markets in virtual worlds

Graduate School of Business, Economics,

Law and Social Sciences

Bachelor thesis

Markets in virtual worlds

Author:

Anton Chirkunov06-606-198

Supervisor:

Prof. Dr. Francesco Audrino

May 12, 2009

1 CONTENTS

Contents

1 Introduction 4

2 Data 6

3 Empirical Findings 9

3.1 Price dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Conclusion 18

A Appendix 19

A.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

A.2 Price dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . 23

A.3 Arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

References 35

2 LIST OF FIGURES

List of Figures

3.1 Price and volume of Eternal Earth (EE) & 10 x Crystallized

Earth (EE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Price and volume of Eternal Shadow (ES) & 10 x Crystallized

Shadow (CS) . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

A.1 Auction house in the player’s perspective . . . . . . . . . . . . 19

A.2 Auctions saved in a textfile . . . . . . . . . . . . . . . . . . . . 19

A.3 Auctions in the SQL database . . . . . . . . . . . . . . . . . . 20

A.4 Absolute price gap over time of Greater Cosmic Essence . . . 25

A.5 Absolute price gap over time of Infinite Dust . . . . . . . . . . 26

A.6 Absolute price gap over time of Netherweave Cloth . . . . . . 26

A.7 Price and volume of Greater Cosmic Essence (GCE) & 3 x

Lesser Cosmic Essence (LCE) . . . . . . . . . . . . . . . . . . 26

A.8 Price and volume of Dream Shard (DS) & 3 x Small Dream

Shard (SDS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

A.9 Arbitrage profits of Dream Shards & Small Dream Shards . . 31

A.10 Arbitrage profits of Eternal Life & Crystallized Life . . . . . . 32

A.11 Arbitrage profits of Greater Eternal Essence & Lesser Eternal

Essence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

A.12 Arbitrage profits of Greater Magic Essence & Lesser Magic

Essence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3 LIST OF TABLES

List of Tables

2.1 Exemplary auction listing sample . . . . . . . . . . . . . . . . 8

A.1 Descriptive statistic for the most popular items . . . . . . . . 20

A.2 Descriptive statistic for the most popular items, clear from

outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

A.3 p-Values of statistical tests for returns . . . . . . . . . . . . . 22

A.4 Price gaps of the most popular goods . . . . . . . . . . . . . . 23

A.5 Regression results between price gaps and number of sellers . . 24

A.6 Regression results between price gaps and logarithmic number

of sellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

A.7 Volumes of interconvertible goods over the observation period 28

A.8 Correlations of interconvertible goods . . . . . . . . . . . . . . 29

A.9 Correlations of partially interconvertible goods . . . . . . . . . 29

A.10 Arbitrage profits of interconvertible goods over the observation

period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

A.11 Arbitrage profits of partially interconvertible goods over the

observation period . . . . . . . . . . . . . . . . . . . . . . . . 30

4 1 INTRODUCTION

1 Introduction

Virtual reality has been the object of much speculation by the end of the

20th century. Back at that time, science-fiction and self-named ”experts”

predicted that in a few years we could use a brain-computer interface to in-

teract with a simulated reality (take for example the movie Matrix). History

tends to be unpredictable, and respectively they were wrong. Instead, com-

puter games emerged recently where thousands of players interact with each

other in a fictional universe. Players simply use their keyboard, mouse and

microphone to move and talk inside this virtual world. Online games run

endlessly and are persistent (the world continues to exist when you are not

playing). The goal of playing is recreational: developing the player’s char-

acter, achieving objectives in a team, fighting against other players, social

interaction etc..

This paper analyzes the items market of the most popular online game

to date, World of Warcraft (WoW ). Blizzard released an expansion pack in

the middle of November 2008 called Wrath of the Lich King (WotLK ). It

introduced new content for players and naturally new items. I will further

refer to goods released in the expansion as WotLK goods. Goods released

before the expasion will be referred to as pre-Expansion or pre-WotLK goods.

World of Warcraft has about 11.5 millions subscribers as of December 2008

(Blizzard, 2008). The players are distributed on over 700 servers. Each server

is an identical copy of the game world with a population ranging from 10 to

30 thousand characters. The character are tied to their particular server1 and

cannot interact with players on other servers2. You might think of servers as

multiple countries or even multiple identical universes.

