ARBITRAGE AND EQUILIBRIUM IN THE TEAM FORTRESS 2 ECONOMY

Arbitrage is the holy grail of every trader. The dream of buying low and selling high (for this is what arbitrage is all about) is the driver of all commerce but also its own worst enemy: for as everyone is trying to pursue it, the potential for arbitrage disappears. And when it does disappear totally, we have equilibrium (the holy grail of the economists).

One of the problems of living in the analogue world is that these concepts (e.g. arbitrage and equilibrium) are extremely hard to pin down. No one has enough information on how actual prices diverge from their ‘equilibrium’ level so as to be able to measure, or to visualise, the potential for arbitrage. All we can do is guess what it might be. Not so in our digital economies. The following diagram, for instance, captures the room for arbitrage (what we call an Index of Arbitrage Potential for Steam trades of Team Fortress 2 items) as it arose during the period 13th November 2011 to 23rd May 2012.

The peaks represent moments when there was a great deal of room for arbitrage (i.e. for buying low and selling high), while the line’s thickness reflects the volume of actual trades. It is no great surprise that these peaks coincided with major new releases and sales (e.g. the Christmas sale) that the community required some time to price properly.  Where did this Index of ours come from? How come we could compile it for our economy when no economist can compile a similar index for the ‘real economy’ out there? The answer to the second question is simple: Unlike the analogue economy (where we can at best sample some prices at discrete points in time), at Valve we have all the real time data there is, courtesy of Steam: a peculiarly sophisticated barter economy. Let me explain why I am calling it ‘peculiarly sophisticated’ before explaining how we put together our graph above.

A peculiarly sophisticated barter economy

Steam enables Valve’s gamers to trade freely with one another, effectively to establish a substantial economy in which thousands of items, also imaginable as assets, are exchanged for one another. This is a typical barter economy, in that every exchange necessitates a double coincidence of wants (i.e. when Jack offers Jill some Team Fortress 2 hat in exchange for a couple of keys, the trade will go ahead if, at the same time, Jill also prefers that particular hat to her two keys).

Barter economies are cumbersome precisely because they require this double coincidence of wants before any bilateral trade proceeds. For this reason, throughout history, whenever the number of transactions (and ‘assets’) grew in number, one of those assets soon emerged as a numéraire – a basic form of money that is. Once the numéraire acquired currency, suddenly the prerequisite of some double coincidence of wants vanished and people could trade anything for the numéraire–asset which they could then use in order to buy whatever else tickled their fancy. In short, as economies grew in sophistication, they ‘monetised’ and ceased functioning on the basis of barter. This is why never in history have we witnessed truly sophisticated barter economies (for reasons similar to why we have not developed hugely sophisticated training wheels for professional cyclists).

Initially, I had expected that a similar pattern would be replicated in digital economies, like Valve’s. I was expecting to find that some item or asset would emerge as currency in the context of games such as Team Fortress 2. However, a close study of our Team Fortress 2 economy revealed a more complex picture; one in which barter still prevails even though the volume of trading is skyrocketing and the sophistication of the participants’ economic behavior is progressing in leaps and bounds. 

What is an economic equilibrium?

Those of you unlucky enough to have suffered the privilege of studying economics 101, will recall our fixation with something we call equilibrium. Why is equilibrium such a central concept in economics? The simple answer is that, without it, we economists stand no chance of explaining anything, let alone predicting (prices, quantities, etc.).

The idea of an equilibrium sprang up, like most scientific ideas, from physics. Suppose that you see a rock rolling down a mountain. Can you predict its path? Or, equivalently, can you predict its final resting point? If you can, then you have a pretty decent idea of its actual path. Well, this ‘resting point’ is what we mean by equilibrium: the point at which some ‘system’ will reach a resting place; a place in which there will be no tendency to carry on ‘moving’. Back to economics, suppose that we are witnessing the price of oil increasing, after (say) a period of relative stability. Will it stop at some level? Which level will that be? In other words, will it reach a new equilibrium, and if so what is the equilibrium price?

To complicate things a little, both in Nature and in some economy, an equilibrium can be either static or dynamic. A static equilibrium means no change. The ‘system’ under study is in complete standstill. Like the rock that stopped rolling. A dynamic equilibrium, by contrast, entails movement but of the sort that is eminently predictable, periodic. For example, the Earth’s orbit around the Sun (while neither the Earth or the Sun are stationary, the Earth’s orbit is). Or the demand for toys which, predictably, peaks before Christmas, every Christmas.

Equilibrium in a barter economy

Consider a small scale version of an economy like that of Team Fortress 2 (TF2) – the first Valve economy that I had the pleasure of studying. Suppose that there are four tradable items only: Some laser gun (G), one type of hat (H), earmuffs (E) and keys (K). Now suppose that we observe that players trade these items in the following proportions, or exchange rates (also known in the economics trade as ‘relative prices’):

  • 2 hats for 1 laser gun
  • 1 key for 2 laser guns
  • 3 earmuffs for 1 laser gun

Question:       Recalling that equilibrium is reached when there is no further room for arbitrage, how many hats should 1 ear muff buy if this economy is to be in equilibrium?

Answer:          From the ‘numbers’ above, we know that, in terms of exchange values:

Value of 1 laser gun = value of 2 hats = value of 3 ear muffs = ½ a key

OR

1 key buys 4 hats, or 6 ear muffs, or 2 laser guns.

Thus, the relative price of hats to ear muffs ought to be 4-to-6, which is the same as an exchange ratio of 2:3 hats to earmuffs, or 3:2 earmuffs to hats. In terms of a table, or matrix, the above reduces to the simple question: What should the missing entries be (i.e. the numbers in the red, blue and orange cells) if this tiny economy can be said to be in equilibrium?

We have already found the missing number in the case of the red cell: It is 3/2, i.e. the exchange ratio, or relative price, 1.5 earmuffs to one hat (or 2 hats for 3 ear muffs). Before moving to the missing numbers in the blue and orange cells, let’s first make sure we understand that unless the number in the red cell is 3/2 there will be room for arbitrage – which, in turn, means that some entrepreneurial person will try to exploit, with the result that the prices in the first row will end up changing.

Suppose that the number we actually observe (from our trading data) in the red cell was 3 (as opposed to 3/2). What would that mean? It would mean that a smart Jill, some fictitious player, could do the following starting with, say, 6 earmuffs:

  1. Jill could trade her 6 earmuffs for 2 laser guns (since, from the first row, we know that she needs 3 earmuffs to get 1 laser gun)
  2. Jill could then trade these 2 laser guns for 4 hats (since, again from the first row, we see that the exchange rate is 2 hats per laser gun)
  3. Finally, if the number in the red cell is 3, she could trade each of her 4 hats for 3 earmuffs – ending up with 12 earmuffs.

This is a typical case of arbitrage. Jill starts with 6 earmuffs and, just by bartering, she ends up with more earmuffs than she started off with. While this is great for Jill, economists believe that arbitrage opportunities of that sort cannot survive for long. Why? Because, if these opportunities for gain (without pain) are freely available, they will be exploited. So, others will emulate Jill, trying to trade earmuffs for laser guns and then laser guns for hats, before trading hats back to earmuffs. But all these offers of earmuffs (corresponding to what Jill did in the first step above) will exert downward pressure on the relative value of earmuffs. E.g. it will cause players selling their laser guns to demand more earmuffs for each of their laser guns. Thus, the price of earmuffs will fall (relative to laser guns) and, therefore, the opportunity to end up with more earmuffs (through selling them before buying them again) will disappear.

In short, as players take advantage of arbitrage opportunities, the economy tends to equilibrium and, when it gets there, there are no arbitrage opportunities left! What would our economy look like in such a state of equilibrium? The following tables answer the question: Each relative price in the oval shape must equal the relative price in the rectangle divided by the relative price in the triangle.

