Monday, November 16, 2009

Arbitrage, Comparative Advantage, and World of Warcraft

Characters in World of Warcraft are in one of two factions, Horde or Alliance. The game is designed to make communication and trade difficult or impossible between characters of different factions.

There is, however, a loophole—the neutral auction house. Goods can be put up by someone in one faction, bought by someone in the other. Two players can cheaply transfer goods between a horde character of one player and an alliance character of the other by offering the goods at a negligible buy-out price (the auction house charges a commission based on the price), with the timing such that as soon as one puts the goods up the other buys them. Ideally, it's done at four A.M., when nobody is likely to be watching the auction house for good deals.

My wife, who has characters in both factions (I don't), has observed that the prices of many goods are higher, at least on our server, on the Horde auction house than on the Alliance auction house. This suggests, to an economist, an obvious question. Given the loophole provided by the neutral auction house, why don't players engage in arbitrage? Buy goods Alliance side, transfer to Horde side, sell them. Doing that would drive up prices on one side, drive down prices on the other, resulting in roughly equal prices for both factions.

The answer is that although the neutral auction house provides an inexpensive way of getting goods from one side to the other, it does not provide an inexpensive way of getting money from one side to the other. Horde gold and Alliance gold are separate currencies; there is no mechanism that lets you inexpensively convert one into the other. It is no more surprising that prices Horde side in Horde gold are higher than prices Alliance side in Alliance gold than it is that prices in the U.S. in dollars are higher than prices in the U.K. in pounds.

Higher prices on one side do not, by themselves, provide an opportunity for a profitable exchange. What does provide such an opportunity is a difference in relative prices. If some goods are considerably more expensive on one side and others on the other, or even if some goods are considerably more expensive on one side and others about the same price, or even if some are much more expensive Horde side and some slightly more expensive Horde side, then trading goods for goods through the neutral auction house does provide the opportunity for profit—a fact that my wife and daughter long ago discovered and demonstrated.

A player who understands this, who sees that in order to profit from trade you need to exchange something relatively more expensive Horde side for something relatively more expensive Alliance side, has gone a long way towards intuiting the principle of comparative advantage and so towards seeing that most of what he reads about trade deficits and associated problems is nonsense. It makes no more sense to say "China can produce everything cheaper than the U.S., so U.S. producers can't compete" than it would to say "everything is cheaper alliance side, so how can Horde crafters compete?"

Putting it in terms of two different currencies oversimplifies the situation a little. There are at least two ways in which it is possible to transfer gold from one side to the other—at a cost. One is to use the neutral auction house, buying goods from your trading partner at an inflated price and paying the auction house's 15% commission. The other is to shift a character from one faction to another, for which Blizzard, when it permits it, charges $25. The character takes with him his possessions, including his gold. There is, however, a limit—even a top level character cannot bring more than 20,000 gold with him.

Suppose prices are 40% higher Horde side, which seems at least roughly the case for some goods on our server (Feathermoon). You buy 15,000 gold worth of goods from the Alliance side auction house, smuggle them across to the character of a Horde side friend through the neutral auction house, sell them for 21,000 gold, of which you get 20,000, with the extra going as a commission to the Horde auction house. One of you then gets a character transfer from Horde to Alliance, taking with him the 20,000 gold.

On net, you have turned 15,000 Alliance side gold into 20,000 Alliance side gold, at a cost of $25 plus a good deal of (hopefully entertaining) time and effort. The current gray market exchange rate of WoW gold for dollars makes one gold equal to about .7 cents, judging by ads spammed on my server. You have made 5,000 gold, worth about $35, at a cost of $25. Not a very profitable transaction—you would be better off using the neutral auction house, which would let you convert 20,000 Horde side gold into 17,000 Alliance side, paying 15% to the goblins in gold but leaving you with a clear profit of 2000 gold, worth about $14.

All of which suggests why arbitrage does not wipe out the Horde/Alliance price difference.

I looked for realspace equivalents to moving character and gold from one faction to the other and found one. When Germany was reunified, the government decided—in my view foolishly—to treat East German marks as equivalent to West German marks, despite the fact that, prior to that, one West German mark exchanged for substantially more than one East German mark. An enterprising German who correctly predicted that decision could have bought goods in West Germany, smuggled them into East Germany and sold them—no doubt at some risk, but I do not know how great a risk during the period just before unification—and then turned his East German money back into West German money at one to one when Germany unified. I do not know if anyone actually did so or not.

Some time back, I suggested that WoW had potential for teaching economics. This post is an attempt to support that claim.


Johannes said...

It is not entirely correct that East German currency was converted on a 1:1 basis. Only a certain, relatively low amount of money per capita was converted 1:1, everything above was converted 1:2. That leaves your actual point untouched though.,_Wirtschafts-_und_Sozialunion#W.C3.A4hrungsunion

Unknown said...