World of Warcraft uses levels to measure the character’s progress, ranging

from 1 to 80. At higher levels the character is more powerful and is able to

perform more abilities. The player needs a certain amount of experience

points to progress to the next level. He earns them by slaying monsters or

1The only exception is to transfer to another server of the same geographical boundaryby paying a small fee. It is not possible to transfer from a Chinese server to a Europeanone, but you can transfer between European servers.

2The exception is multi-server ”battlegroups”, but it is irrelevant for this paper.

5 1 INTRODUCTION

completing quests given by non player characters (NPC ). In turn, equipment

- weapons and armor - improves the character’s abilities to perform these

tasks faster. Players acquire items3 by performing activities or trading them

among other players. The key point why items have a certain value is because

the world is persistent. If I gather an item today, it is still present tomorrow,

because the world runs independently of whether I am playing or not. Players

purchase items using a virtual currency called Gold. It has the characteristics

money ought to have as defined by Yamaguchi (2004): medium of exchange,

measure of value and mean of storage. It is used to denominate the value

of items, pay for them and can be stored for future use. You may argue

that World of Warcraft gold is nothing more but worthless Monopoly money,

but it is nevertheless exchangeable to real currencies. Not because Blizzard

wanted this to occur, but because players have the desire to do so. The

reason is that some players have much time to play but a low income, while

others are busy working but earn more than enough to finance this hobby.

An in-depth analysis of this phenomenon is given by Heeks (2008).

There is a wide range of economic literature on virtual worlds, most

notably Castronova (2001) (estimation of a virtual world’s GDP), Yamaguchi

(2004) (virtual currencies) and Lehtiniemi (2008) (macroeconomic modeling).

This paper does not give a recapitulation of the literature, which is most

wonderfully described by Lehdonvirta (2005) and Lehtiniemi (2008).

The reason I analyze the virtual market of World of Warcraft is to gain

insights about the real world. The obvious advantage of virtual worlds here

is that the environment isn’t a laboratory experiment. The players are not

aware that they are observed and act naturally. Virtual worlds have very

desired characteristics (e.g the goods are absolutely homogenous) otherwise

absent in the real world. It allows to verify economic theories which are

untestable in the real world. The approach is only viable if players make

decisions in the same way as in the real world. Don’t confuse this statement

with neoclassical economists thinking that humans (and therefor players) are

rational. These economists say that humans are rational and make optimal

decisions based on rigorous economic theory. Taleb (2007) notes that this

3Objects than can be collected within the game

6 2 DATA

would be as absurd as requiring birds to study engineering in order to fly.

Experiments by Kahneman and Tversky showed that people solve problems

using heuristics, i.e. rules of thumb, instead of rational analysis (Taleb,

2007). The usefulness of virtual worlds for economics cannot be judged by

how humans & players should behave, but on how they actually behave.

There are therefor two significant aspects for research. First, you should

conduct experiments in online games and compare the results to those of

behavioral economics. The second part is about gaining insights. This paper

concentrates on the second aspect of virtual world research.

The thesis is structured as follow: In Section 2, I will give an overview

on how the data has been gathered and what the main problems are when

working with it. Section 3 will present empirical findings on price dispersion

and arbitrage in the virtual world.

2 Data

The auction house is the trading hub for buying and selling goods to other

players in World of Warcraft. Sellers may place goods up for auction, set a

starting price, optionally a buyout price and the auction duration (12, 24 or

48 hours) (Blizzard, 2009). Most goods require a upfront deposit fee, which

is refunded upon the successful sale of the good (Blizzard, 2009). Successful

sales are charged a cut rate of 5% based on the final sale price. The auction

house shares many similarities with eBay, except it uses first-price English

auctions. It means the player pays the amount of his bid, regardless of the bid

of his competitors 4. In addition, auctions can be immediately won by paying

the buyout price set by the seller. This is the way most auctions are won,

since many players are not willing to wait and want the item now, despite the

buyout price being higher than the current bid. For this reason, we ignore

bids in our analysis and concentrate on buyout prices in this paper. The

security of the auction is guaranteed by requiring buyers/sellers to deposit

their bids respectively goods upfront. You might think of it as the equivalent

4On eBay the winner pays the second-highest bid plus a given increment

7 2 DATA

of an escrow account. The alternative to the Auction House is the trade chat.