More generally speaking, in economies like (our TF2 one) with many, many items that are being traded, say N, there will be (N=1)N/2 relative prices; e.g. even if we only had 100 assets, we would end up with 4950 relative prices. Imagine the complexity of the TF2 economy where we have more than 35 thousand items. We are talking about more than 600 million relative prices at any one point in time. What would an equilibrium look like? The answer is less complex than you may think. This is what our N by N matrix of relative prices looks like when assuming that keys (k) are the Nth item:

Just like in the simple 4 item example above, our prices are in equilibrium when the following equalities hold – which are no more than an extension of the conclusion above that each relative price in the oval shape must equal the relative price in the rectangle divided by the relative price in the triangle:

Why care about equilibrium?

The simple answer is because it makes our lives (as economic analysts) much, much easier. Take again the simple 4-item example above, in a state of equilibrium:

The beauty of equilibrium is that it makes it possible for us to quote only one price per item. Indeed, the matrix above can be reduced to a simple menu list which gives us the price of laser guns, hats and earmuffs in terms of number of keys necessary to purchase one unit of each:

Suddenly, instead of 6 prices we have 3. And in the case of 99 items, the number of prices reduces drastically from 4950 to just… 98 (one per item, excluding the keys that have no price, as they are the effective currency).

Should we expect the economy to be in equilibrium?

We wish! But if we assume, as economists tend to, that equilibrium prevails most of the time we are inhabiting La La Land. Indeed, the first great economists (people like Adam Smith and David Ricardo) never thought that an economy would ‘equilibrate’; that it would ever reach equilibrium. They just hoped that competition will cause economies to tend to an equilibrium, which is quite different to saying that they will actually get there. So, to cut to the chase, we should never assume that our economy is in equilibrium.

Now, the beauty of digital economies is that we have all the data at our disposal. We can actually observe how far or how close to equilibrium our economies are. So, one of the first things I did at Valve was to put the TF2 economy under the microscope to see whether it is in equilibrium or not. Guess what: it is nowhere near it. So, folks, it is official: There is plenty of room for arbitrage. Moreover, this arbitrage window varies in size constantly – as we shall see below via the medium of some nice graphs.

But first, to measure the arbitrage potential, or window, we needed to develop a method for assigning one price per item even though our economies are hardly ever in equilibrium (a fact that, according to what I just wrote above, should rule out assigning one price per item). This is how we did it:

Measuring the relative prices/values of the TF2 economy

Having observed that the TF2 economy is never in equilibrium  long enough for us to be able to derive one price per item, we asked ourselves: Is it possible to measure the size of our economy? To offer a valuation of some hat or other item? To answer any of these questions, we had to find a way of pinpointing one price per item (e.g. some hat) when, in reality, there is not one but many (e.g. one in terms of laser guns, one in terms of keys, one in terms of earmuffs and, to boot, these prices are in conflict with one another – thus giving rise to arbitrage opportunities). How could we do this?

Suppose that, returning to our trusted 4-item example, we have the following disequilbrium prices (averaged out over a period of, say, a week):

Because we are in disequilibrium, it makes no sense to take the last column as a vector of our relative prices for G, H and E. We need to take into consideration the fact that the other numbers (in the other columns) are inconsistent with the last column and pack important information about the value of each item (that we should not throw out). Here is what we did in order to compute single price estimates for each item:

We began by noting that, if the economy were in equilibrium, the following equations would hold:

Then we observed how many times, during the same period of observation (week in our case), guns were traded for keys (say NGK), guns were swapped for hats (NGH), guns for earmuffs (NGE), hats for keys (NHK) etc. Beginning with the item that was traded most often, we computed the price of guns as its exchange ratio with that most heavily traded item. E.g. if keys were the most traded, we would define the price of guns as . Next to compute the price of hats in terms of keys we would use the equation (see above) =, which would have held in equilibrium. But because we are not in equilibrium, we augment it by the relative frequency of trades as follows:

Estimated price of hats in terms of keys =

In other words we weighed the two sides of the equation that would have held in equilibrium in a way that reflects which of these bilateral trades were relatively more frequent (and thus influential). In this manner, and after having dealt with a significant number of computational issues that I shall not bother you with here, we ended up with a method deriving a list (or vector) of prices per item. What were they expressed in? They were expressed in something I call notional keys; i.e. the ‘keys’ that would have been observed if our economy were in equilibrium. In other words, a made-up currency that converges to the actual keys of the TF2 economy when the latter approaches to equilibrium, as arbitrage opportunities vanish.

And the result? Here is a graph depicting our estimates of the (relative) price of three popular TF2 items: earbuds (in red), Bill’s hat (in blue) and refined metal (in purple). [Note that this diagram pertains to the period between November 2011 and 1st June 2012.]  

Arbitrage opportunities come and go in the TF2 economy

So, the time has come to explain the derivation of our Index of Arbitrage Potential as it appeared in the diagram with which this post began.

In the preceding analysis (as evidenced by the last diagram) we managed to compute one price per item in the TF2 economy. From these it was easy to derive our Index of Arbitrage Potential. Here is how we did it: We have already worked out that the following equations must hold in equilibrium:

By computing the extent to which these equations do not hold (by means of computing the least squares of the differences between the left hand and the right hand side of these equations, all added together), we can gauge how far our economy is from equilibrium at any point in time. And we can then graph these against real time, looking out for fluctuations in the presence of arbitrage opportunities as new items (ones not previously priced by the community) enter the game. The result is a series of rather cool graphs, one which you saw at the beginning of this post.

Conclusion

When trading on Steam, there is always potential for gaining by buying items cheaply and selling them expensively. By the same token, you may be short-changed, so to speak. In this post I tried to show you how these opportunities and dangers come and go; how they expand when new items or sales are released and then wane as the community learns to price things more consistently (i.e. as arbitrage gives way to equilibrium). I think this is fun to see. The tantalising thought also comes to mind that we could, perhaps, let you see this graph in real time, to guide your trading. Or perhaps not? What do you think?

90 Responses to ARBITRAGE AND EQUILIBRIUM IN THE TEAM FORTRESS 2 ECONOMY

  1. Warren Blyth says:

    It would be interesting to show a graph of arbitrage in conjunction with a community event. (just as the War event challenged players to focus on demoman or soldier, it would be interesting to challenge the community to take sides in a scarcity event that tied into the greater story. perhaps offering knock offs of popular items in Australium, or cheap Taiwanese plastics, and claiming the knock offs will only exist as long as people push the arbitrage graph way out of wack. call it Black Friday. or The Great Impression.) (…or The Hats Depression.)

    I’m still not on board with the TF2 barter system. (seems like a secondary game, that distracts from what I enjoyed about the core game). But reading your post certainly makes it seem more substantial and worthwhile (less of a mystery of which to be suspicious).

    *one big question:
    You note “at Valve we have all the real time data there is, courtesy of Steam” – can you/anyone speak more to how you’re storing or interpreting that data? I’ve been fooling around with gathering massive amounts of data for biometric feedback, and I’m more and more baffled as to the details of sifting though garbillions of points of data per second.
    (maybe a future blog post could be about how to sort through tons of data in meaningful way, in real time? or how one stores it for sorting through later?)

    (*also, i think there’s a typo in your post. one line reads just : “E.g. if keys were the most traded, we would define the price of guns as .”)

    Thanks for sharing all this!

  2. Vash says:

    Let us see this in real time. Allowing the community to see this information would promote fairer trading with zero negative effects.

  3. Warren Kertis says:

    Very interesting indeed! :D

  4. William Eagle says:

    Good read. It is my opinion that Valve should remain “out-of-the-loop” regarding trading activities. I have always held a high-regard for Valve and their approach to this economy. To have an active hand in publishing these prices may cure the “spreadsheet” blues..but it may also form a falsely restrictive market..much like what has happened with the spreadsheet readers/believers.