Back in the old days, I'd just avoid the 15% neutral AH fee by putting up high-value items (Zul'Gurub bijous at the time, went for about 50g each) at the AH and coordinating with someone on an opposite-faction toon to buy them out just as quickly as they were listed... for 1g each, expensive enough to discourage low-level toons from buying them impulsively ("blue items on the AH for 1s! Oooh!"), but cheap enough to avoid 98% of the transaction cost. We'd make sure that the neutral AH was empty beforehand for extra security - later, neutral AHs were added to the goblin cities other than Gadgetzan, in which case we'd just monitor Everlook and Gadgetzan and hope nobody was looking in Booty Bay or Ratchet.

It worked well, and yes there definitely was a significant price differential... in my experience, the lower-population faction will have a sparser market and thus there will generally be more opportunities to exercise market power. If I was really trying to be sophisticated, I wouldn't have moved gold OR bijous through the neutral AH, but instead only traded back and forth items whose comparitive advantage dictated they be sold on one side of the market or the other. If I wanted more money on the Horde side, I'd buy the items with the highest Horde / Alliance price ratio and smuggle it over with a friend, and vice-versa for the Alliance.

Nowadays I don't bother playing both sides anymore, but one interesting thing I recall is that in patch 3.1, I think, a bunch of minipets were added to the game... each faction had access to five of them, and thus there were significant returns to be had by smuggling one faction's pets over to the opposite-faction AH (to some extent, this was already the case with more-common faction-specific pets.) You still see a markup of several hundred gold on smuggled pets on Elune Alliance nowadays.

Anonymous said...

There are other parts to the story you can add. One is that the transaction costs of the neutral AH are very high. It has a high fee (Peter says 15%), and worse, you have to spend real time travelling over there and then back to your faction's auction hause. Real time is dear for people playing a game.

There's also a large opportunity cost. Many, probably most, players that play the auction house earn considerable gold/hour simply sitting at their own faction's AH. They often stop from boredom long before diminishing returns become too steep. The travel time to go to a neutral AH is not only bad in real time, but that time in transit is time you lose from making money at the more convenient AH.

On the other hand, I don't understand your comments about the two currencies being separate.

First, the absolute prices seem important to me, at least when there are large differences. If all prices on one side are twice those on the other, then there are very profitable sales to be made by moving items from the low-price side to the high-price side. People in the low-price faction would rather sell on the neutral AH than on their faction. People in the high-price faction can pick up items at the neutral AH and resell them on their local AH. 40% might well simply be the amount necessary to overcome the transaction and opportunity costs.

Second, you glaze over the easier way to transfer money. At least on a PVE server, you can make characters on both sides. To transfer money from side A to side B, the character on B lists a low-value item, and the character on A pays an exhorbitant amount for it. The result is that money transfers from A to B, minus the AH fees. The AH fees, meanwhile, are a simple percantage, so unlike in the mechanisms you emphasize you don't have to spend real money on it.

Overall, I believe Blizzard has done an excellent job creating an in-game market that encourages people to follow their comparative advantage in what they enjoy doing. Whenever something is done rarely, the price of that activity's results becomes higher. Whenever something is done rarely by an entire faction, the neutral AH's can correct the difference.

Matt Ruff said...

Anonymous: and worse, you have to spend real time travelling over there and then back to your faction's auction hause.

Not necessarily.

Probably the most "efficient" way to handle a scheme like this would involve four alts, two from each faction. A Horde alt stationed at a Horde AH buys a bunch of goods, mails them to a Horde alt in Booty Bay or Gadgetzan, who puts the goods on the neutral AH to be bought by an Alliance alt, who mails them to a second Alliance alt stationed at an Alliance AH. And reverse...

Still a significant hassle, of course, and you'd need to devote four alt slots and a fair chunk of time, but possibly worth it if the margins are as high as Dave says.

ALF said...

The East German official exchange rate prior to the fall of the wall was 1 East Mark for one West Mark.
The exchange was strictly regulated. West Germans who travelled to the east had to exchange at least 20 West Mark per day. The East German State profited. To officially change East Mark to West Mark was only possible in very narrow circumstances. And I don´t think there was any possibility to change large amounts of East German Mark at the official rate.

The black market was between 3 to 10 East for 1 West. The black market was strictly forbidden with very severe punishments.

After the fall of the wall the black market price fell quickly to about 20 East for 1 West and stabalized at 10 to 1. And nobody cared any longer about the black market.

When the monetary union was established, the German Central Bank announced the terms of exchange on short notice to avoid speculation: East German people got some amount exchanged at 1 West Mark for one East Mark and the rest 1 West Mark for 2 East Mark.

Some people made a profit. And the German State lost Billions in the process. But it was psychologically very important to avoid that the East Germans felt that their savings and their economy was worthless.

Unknown said...

Dr. Friedman, do you and/or your wife Raid? I'm just curious if you were in a raiding guild, and if you have cleared any high end content.

If not, i highly recommend it. The strategy of synchronizing 25 people to one objective is fun!

David Friedman said...

Michael asks about raiding. I, my wife, our son and our daughter are all in a weekly 25 man raid, currently doing Ulduar. My son and I are also in a 10 man. Not a guild, but for these purposes the functional equivalent.