Players simply tell others what they are willing to buy or sell for which price.

Then they meet in the virtual world to close the trade without paying any

fees. Is it not possible to quantify the significance of the trade chat.

Data collection is a triviality in most economic & financial studies, since

the data is either freely available or can be purchased from an institution.

Data collection is a challenge in virtual worlds, since it resides entirely within

the game. Nash and Scheneyer (2004) faced the same problem when collect-

ing data for the online game Final Fantasy Online. Figure A.1 shows how

the auctions are seen in the game from the player’s perspective.

The only existing database for auction prices in World of Warcraft is

Wowecon5. It has two major drawbacks:

Bias Wowecon collects only data from auctions bought or sold by its users,

and not the observable auctions themselves. There are currently about

600’000 registered users, or less than 5% of the total population. The

number of active users is probably much lower.

Limited number of observations The limited amount of Wowecon users

means that the data sample for each server is very small. In return,

the website merges all observations from every server to come up with

the limited number of observations. For some items, the total observed

volume for all 700 servers is three to ten times lower than the actual

volume on a single server.

These disadvantages led me to collect the data by myself. World of War-

craft allows users to write add-ons using the LUA programming language

that can interact with the game to some extent. One of the most popular

add-ons is Auctioneer. It store statistics of auction prices locally on the

player’s computer. The problem is that the statistics are not related to sep-

arate points in time. For example, instead of calculating the median on a

daily basis, it simply saves the price median over the last few days. This

approach is not suitable for time series analysis. I modified Auctioneer by

5http://www.wowecon.com/

8 2 DATA

Table 2.1: Exemplary auction listing sample

Item Quantity Bid Buyout

Eternal Earth 1 4.95 5.23Eternal Earth 1 12.00 15.00Eternal Earth 10 47.20 51.00Eternal Earth 10 48.90 50.49

reducing its functionality to making a snapshot of all current auctions. The

snapshot was saved to a text file by the add-on. A special script written in

C# would then parse the text file A.2 and export its content to a SQL Server

database A.3.

Sporeggar (Horde) was randomly chosen as the observation server. I

recorded daily observations from the 14th October 2008 to the 15th De-

cember 2008. The data collected differs from financial data in a number of

ways. The auctions do not represent actual transactions, but ask prices and

volumes. Table 2.1 illustrates the need to differentiate the need between ask

price and actual transactions.

Table 2.1 shows 4 auctions for a total of 22 items. It can be observed

that the second auction from the top has a buyout price almost three times

as high as the other auctions. I emphasize that this is not a recording error.

This does not imply by any means that the auction will be sold. But why

does the seller list an auction that deviates from the mean? He hopes that a

buyer will purchase the wrong auction because he is in a hurry, only noticing

after the sale that he bought an overpriced item.

In other words there exist auctions listed far above the real market price

(which is not observable). We know that these auctions won’t be realized.

It means we have to find measures to get rid of them. Figure A.1 shows

the mean, median, standard deviation, skewness and kurtosis of the most

popular items sold. The price distribution is right-skewed for all goods.

The extreme kurtosis varies between items and might be as low as 3 and

as high as 686. This extreme kurtosis is the manifestation of the behavior

of some sellers I described before. An approach to solve the problem is to

9 3 EMPIRICAL FINDINGS

use the median instead of the mean, since the latter is more outlier prone.

In addition, outliers outside of a 2 standard deviation interval from the the

median are removed. The approach is purely practical and has no theoretical

background. Figure A.2 shows the results of the data cleanup. The data

retains its main characteristics (asymmetry and fat tails), but it is at least

clean from extreme outliers. Note that these outliers can only be detected in

a large sample, this is the reason why I will stick to the most traded goods

in my further analysis.