    I think it’s a good idea in theory..but in practice…it may lead the blind more.

  5. James says:

    Sooooooo TF2 has its own economy…..

  6. nickk says:

    Thanks for putting these out valve, as a fan of TF2 and an economics student i think this is incredibly interesting.

  7. Connor Huffine says:

    There is also an interesting room for arbitrage within the TF2 ‘Black market’ of paypal for items. For example, most people value a ref at $0.50 or less. Keys are valued at 2.55-2.66 in ref, but are sold for $1.25-1.50. Thus, buying ref, using those to get keys, and then selling the keys will lead to real money profit. The only reason the entrepreneur types avoid this is because of the inherent risk in paypal exchanges, ie Chargebacks. This leads to an interesting region for profit that is only for risk takers. The inherent danger keeps the profit window open, but I still don’t understand why it hasn’t narrowed at all. The price for ref is always on the low side, and keys the high side. An interesting disparity. I don’t know if you plan to delve into the black market side of trading, as it’s not as trackable as the purely digital transactions, but it’s certainly an interesting dynamic. I look forward to more posts from you! It’s neat to see an economist take a look at the TF2 economy, especially when you reaffirm conclusions I’ve reached. I’m learning much about how these systems work, and plan to take macroeconomics next semester. I am proud of the fact that I saw the trend and bought festive weapons when they were going for 1 or 2 rec, and sold them when they were a ref each. I’m collecting now that they’re a bit under a key each, and I’ll sell them this fall when they should be higher, before the market tanks when everyone puts them on the market in November/December. Anyways, keep up the neat analysis! Looking forward to more posts!

  8. Joaquin says:

    In conclusion, would it be better if Valve added a money system or not? I know direct trading is doesnt conclude well (i can have a hat my trader wants, but he does not have a thing to give me that i value more than my hat, and viceversa). The introduction to the “coin” may be the key to a whole new and bigger market world. People would get more chances to trade their items, as they could buy others. It doesnt have to be real money, but a type of coin made just for Steam/Valve. I kindly ask you, and sorry if Im wrong, I´ve just started economy classes and it confuses me. Thank you.

  9. Cory says:

    There is in fact a currency of sort in TF2. Everything is traded in terms of Refined Metal. Check the spreadsheet that is used for trading. http://tf2spreadsheet.blogspot.com/

  10. marcadia says:

    Fascinating article I must say. It is very interesting to take in the thoughts of a professional on the matter. As a sometime TF2 Unusual hat trader I completely agree with your conclusions drawn from the Index of Arbitrage. I have made a decent profit several times by acquiring new items (particularly Genuines, Strange Parts, etc…) cheaply and selling them on at a premium to people desperate for the newest shiny pixels. The following thoughts are from somebody who hasn’t even taken Economics 101, however I will give it a shot.

    I would disagree with your inference that “an item or asset” hasn’t emerged as currency, as I believe that an ingame currency has emerged for medium to high level trading, at least over the last few months I have actively been trading. I believe that some data may be missing from your sample – namely, items traded for real world cash. This happens quite frequently, both from people aiming to make real world money from their arbitrage, and from those who are moving on from TF2 and ‘selling up’ to extract all the value they can from their playing hours by flogging their virtual items to the highest bidder. I don’t know if you have controlled for this factor, but the information pertaining to one half of all these trades wouldn’t be known to Steam. I’m fairly sure that trades where real world cash is involved are a mere fraction of the overall trading volume, however I would suggest that they heavily influence the ingame economy, as they offer ingame traders the opportunity to profit in real cash terms from their gaming/trading hobby. Thus the rarest items are not only a mark of prestige – they can be (and often are) sold for a hefty return.

    The data and examples below are taken from a few sources, primarily http://www.sourceop.com. This is a community site which houses a very active trading forum for item buying, selling (both in real world money, normally USD via PayPal) and trading items. Interestingly, it is also where the trustworthiness of an individual is vouched for via their ‘Reputation’ forum thread. The purpose of these posts is to deter scammers and ‘sharks’ (a dishonest trader who exploits the ignorance of trading newbies to acquire their valuable items for a pittance). You can also see the emergence of trading confraternities – a class of ‘Reputable traders’ complete with rigorous membership conditions. Other important sites include http://tf2spreadsheet.blogspot.co.uk (a price index for every ingame item) and http://www.tf2op.com and http://www.tf2tp.com (informal, real-time auction houses). This is not an exhaustive list, but a quick visit to each will give you an idea of the sheer scale of the medium-high value trading market.

    I would argue that Refined Metal, Keys, Bill’s and Earbuds have emerged as a de facto currency, particularly at the high levels of trading. I would also argue that this currency (for ease of use I will call it Promo currency, as the higher denominations are Promotional items that exist in finite numbers) is ‘pegged’ to real world USD, at an exchange rate of 1 Earbud = $30USD. So, I suppose the Promo is more of a shadow currency. Its raison d’etre is to minimise the credit risk posed to sellers of high-value items seeking to turn their online items into real world cash.

    The risk exists due to three key factors:
    1/ There is no way to exchange money on Steam, which means the trading interface isn’t useful for this purpose.
    2/ The ubiquity of PayPal and its inherent bias towards buyers. PayPal offer very little protection to virtual item sellers and will 9/10 times side with the buyer in payment disputes. This is due to virtual item trading being a misunderstood, niche activity. PayPal see the lack of physical shipment proof on behalf of the seller and will ‘chargeback’ the cash paid by the buyer. Thus it is trivial for an item buyer to ‘pay’ for an item and, once received, file a complaint with PayPal safe in the knowledge that they will get their money refunded and get to keep the item.
    3/ Lack of faith in real world cash internet trading. While some high-volume traders will have the aforementioned ‘Reputation’ post that can vouch for their integrity, most traders will not. There is no easy way on the internet to distinguish between the trustworthy individual and the scammer, and it is even harder for the uninitiated trader to do so. His risk of getting scammed is high – see the http://www.steamrep.com forums for daily evidence of hapless newbie traders being scammed for not inconsiderable sums.
    So, an easy way to the seller to mitigate his credit risk is to demand payment in the Promo currency. This takes place via the Steam trading interface, and thus it is virtually impossible for the buyer to scam him. As I will explain below, he is safe in the knowledge there will always be a demand for Earbuds at a standardised price of approximately $30/Earbud. Once he has acquired said Earbuds in a risk-free manner, it will be easy to sell them on to one of the reputable, high-volume sellers found on a trading website, who are always eager to purchase them.

    At this level it isn’t uncommon to see Unusual Hats and rare items such as the Hat of Undeniable Wealth and Respect, Gentle Manne’s Service Medal etc… change hands for upwards of $300. You quite rightly point out the static value over time of Refined Metal. This item has also held a consistent cash value of ~$0.55 USD, and is normally used to denominate trades in Genuine Hats, Miscs and other (non-rare) Craftables.

    Mann Co keys again have held a fairly static value of ~$1.45 USD/2.5 Refined Metal per Key for the last few months, and while they can be used in trades of practically any value, they are generally used to trade Vintage hats, Misc items and Genuine items. Bill’s Hat (with black/white paint applied) is used as a convenient way to denote ~10 keys (Decimalisation of currency? Coincidence?). Basically, keys are your dimes, Bill’s are your dollars, and Refined Metal is your pocket change.

    Earbuds have held a static value of ~$30 USD over the last few months. Their scarcity begets a high price and makes them perfect for use in the trading of high-value Unusuals, where trades are almost exclusively denominated in Earbuds. While it is not unheard of for keys to be used for Unusual trading, using Earbuds is alot simpler and quicker, and thus the vast bulk of Unusual trading is denominated in Earbud prices. For example, typically Bidder A stats that he will buy for 2 Earbuds and Bidder B trumps this with a 2.5 Earbud bid. This makes them highly liquid. Thus traders overwhelmingly prefer Earbuds over bartering when selling their Unusual. They know that Earbuds will hold their value over time and are the lynchpin of the high-level economy.

