. It could also have the perverse effect of raising the price of many items. Since the market works as a blind auction, bidders may choose to bid values very close to their actual valuation of the good in question, since they may not have a chance to do so again before the end of the auction.

They could flood the market with goods, lowering their price. I have a sneaking suspicion that they already do this for certain items. Some salvage is only available for production in October. One would expect that as time went on, the price of this salvage would rise, and then fall as October neared again. Instead, the price of this salvage has stayed remarkably constant. Other prices in the market have been very volatile, but the price of this salvage has stayed at 300,000 units of currency for months, only falling again in October, quite suddenly, to 50,000 units. This suggests that the game's developers have used their control of the game world to create 'helicopter drops' of this product in exactly the quantity required to keep its price constant, and affordable. This is a rather roundabout, but quite effective, way of enforcing price controls. It works here because the goods are entirely identical, may be created by the government at zero cost, and cannot be created by the citizenry except during the month of October. These conditions are unlikely to hold in the real world, where, alas, price controls seldom work.

Another possibility: due to their absolute control of the game world, the developers may have set the price of that salvage to be equal to 300,000, no matter what. This is less likely. Due to the way in which the market works, it could be discovered by players attempting arbitrage. Such a discovery would have led to scandal. Quantity manipulation works better than price-setting because due to the anonymous nature of the market, it is not possible to tell who put a particular item up for sale.

Textbooks, lectures and problem sets are, of course, essential for obtaining a detailed understanding of modern economics.

There's a lot to be said for spending some time in these 'sandbox' economies, though.


Anonymous said...

How would changing the AH system in CoX from a blind system as it is now to a more open system. Not so much to see who is selling what but what things are available at what prices. Change the current prices and in-game economy?

efan78 said...

I just thought it may be an idea to mention another factor that makes the CoH economy richer than CoV - the relative ages. CoH was around for over a year before CoV came along - causing the Heroes to have more inf.

Stray Silvers said...

An open system would encourage serious sellers to post higher reserve prices, and buyers to lower their bids (more than they already do).

The reason is that buyers and sellers would use the extra information, if at all, to find what the actual valuation of the good is by the other type of party.

This would allow them to be able to bid above their actual reserve price (sellers) or below their valuation of the good (buyers).

The effect would be most noticeable on items in short supply, where there are a lot of bids and no items available.

Bargains would also become very difficult to find. Dedicated traders would snap them up for resale even more quickly than they already do.

Stray Silvers said...

It is absolutely true that CoV has less money and product than CoH.

I don't think this matters a lot, though, precisely because the velocity of money would increase after merging.

For the first week or four, wealthy CoH players may consistently outbid poor CoV players, but very soon that money would be flowing back into villain pockets. After all, some of what heroes would be bidding high on are villain-posted items.

It's the same as trade between Canada and Mexico. Canada is a LOT wealthier than Mexico. Does that mean we shouldn't trade, or that trade is bad for Mexico? Not at all. If anything, complaints in the media usually run the other way.

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Sharp Focus said...

This was EXTREMELY interesting, and got me thinking about video game economies. It also got me wanting to play CoV/H again...

It also raises the question: do developers of MMORPGs hire economists to figure all of this out for them? If you look at a more popular MMO (World of Warcraft) you can, no doubt, see that it gets pretty complicated.

If they do hire economists, I think I just found a career to go with my future degree in Economics :).

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