Asymmetry and fat tails are compatible with the real world. Stock prices

aren’t random or normally distributed either. However, their returns are

often assumed to be independent and identically distributed (iid) under a

normal distribution, even if it isn’t the case empirically. What is most striking

most is that in World of Warcraft, the daily returns of the most popular

goods are random. There are of course exceptions like the item Saronite

Bar. Saronite Bar shows a strong deflationary trend in the first weeks after

the release of WotLK. The residuals are however iid if the trend is removed

using a quadratic approximation. Linen Cloth and Wool Cloth daily returns

aren’t iid either. They show strong empirical evidence of autocorrelation.

The only similarity between Linen Cloth and Wool Cloth is that they are

relatively cheap and aren’t actively gathered by players.

3 Empirical Findings

3.1 Price dispersion

Price dispersion is a violation of the law of one price (which is actually

no law at all). Price dispersion means that prices vary across sellers even

for homogenous goods. The existence of price dispersion is erroneously at-

tributed to subtle differences among the products. Empirical research over

four decades has shown that price dispersion is omnipresent, regardless of

the goods sold and the distribution channel (online or offline) (Baye & Mor-

gan, 2006). Theoretical and empirical evidence suggests that the cause is

information costs - the cost of consumers and firms to acquire respectively


transmit information (Baye & Morgan, 2006).

The relevance of virtual worlds lies in its idealized characteristics: virtual

goods are absolutely homogenous and search costs are inexistent (or limited

at looking up the auction house). There are several differences to the real

world that may impact price dispersion. First, there is no price stickiness.

The short term auction duration (12 to 48 hours) allows prices to fluctuate

in a matter of hours. Second, the auction house is both a place where players

are able to access a list of prices (so called clearinghouse) and a point of sale.

Similar to price listings in newspapers or websites, it is (most of of the time)

costly for sellers to advertise prices. They pay a deposit fee when listing an

auction. The homogeneity of the goods and the lack of difference between

sellers allowed me to conclude that players cannot consider the reputation of

sellers or exhibit loyalty.

I used the ”gap” to measure price dispersion, which is the difference

between the two lowest prices in the market (Baye & Morgan, 2006). It is

defined as

G(t) = p(t)2 − p

(t)min (3.1)

where p(t)2 is the second lowest price at time t. The sample gap can be

normalized in order to be comparable across different time series:

g(t) =p

(t)2 − p

(t)min

p(t)min

(3.2)

The relative price dispersion g(t) is then the absolute gap divided by the

lowest price (Baye & Morgan, 2006).

Other ways to measure price dispersion are impractical in our case, e.g.:

The range defined as R(t) = p(t)max − p

(t)min. Our data has however a high

kurtosis and may have extreme outliers to the right. p(t)max is often not

meaningful at all.

The sample variance has several problems when comparing price disper-

sion across different goods or over time. It needs to be standardized in

some way, for example by using the coefficient of variation CV = σµ.


The coefficient of variation is most useful over long periods of time

(Baye & Morgan, 2006). The two month observation period is however

too short for the use of the coefficient of variation.

I calculated the daily price gap for the twenty most popular goods in

terms of volume. The results are displayed in Table A.4. Price dispersion

is unsurprisingly omnipresent and even higher than in the real world. The

following observations can be made:

1. The relative price gap is significantly lower for expensive goods (median

price over ten gold) than for cheap goods (median price under one gold).

This is in line with Stigler’s first hypothesis and empirical results over

four decades - dispersion is lower for goods that account for a large

share of the consumer’s budget than those that account for a small

share (Baye & Morgan, 2006).

2. There is no deposit fee for the items Infinite Dust and Greater Cosmic

Essence. In other words it costs nothing for sellers to advertise their

prices. As we already ruled out the existence of search costs for buyers,

the existence of price dispersion thus seems to be independent of all

information costs.

3. The theory suggests that dispersion depends on the number of sellers.

Depending on the model, price dispersion either increases or decreases

with the number of sellers. Empirical results often depend on the way

the number of sellers is measured - be it logarithm of number of sellers

or the density of sellers in a geographic region (Baye & Morgan, 2006).