    Witness the rise of the infamous refrain “you will overpay in Unusuals” from Unusual hat sellers. They are putting a premium on bartering – almost a tariff, though that terminology is probably wrong. This is to mitigate their risk, as Unusual Hat values can be very fickle and are very much dependent upon what the flavour of the month is. Outside of the 10-15 commonly accepted top-tier and low-tier Unusual hats, they are very much an unknown quantity, and a lot of the buying/selling is speculative. This is where Earbuds are useful to the Unusual hat trader. If he wants to ‘cash out’ of TF2 down the line, he knows there is always a demand for Earbuds at $30 USD, whereas in the future his Unusual Hat might not be worth the $60 (2x Earbuds) he can trade it for now. If a buyer is unsure of the value of a particular hat, he can offer in Earbud multiples (generally the minimum pricing for an Unusual hat) until the seller accepts. If the item is priced too high, he can take his Earbuds and purchase an Unusual of similar quality/scarcity from a competing seller; whereas they may have had no interest in the Unusual hat that he sold to acquire said Earbuds. He can also research what the current Earbud price is for other hats of a similar standard and offer accordingly. Thus I would posit that Earbuds have not become the numéraire of the Unusual hat trading world, they are at least the shadow currency.

    Well, I have well and truly rambled on, much more than I intended. It is late and this is probably full of errors. Sorry for the train-of-thought attack, hopefully it makes some sense at least!

  11. Skizem says:

    I will say that I am loving these articles already. Amazing to see real world economic principle being applied to a digital economy.

  12. Jeff Stewart says:

    Fascinating!

    The reason that TF2′s economy has remained a barter economy despite its scale seems straightforward, though: there is no numéraire because no asset is useless. That is, every asset can be applied toward the game to affect some desirable change in gameplay or character.

    If pennies could suddenly (magically) be used to open locked doors, then wouldn’t pennies suddenly lose their numéraire status?

    (BTW, how did you produce the graphs with varying line thickness?)

    • yanis says:

      Cigarettes in prison evolve as a numeraire and they are certainly not useless – at least not to the smokers!

    • Martin G. says:

      I actually think that numeraires evolve from goods that are useful for everyone (so by giving them away, you actually lose something and the one getting them knows, that he will easily find someone that trades other items for those ). They should optimally also be available to everyone by investing playtime (but probably not in excess)
      Look at Diablo 2: Stones of Jordan were used as “currency” and later on high-tier runes. Both Runes and the SoJ gave great benefits.
      Big demand and supply will mean that trades with those goods will happen more often and a wide range of people will recognize that they can actually always find someone that is willing to trade that good for something they want (because other people feel the same way). -> numeraire is born. How are people ment to recognize this without enough public attention (aka useless items, that noone wants and because of that also noone actively sells).
      It is unlikely that cosmetic items will become a numeraire – the estimation of value differs greatly from player to player, since tastes are different as we all know. Combine that with the amount of different items (-> smaller chance to obtain them by playing) and it will be quite unlikely to always find players offering oder demanding those items -> small volume.
      Now the crafting metals: useful for everyone and obtainable for everyone -> good candidate for numeraire.

      • Sabres says:

        I don’t know about that either. Paper money is quite useless in function, but commands a value for trading purposes.

  13. Ryan says:

    Very interesting study around virtual economies! I do have a couple of questions for you though Yanis. Firstly, why do you think the TF2 community gravitated towards the ear buds as a currency item and not that of the key which has a direct link to a real world dollar amount? Could the relative safety (inflation wise) of the key have driven people to the more risky, yet rewarding, ear bud currency? Lastly how do you see the future economy of Dota 2 playing out where items have no direct effect on game play but instead really more heavily on appearance for their value? Thanks again for the informative look into TF2′s economy!

  14. Andrew Silva says:

    It’s so great that Valve has hired such an awesome person to be their economist! I really enjoyed this post-it gave me insight into the real way TF2′s economy works and what makes it tick. Thanks a lot for the experience! To answer the question you left us all with, I think a real-time graph would be a fantastic idea!

  15. Bugefun says:

    The whole hats and earmuffs thing has me confused. I think there might be an error.
    Specifically: 1.5 hats to one earmuff (or 2 hats for 3 ear muffs)

  16. john doe says:

    That was a very enjoyable post.

    A small typo– you said: “More generally speaking, in economies like (our TF2 one) with many, many items that are being traded, say N, there will be (N=1)N/2 relative prices…”

    should be (N-1)*N/2.

    A couple of questions:

    1) for the estimated price of hats in terms of keys, you’re weighting the sum by the number of times the things are traded. Is there a particular reason you weight it like this and not with some other data instead of times traded? I’m guessing you’re assuming items that are traded more often are nearer to their equilibrium price?… If that is so, do you think, after doing all this analysis, that such an assumption is reasonable for the TF2 economy?

    2) This is more of a general economics question since I’m not an economist–
    to calculate the index of arbitrage potential, you use the sum of least squares. Do economists ever use other distance functions to measure such an index? If so, is there anywhere I could read more about it?

  17. Jordan says:

    Thank you very much for posting this surveying theory on the theory behind the system of TF2 trading; it is an enlightening experience, especially with the mathematics that you implemented. I, not speaking for others – but I’d assume this’d be the case – would be interested in some sort of real time graph for predictability and general knowledge of the status at the time. Plus, it’d be an interesting qausi-metagame.

  18. mikeygaw says:

    There are at least six items currently functioning as currency.

  19. Joel Dettweiler says:

    I don’t play TF2, but the economics interested me and the question at the end was very thought-provoking. If the graph was available to everyone as they traded, that would increase the speed at which the system tended towards equilibrium because it would become instantly obvious what was most valuable and the market would quickly even it out again. This would be good in a real system because it would then be more easily studied, but since in the TF2 economic data is already so easy to use, it is better for the players to maximize arbitrage, i.e. don’t show the graph. This lets interested players invest more time (and money) into the game.

  20. Jason says:

    You gave me early morning economic class flash backs, but because of those i was able to understand this, and that is freaking awesome.

  21. Jon Scott says:

    This is really fascinating and a great opportunity to look under the hood of an economy! This’ll be on my regular reading list for sure!

  22. bobaka says:

    Hi,
    Since when there’s 35 000 items in my tf2!? As far as I’m aware http://www.tf2items.com/item/schema/ are the only items available, there’s different quality and some items are not tradable I’m sure we are far from 35 000 tradable items!
    And since I’m here what I see of the TF2 economy is this: traders who refers only to “the spreadsheet” (http://tf2spreadsheet.blogspot.fr/) who trade among themselves and occasionnaly scam people and there’s normal people who don’t give a fuck and trade with their friends at prices that are nowhere near the spreasheet prices. Personnaly I think the second community is by far the most populated and make it hard to tell if there’s an equilibrium or not because they trade regardless of value (it’s just: “oh look I craft this hat! Do you want it?”). I could wrong though, I’m no economist.
    Good luck with your new job, you make interesting posts

  23. G.C. says:

    Incredibly insightful.
    I’m no economist, so I’m (usually) skeptical about the foundations of economic analysis (and therefore the conclusions).
    This paper is different though : data in, data out, can’t argue with anything here.

    As a Steam user, it seems to me that the relatively resilient arbitrage in this whole economy can be linked to the volatility of the notion of value in a virtual economy :

    - Rarity guides the value of an object like in the real world, but only to a certain degree.
    - “Network” effects increase the value of an asset when integrated in a social context : a community of gamers make a game attractive. No-one will pay for game if there’s no one playing it on Steam; a Team Fortress 2 hat is valuable because it can be seen, etc.

    “Fun” is a very weird currency.

    I think it would be interesting to see the price evolution of a DOTA 2 key, especially if you integrate the effects of Valve’s giveaways that periodically “flood” the market.

    I can’t wait to see more. Awesome stuff Professor.

  24. fuzzybOotz says:

    In the first graph, there was a time period (near the beginning) where the TF2 economy stayed for quite a long window near the 0 Arbitrage Index mark (equilibrium). Do you have any input/hypothesis to try to explain why, in this period, we observed a very distinct pattern than in the in the rest of the data?

    Thanks for sharing this with the community! I’m having a great time reading about those “alternate economies”.

  25. Von Epp says:

    Are you thinking of looking into how crafting complicates this economy?

    No matter what their nominal trading value, items should also have a fixed crafting value (completely controlled by Valve), which should conceivably anchor or drive items towards an equilibrium. That is, items X and Y will always equal Z, by crafting, regardless of their current trading value.

    • yanis says:

      Absolutely. And, yes, the fixed production function of crafting gives rise to great opportunities for empirical tests of interesting propositions.

  26. AF says:

    Greetings!

    I cannot answer the question regarding RT trading graphs, since I’m not even a player of TF2, much less a trader in it.

    But, even being a complete ignoramus in all economic matters, I (tentatively) pose you a question: Why are “prices” of items (in nominal keys), excluding refined metal, always appreciating (inflating?), as can be seen on the last above graphic?

    Best regards!

  27. OotTheMonk says:

    What makes you think that TF2 is still a barter economy, when metal and keys have been a sort of currency since they have been around? Particularly with keys, since they have a real money value, it would always be possible for someone to offer me enough keys that I would trade one of my items, because I know with relative certainty that I could either buy back the asset that I sold for a profit, or convert them to a more useful currency (US dollars, by trading them for a steam game that I would have bought anyway). There used to even be players that organized storefronts in the forums for various things (weapons, steam games) in exchange for a pre-defined amount of metal or keys (usually at a significant profit to the seller).

    All these things seem to remove the necessity of the double coincidence of wants that you are talking about, so I’m curious as to why you call the TF2 economy a barter economy?

    • gt says:

      Trading keys for a Steam game does not convert keys to US dollars – while the Steam game you acquire with keys might have a value in US dollars, the trade was accomplished using Steam’s internal barter system, with dollars not involved at any point.

  28. Jak Lew says:

    Very interesting read, thanks for the article

  29. M. C. Means says:

    If you want this market in equilibrium, I would want to see this information published. A spike in the the arbitrage metric would enduce people to search for exploitable trades which would expidite movement towards the equilibrium.

    That said: there could be something “fun” about trading in a market which is well out of equilibrium. It lets people fulfill their secret dreams of high powered stock trading.

  30. dave says:

    pretty enjoyable, informative read. I would love to see that real time graph.

  31. Aaron says:

    Kudos, Yanis, on an amazing article. I love studying game economies, and I totally geeked out over this. The concept that a pure barter economy could effectively push towards equilibrium is eye opening and exciting.

    Before I even got to the end of your article, I was already thinking, “Can you imagine if this graph was available in real time? How cool would that be? What effect would that have on the market it measured?” I’m not sure if it would be a Good Thing, but it would certainly be a catalyst towards equilibrium — not to mention it would just be doggone fun.

    I’ve worked behind the scenes on a couple of small-scale MMOs, and one of the most common support questions our new players asked was, “How much is item X worth?” I always assumed they were missing the point of the game. Isn’t part of the fun going out and discovering how much things are worth? But now I’m wondering if I was the guy missing the point. Maybe there was an answer, and maybe it would have been more fun to give it to them.

  32. Robert McAshan says:

    If you do manage to get a live graph publicly available for the relative value of an item you would get to see some interesting data. You could measure how fast it takes for this new source of information to propagate itself through the system. Near Equilibrium would be achieved at a much much faster rate.

    However, it could end up turning the system into a non-Sophisticated Barter economy, since in essence you have created that item that everyone wants. Except in this case that item is directly equated to value. Might end up with a miniature Stock-market to track and measure ;)

    Robert

  33. Leonard says:

    This Blog is fascinating, I will need to review this a few times to wrap my brain around the concepts, but this is intriguing. Thanks for taking the time to analyze and report on this economy.

  34. Leo says:

    Wouldn’t keys or metal serve as a type of currency in the TF2 economy? many people price their items at __ keys or _.__ refined metal. I think metal and Keys have become a currency in the TF2 system.

  35. Kevin van Rijn says:

    I’m not sure if the real time graph will do any good. It might just create more unsability in the prices of well… everything. If this is a good thing or not… I’m not sure. I think most traders won’t mind this though. (Due to knowing when to sell items for the most they can get for them.)

  36. Nicholas Cusella says:

    I’d like to thank Professor Varoufakis for exploring the TF2 digital economy in an academic fashion and then being gracious enough to publish some of the results on an open web blog. As both a gamer and a student of statistics, I’m finding an immense amount of joy in reading this blog. I’m looking forward to the eventual exploration of trades across digital economies (TF2/Dota 2), and I’m fascinated by the possibility that this work could help elucidate some real world economic phenomena.

    Again, I just really wish to thank Professor Varoufakis and Valve for making all of this public.

  37. Taha Ziad says:

    To be honest, a lot of this was extremely difficult to understand at my level. As an avid TF2 player I was always interested at how complex and intricate the trading system had been. I really appreciate you explaining this. This will help me understand exactly how I can make more out of my hats, as we all know “Hats, hats ,hats”. You see taking your “Jill” reference, I was said Jill. With some crafty trading I gain more “earmuffs” then I had originally. Yet I kept them, thus eventually my “earmuffs” reduced in value. This is a pretty convoluted comment so really all I am trying to say is that this really is accurate and helpful. I hope to read more from you over the coming weeks. At your convenience of course :)

  38. Ingwaz says:

    Interesting read, please do more of these!
    Oh and you can’t let us see the graph in real time, that would be market interference :)

  39. Leonardo says:

    Great post.

    I don’t think releasing real-time statistics would be a good idea though. It would kill most of the arbitrage opportunities wouldn’t it?

  40. Manormalulo says:

    Is there any chance of hearing more on the role of certain items as currency? I find it interesting that, in order to calculate this, a theoretical currency had to be abstracted. I don’t doubt that it had to be done, but now I’m curious as to the factors that make it necessary — particularly because, in practice, there are certain items used much like currency, to varying extents: mundane weapons, metal, keys, and earbuds.

    Metal in particular is of very stable value — as your graph showed. Its production is very much like real currency, too: it is derived from weapons, which drop at a very predictable rate dictated by Valve (here analogous to a gov’t mint). In fact, in my experience, items are almost always bought and sold for metal, with other items mostly given as part of counteroffers (in an unusual hybrid of bartering and haggling). This is so common that item prices are often given as a bare number, with the unit assumed to be refined metal. So what makes it an unreliable currency for the purpose of analysis?

    And, if I may, I’d like to suggest one other research topic that I think the trading community would be very interested in: The TF2 Spreadsheet and its impact on arbitrage. It’s a community project that seeks to do exactly what you proposed: list the market prices of every object. The problem is that they use very limited data and the sheet is updated only occasionally, so the prices are not generally considered accurate by shrewd traders. Nevertheless, I find myself often stymied when I try to trade at prices based on my own observations, because potential buyers/sellers frequently declare my price too high or too low, basing their opinion that the Spreadsheet is gospel truth. In this way, the sheet has drastically lowered my personal potential for arbitrage — which is, academically, very interesting to begin with. What makes it more interesting is that it pushes prices towards an equilibrium which is inaccurate. I’d personally love to see a professional view on the consequences here. It might also give you some clues as to the potential impact of that price listing you proposed.

    This was a very interesting read. I look forward to your next article!

  41. Henry Tappen says:

    Great post, Yanis. I’d be interested to see what kind of model you use to determine what causes the difference in prices. The most obvious friction seems to come from search costs–without a centralized method of advertising trades and prices, individuals are left to search among their friends and competitors for those willing to take a trade. It seems you could model the search for an exchange as a secretary problem with an unknown number of applicants, where individuals stop searching once they hit a given price. Estimating the individuals’ discount factor might give a clue as to why they settle for prices below the equilibrium so often. Of course, the challenge there is that the distribution of prices is mostly unknown to the users, but they gain information about that distribution with each trade they start to negotiate.

    You also mentioned in your post spikes around the holiday season. Have you looked into the effect of economic shocks (e.g. handing out free hats like Valve is doing right now with Adult Swim) on exchange rates for prices?

  42. JR says:

    I’d just like to say thank you for writing these interesting blogs.

  43. Taioko says:

    I really, really enjoyed reading this. I feel like I’ve learned something, and I like the game-relevant information. (TF2 nowhere near equilibrium, TF2′s unexpected amount of arbitrage and usage of bartering, etc.,) I’m really looking forward to the next post. I do hope it will be similarly entertaining and enlightening.

    The graph idea sounds like it’s got a whole, whole lot of potential. But I think it should be rather unobtrusive to the current trading setup, were it to be implemented. I don’t know if I want something to guide my trading like that every waking moment…
    …but the option could be appreciated in many-a-case, I think.

  44. Beansly Jones says:

    I will have to take your word for all the equations :) Sounds like you are enjoying what you do. That is the sign of a good career fit. I enjoy reading your posts though I do not fullly understand all of it (but I do wiki alot of it as I go!)

    Thanks for your in-site and I do think you should make the forecasts graphs public.
    Beansly Jones

  45. Pasi Virtanen says:

    Very interesting stuff.

    So here’s a follow-up question…

    As the TF2 apparently always offers arbitrage possibilities, can the traders participating in the economy be divided into “sharks” who realize this, know the general valuation of items compared to each other and use this knowledge to make profitable trades and “suckers” who just want an item for gameplay and/or vanity reasons and don’t care about the prices of items that much and are OK “trading down”?

    In practice there would be fewer sharks than suckers, but the sharks would trade more frequently than suckers and would be more prone to trade forward stuff they traded for from someone else whereas suckers would put their purchases to good use and hang on to them.

    I’d think that this is the case and could be verified by categorizing traders by volume and average “notional keys” gained per trade.

    I think one of the potentially key (no pun intended) differences to understand between virtual economies and real ones are how much “suckers” (who don’t actually really care about being “ripped off” virtual keys or hats, but would act differently if real money was explicitly on the line) there are in a particular economy and how this shapes the economy and how things change if this balance is changed. This becomes particularly interesting when mechanisms are introduced that allow traders exchange their virtual goods for real money.

  46. P. Hayden says:

    Sir,
    A fascinating read. Speaking as a mathematist and seasoned (28!) gamer, the economical potential of the free-to-play model of games as [para] ‘a service rather than a product’ is very interesting to me, and surely to many others. Congratulations on breaking new ground with this blog. The potential in this analysis could yield substantial benefit for our increasingly digitised currencies. Long may it continue!

    As for the post itself, it would be interesting if gamers worldwide graduate toward an exchangeable currency such as XBox points or the system aforementioned. With the sharp increase in these forms of monetisation for publishers/developers that we are likely to see in the near future, might this model be able to keep interactive media directly financed, as opposed to the mass advertisation preferred by the general public? It would certainly seem an interesting future for Steam and the quality of its titles.

  47. Todd says:

    Hey,

    Interesting read and I look forward to seeing what you come up with. As a gaming nerd with an undergrad in econ I’ve always thought the virtual economies set up in games would be interesting for someone to study. I never really played TF2 much but it looks like valve has successively managed to eliminate the black-market economies that exist with other games. Is this correct? or have you come across any evidence of underground markets existing within the TF2 world?

  48. Zach Pennington says:

    I bookmarked this page the second I found out about it. I’m a junior undergraduate University student studying Physics and Mathematics. My interest in mathematics has caused me always to be fascinated with economic systems and theories, and finding out that a simulated economy with hundreds of thousands of actual human participants exists in a video game (designed by my favorite video game company!) is incredible. The amount of data that can be collected and used to model real life situations is staggering. Professor Varoufakis, your analysis of the data and the clear way in which you present it is much appreciated! I can’t wait to see more on this page in the future.

  49. Angry Pyro says:

    Why hello there.

    I’m quite curious to see what you are doing with the diary and capacitor :)

    Oh, and could you see if there are going to be new pyro weapons, and if not, why?

    Thanks

  50. Wow, I think I will have to come here more often. This was a very insightful and easy-to-digest read.

    I wonder, though, what exactly you mean by the price of an item as opposed to its value. That was one concept I never quite got in Econ 101 – there is a distinction made between those two terms, but it was always very vague to me. “Price” may be numbers we can calculate, but the line I was given is that economists always try to either base it on value or differentiate it from actual value. When I asked what that meant, I was told that we can estimate the value of an item relative to the prices of similar items, but that always seemed like hand-waving to me. Can you elaborate on this – I think it would be very interesting.

    Also, when I look at the barter system in TF2, I am struck by how much it looks like a series of linked economies each dependent on one item rather than a single large one. If this were true, you would expect that as trade volume goes up, volatility would increase but variability would decrease (since there would be multiple monies competing for currency) – and that is what the graph you provided seems to suggest. I wonder if it’s just the fact that there is a relatively limited set of items on the market, or whether it even matters. Could you enlighten us on this?

    • yanis says:

      The reason you did not learn about this difference at Ec101 is that we economists, to quote Oscar Wilde, “know the price of everything and the value of nothing!”

  51. Don Quigleone says:

    There was a case in another online game, that I am aware of, where an item became a “numéraire” you were referring to. In Diablo 2, developed by Blizzard Entertainment, Gold (the default “currency”) was considered worthless by most players, for a variety of reasons. At some point, everyone started trading in terms of “Stone of Jordan” (A ring characters could wear). Stones of Jordan were considered generically valuable by everyone, so they served as a useful currency. Eventually they faded away into obscurity.

    If you can talk to Blizzard, you may find this interesting to investigate.

    My prediction is that in such games there’s always a lot of room for arbitrage because the environments of such games provide little room for information exchange. You cannot consult an index of previously made transactions, the way you can at a stock exchange. Ultimately this results in one group of people who “know” the market being able to exploit those who spend less time on it, and know less.

    Believe it or not, such systems also come into existence in children’s trading card games. When I was a child(around 1999-2000), I was able to develop a large collection of Pokémon trading cards purely through arbitrage. I started out with no cards whatsoever, and started my collection from cards given to me by other children because they thought they were “worthless”. Other opportunities came to me later when I bought cards abroad that were currently unreleased in my own country, which I was able to exploit for even larger gains. Spending everyday trading cards, my collection eventually was one of the larger and more valuable ones at the school.

    Ultimately the school banned those cards, and my entire collection became worthless overnight…

  52. Zachary says:

    We have had an example in gaming of a barter system producing a numéraire. In the Diablo series there are items know as “Stones of Jordan.” They are rare drops and highly sought after for specific game mechanic purposes. There was no currency to begin with in the game, but over a short period of time, ‘SoJs’ were the standard unit for trading in the game.

  53. mkl says:

    As a computer scientist the obvious question for me is: is it possible to automate trading? That is, let a bot calculate as fast as possible which items currently give the best arbitrage and then try to focus on these items? Does Steam prevent this in some way? Could bots benefit from such a graph, or are all data points needed to calculate it available to the user?

    Disclaimer: I have never played TF nor used steam.

  54. Ancillas says:

    If everyone had access to this data in real-time, would it reduce the potential for arbitrage? The scenario reminds me of a flea market. When I visit a flea market, I don’t have a reliable way of identifying the value of the items that different merchants are selling, so I assign them an intrinsic value, and purchase them if the price of the items are less than the value that I’ve assigned. The presents an opportunity for merchants to “hustle” buyers who don’t shop the market very often.

    This scenario also applies when I trade TF2 items. I’m not regularly in the market, so I have no idea what items are worth. It’s very possible that the intrinsic value of the items in my inventory are not at all in sync with their market value. If I had access to real-time sales data, I wouldn’t have to guess about the value of my items, and the opportunity to be “hustled” would be greatly reduced.

  55. Dale says:

    Nice.

    Didn’t understand most of it, but nice.

    And yes, I’d love to see that graph in real time.

  56. MondSemmel says:

    Thanks for the article! I always enjoy reading about economics written for those, like me, who have no formal training in the subject. (I’m a physics student.)
    And thanks for actually making commenting possible. Last time I saw your post, I saw you ended your blog post with a question, but there was no way for readers to actually answer it.

    A few questions:
    1) In a game like TF 2 where essentially any item could end up on sale, couldn’t it be dangerous to have a single item as currency? If Steam put a sale on that currency, its supply would skyrocket, leading to inflation, right? Perhaps this effect could be mitigated by having a set of items serve as currency, or something similar.

    2) If the assumption that economies are mostly in equilibrium is unjustified, what about the assumption that economies tend to equilibrium? If economies always tended to equilibrium, a ‘higher power’ (i.e. Valve) could put an economy into equilibrium at the start, and it would remain there forever. Is this possible? If not, what (presumably rare) circumstances tend to throw an equilibrium out of whack?

    3) I am interested in economics, but have had no formal training in it whatsoever. But the content of this post sounded quite interesting. What field of economics is this blog post about? Is this microeconomics?

    PS: There seem to be several formatting problems with math formula in your article. I found:
    - In your paragraph beginning with “More generally speaking, in economies”, there’s a “(N=1)N/2″ there instead of a proper series symbol.
    - There’s this sentence, which looks awkward: “E.g. if keys were the most traded, we would define the price of guns as . ”
    - And this: “Next to compute the price of hats in terms of keys we would use the equation (see above) =,”
    - And this sentence looks strange, too: “Estimated price of hats in terms of keys =” (the formula seems bugged)
    (Actually, you may want to briefly check all math in the whole article.)

    • yanis says:

      1) Sure. If a numeraire had emerged and Valve boosts its quantity/supply, the money supply would rise and, others things remaining the same, inflation would result.
      2) First, Valve does not now, at the outset, the equilibrium prices. Secondly, even if it did, changes in preferences etc. would destabilise the original equilibrium.
      3) On the one hand, yes, it is a microeconomic sort of analysis. But shortly we shall introduce macroeconomic concepts, once we gain a better feel of the macro forces at work in our economies.

  57. deadsource says:

    A really great article! I’m looking forward in seeing more :)

  58. Chet Michals says:

    Would it be possible to get some labeling on the chart of relative values of items? Have some month ticks on the X axis, and label what the Y axis is measuring in (I assume the value of the items in terms of keys, but it doesn’t seem to be stated).

    Also, would it be possible to also put the “Max’s Severed Head” on a slimier chart? It is anther high value item that is fairly consistent, but its price seemed to vary at lot and I don’t see it used so much as a numéraire anymore.

  59. alex says:

    Very interesting read, looking forward to hear more.

  60. Saar Golde says:

    What you call ‘arbitrage’ is actually traders’ work wages, or in transient cases – information rents. Calling it ‘arbitrage’ means that trades are costless and there is perfect information everywhere.
    Unfortunately (or for game designer – very much fortunately) information comes at the cost of sifting through buyers’ and sellers’ offering and spending a lot of time and effort buying and selling items (known in the world of gaming as ‘user engagement’).

    The distinction between ‘arbitrage’ and ‘wage’ or ‘rent’ is not just technical distinction, it can direct you towards additional interesting research. For example, if you measured the time it would take to actually complete these trades, you could estimate wages (in in-game goods) for traders. If you tied the number of interactions people make with buyers and sellers before they make each transaction, you could backtrack the cost (and value) of information. This can be an interesting study in how information is propagated (I can postulate, according to economic theory, that the rate at which people ‘run into each other’ will dictate the speed of information dissemination, which will coincide with how fast market clearing prices form, or in your taxonomy – arbitrage opportunity disappear). Add some form of technical change (for example, start publicly posting exchange rates you see), and you’ll probably see prices converge to market-clearing levels faster (what you’ll also probably see is people manipulating these prices by bartering with themselves or their accomplices – so you’ll need a decent way of weeding out these transactions).

    It’s a fascinating and highly observable world – it’s worth observing it carefully.

    • yanis says:

      Baffled by your definition of arbitrage and the insinuation that arbitrage implies zero transaction costs and symmetric/perfect information. This is precisely wrong. Arbitrage simply means buying cheaply and selling more dearly. Perfect information and zero transaction costs would effectively mean that there is no room for arbitrage.

  61. TK says:

    A really interesting post and try to get a single price for an index. Thanks for sharing your work so eagerly and early. Is the way you try to get a single price, something like a standard approach to such a problem?

    What i’m personally wondering is if you looked into the division of the market, from which your data arrived?
    As far as i experienced the steam trading system it seemed as if it was still divided in regions – US players trading through US servers, european players trading through european servers. Maybe it is even more divided between different language regions. – Of course this is only my limited and subjective experience…
    But still i think it might be really interesting looking in the causes of friction within this whole market.

    One more question i would like to ask:
    Did you allready analyze how real-prices (as you can buy the team fortress 2 items for real money) , your price-index, and the drop-chance in team fortress 2 for the items are related to each other?

    As an undergraduate in economics & management and a gamer who is just writing his diploma thesis, it is definately thrilling to see economic research applied to games.
    I found it quite interesting back when i was playing World of Warcraft to experience, how different prices where recieved on different game-servers and how uneven some informations seem to have been distributed. So during certain periods you were able to buy a good from Non-player Characters (which supplied it in unlimited quantities) and sell it for the 100-fold of the purchase price to other players.

    I personally would love to see your price indices in real time. Still i personally think, without any research into it – how could i without data – that it would help quite a bit more to widen the market, by creating a single exchange.
    A single place to find the prices, or be able to compare prices, and actually trade the items might be something to go for, instead of a place to find some benchmark prices while you still need to find somebody who is willing to actually sell for this benchmarkk price.

    Sorry for any errors and the overall length of my post, but i’m really excited about your work with Valve Software and the insights you might get from watching closely an evolving trade system.

    Best Regards
    TK

  62. Ben Reierson says:

    This is great stuff. I look forward to even more in-depth analysis. The topic of virtual economies is only going to get more important in the coming years. Can you share any thoughts on Blizzards Diablo 3 Real Money Auction House?

  63. bgausden says:

    Price discovery in TF2 is pretty inefficient. Let’s get a real-time market up and running. With minimal incentive (probably zero) market-makers would appear and price discovery would be greatly enhanced.

    Of course the associated issues are that we don’t have an effective registry for the traded assets, and of course we’ve not touched on counter-party risk.

    It’d be an interesting thought experiment – what could the Valve equivalent of a stock market (and related clearing functionality) look like?

    I’m sure it’s already under consideration – there’s a ton of money on the table…

  64. Anup says:

    So awesome!!

  65. Amit says:

    I read through your post, and it is interesting, but I fear that if you want to get to that level of detail you should give the readers a much richer explanation of basic economics. Economic must be at least a 3 year course at the university, and, frankly, most people didn’t study economics – so it’s a bit hard to follow…
    Would love to hear more from you, though.

  66. Categories+Sheaves says:

    Cool stuff.

    “In this manner, and after having dealt with a significant number of computational issues that I shall not bother you with here, we ended up with a method deriving a list (or vector) of prices per item.”

    Will you be making any future blogposts where you do bother us with these computational issues? If not: will you please make one? Pretty please? Pretty please with a cherry on top?

  67. Brendon says:

    hello my name is Brendon i am a fair active player in teamfortress 2 (i’ve logged over 1000 hours in the last 2 years). i know that the trading system in TF2 his been in place for roughly a year now but i don’t know if i would call it a bartering system. as a player i’ve seen scrap, reclaimed, and refined metal act more as our currency more than anything. when people talk, on servers about buy or selling item the price is usually is translated into an amount of metal. like keys having a selling price of 2.66 (2 refined and 2 reclaimed worth of metal), although keys can be bought with actual money, scrap metal and the likes is not something you cannot buy in the store.

  68. John von Neuman says:

    I was struck by the time series for arbitrage potential. While not the easiest diagram to read precisely, on the first half of it there appeared to be a strong inverse correlation between arbitrage potential and volume of trades suggesting standard risk-averse behavior. But the second half (maybe a month or two after the Feb. 10 update) trade volume increased almost uniformly across all levels of arbitrage potential. I’d be interested to know if this is explainable solely as the product of the quantity of new goods introduced or if the introduction somehow induced a more fundamental change in people’s willingness to sell independent of the degree of price uncertainty in the economy.

  69. Wacker says:

    If & when we ever get to see graph in real time? Haha you jest Yanis. I’m betting you’ve already created your own Steam account, for research purposes of course ;) & have got hooked on trading amassing a pretty nice back pack in the process. That real time graph is the holy grail of TF2. You’ll know exactly what to sell & when to sell it from all those lovely stats gaining a fortune in “real cash” just like all those greedy bankers who manipulated the…..Ok i’m joking. I don’t pretend to know half of what you said but it was a very interesting read nonetheless and it would be very interesting indeed if they released a real time graph for the players.

  70. James says:

    I’m not sure how much a real-time graph would affect trading, I’ve only been involved in TF2 and the economy for about a year, but I have a fair grip on which items are going to go up and down over time in relation to events.

    One of the major factors that push the economy towards equilibrium that’s accountable for is what items “drop” and which do not. Take the latest introduction of weapons, the easiest way to obtain them is to craft from existing weapons, costing you 8-9 weapons in the process. Yet, prices will drop to a scrap (2 weapons) in the coming months since these weapons will be available more and more from the “random drop” system.

    What are the units used for measuring arbitrage?

  71. Tobias Bacchus says:

    This blog is amazing. I would love to see Valve play around with trading with you in the lead. It would be interesting to see you guys manipulate the market to see what would happen.

  72. Alan Turing says:

    Please do examine and cite the work of those who came before, notably base1024, who produced http://tf2finance.com/ , containing a graph much like yours above, except with labels on the X- and Y-axes, real-time updates, and cash trade data, all without the benefit of access to Valve’s secret data.

  73. Dave says:

    I have a TF-2 Item–iPhone earbuds… this item seems to be highly regarded. I haven’t played TF-2 in a long time, but i have received several emails from random users asking me for my earbuds. most recently one user offered to buy me any steam game of my choice in return for the earbuds. I have declined, due to the fact that If so many people want it, why shouldn’t i be the one to get to keep it?

    I wonder if your system can keep track of these types of behind the scenes datapoints or not–or if they are a valuable part of the big picture that may be overlooked.

  74. Sean says:

    “I think this is fun to see. The tantalising thought also comes to mind that we could, perhaps, let you see this graph in real time, to guide your trading. Or perhaps not? What do you think?”

    Thus far, 99% of your posts have been (understandably) about economics, the social science (my old major). However with this quote, you have crossed into the realm of finance (my current major), and I feel qualified to answer this question drawing upon my tf2 trading experience and my studies.

    Your graph spikes up, alerting traders of market conditions facilitating arbitrage opportunities, when Valve comes out with a major update and new items are put onto the market. The result is complete chaos in the trading community, in every sense of the word.

    No one knows the market values, and not many people even know about all of the items or what they do yet. Item crafters introduce highly illiquid items with craft numbers between 1-100 (which basically means these were the first items to be crafted, and are quite valuable).

    In short, after an update, we are dealing with a market with a lot of uncertainty with an influx of illiquid items. What a paradise for someone looking for arbitrage opportunities.

    Or is it? Arbitrage by definition involves RISK FREE buying and selling of items. This means the trader must buy the item knowing fully well it can be sold without risk for higher than he paid for it.

    But if we take the two characteristics of the post-update market that I mentioned below, one begins to wonder whether these “arbitrage” opportunities are really arbitrage. Illiquidity is a real risk that traders have to deal with. Uncertainty about whether the trader will be able to sell his item for the market price is a risk that traders have to be compensated for in order to trade illiquid items. Furthermore, trading in a market with uncertainty about market prices is inherently risky.

    I would therefore argue that these spikes in your graph do not show arbitrage opportunities, they show conditions in which traders are taking on a lot of risk, with many winners (those willing to flip items in this market and those who are smart enough to be successful), and many losers (those who don’t care for trading and simply will pay whatever it takes to get a new item, or those who make poor decisions and misjudge market prices).

    The basic principle in finance, perhaps, is that traders (or investors) are compensated for the amount of risk that they take. In normal times in the tf2 economy, the amount of risk is rather low, so there is not much profit to be made (as measured by the degree at which items are being traded at prices other than the market price). However after an update, conditions are highly uncertain, so there are plenty of opportunities for traders to take a risk by buying an item and selling it for more.

    To more directly answer the question, the graph will not change my trading behavior, because the spikes are highly predictable, and do not coincide with a free lunch. As a trader, I must gauge the amount of risk I’m willing to take and trade accordingly.

  75. jerome says:

    Dude you only sell hats….

  76. herma says:

    hi, this article is so impressive, so I want it to translate in other language
    Would you permit me?

  77. Joseph DiMitri says:

    Fascinating. To answer your question real time data would benefit all of us the same way a stock market ticker benefits an exchanges trader.

  78. duckie says:

    How about allowing High Frequency Trading tools on Steam ?

    • yanis says:

      What would the point be? It is bad enough to have to deal with flash crashes in ‘real’ stock markets. Do we need such ‘events’ on Steam? Don’t think so.

      • Alan Turing says:

        Hint: Amazon.com is a high frequency trading platform.

        The point is to allow people to participate in the economy without spending hours on a trade server, or paying a convenience fee to those who do.

  79. If the graph is released in real time, a select few will trade their items within themselves to inflate their own values.

    1) Player A will trade his Hat A with his second account for 500 Hat Bs.
    2) The value of Hat A will skyrocket on its graph.
    3) Player A will sell Hat A from his second account for an inflated value, citing the graph of evidence that Hat A is valuable.

    This is what happens in other online economies where these graphs are public, such as Gaia Online.

  80. Jeremy Chen says:

    Nice post. If you’re interested, some time ago, I was looking into “preference ratio matrices” and consistency and how to measure consistency more accurately than this thing called the “Consistency Ratio” (and the “Consistency Index” it is derived from). (It’s late now, so…) Drop me a mail if you have an interest in this and would like to chat about it.

    Also, noting your method for aggregate relative price estimation, there is the question of whether a geometric mean would have been more appropriate for aggregating ratios…… Fun stuff.

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