In our case, there is no empirical evidence that the number of sellers

or the logarithm of it matters (except for Runecloth). The regression

results are displayed in Table A.5 and A.6.

4. Price dispersion is not constant over time. Figure A.4, A.5 and A.6

suggest that price dispersion is cyclical. It might be a hint that price

dispersion is caused by factors varying over time like the competitive-

ness between sellers.


To conclude this section, price dispersion is omnipresent in the virtual

world despite goods being absolutely homogenous and information costs in-

existent. The number of sellers has no impact at all, and price dispersion

varies over time cyclically.

3.2 Arbitrage

Theoretical finance defines arbitrage as a non-negative cash flow in any out-

come and a positive cash flow in at least one outcome (Sandmann, 2001).

The problem of this approach is the assumption of a finite number of out-

comes (also called probabilistic states) and the required knowledge of the

returns of securities in any possible state. Both of these assumption do not

hold in the real world, and cannot be observed in our case. This empirical

study narrows down to detect mispriced goods. The approach is to take a

look at interconvertible goods, i.e. goods that can be converted between

each other at no costs. Take for example the item Eternal Earth. Any player

- independently of his character’s skill - can convert one Eternal Earth to ten

Crystallized Earth. It works the other way too, i.e. converting ten Crystal-

lized Earth to one Eternal Earth. You can safely assume that both should

have the same price. Figure 3.1 confirms that both goods (more precisely one

good and the bundle of the lesser good) have about the same median price.

If you would combine both markets, the combined price would go precisely

trough the median of Eternal Earth. The reason behind this logic is that

Eternal Earth has a higher volume in terms of units of Crystallized Earth

and per se a higher impact on the median.


Figure 3.1: Price and volume of Eternal Earth (EE) & 10 x CrystallizedEarth (EE)

11/16/08 11/23/08 11/30/08 12/07/08 12/14/080

20

40P

rice

,[g

old]

ee

ce x 10

11/16/08 11/23/08 11/30/08 12/07/08 12/14/080

1000

2000

3000

Adj.

vol

The point of the matter is that even if the goods are interconvertible and

their combined price the same, the risks associated with selling Crystallized

Earth is higher than those of Eternal Earth. One market is more liquid than

the other. The higher liquidity of Eternal Earth suggests that the demand for

it is higher - despite the goods being absolutely interconvertible. Players pre-

fer to buy Eternal Earth rather than batches of Crystallized Earth - maybe

purely for convenience. To conclusion, it makes sense to convert Crystallized

Earth to Eternal Earth in order to minimize the sales risk. Both Greater Cos-

mic Essences & Lesser Cosmic Essences and Dream Shards & Small Dream

Shards have the same characteristics, see Figure A.7 respectively Figure A.8

in the Appendix.

Could the price of the bundle of Crystallized Earth be lower than the

lowest price of Eternal Earth? If Crystallized Earth was cheaper, one could

simply buy it, convert it to Eternal Earth and realize a risk free profit by

undercutting the lowest price of Eternal Earth. This observation also implies

that the price of the less liquid good can be higher. The goods Eternal

Shadow and Crystallized Shadow in Figure 3.2 are a perfect example. Eternal

Shadow and Crystallized Shadow can be converted between each other at just

the same ratio as the previous example. However, the bundle consisting of ten


Crystallized Shadow items is significantly more expensive than one Eternal

Shadow. You might argue that this observation is contradictory, but you need

to consider that the illiquidity of the Crystallized Shadow market refrains you

from realizing a risk free profit. There isn’t a arbitrage opportunity in this

case either.

11/20/08 11/27/08 12/04/080

50

100

Pri

ce,

[gol

d] es

cs x 10

11/20/08 11/27/08 12/04/080

500

1000

1500

Adj.

vol

Figure 3.2: Price and volume of Eternal Shadow (ES) & 10 x CrystallizedShadow (CS)

We’ve noted earlier in this section that Eternal Earth & Crystallized Earth

seem to form a single market. In contrast, Eternal Shadow & Crystallized

Shadow are two distinct markets. The reason why some interconvertible

goods form distinct markets lies in the nature of players’ preferences. Crys-

tallized Shadow could have some use for players on its own. The player

prefers to buy one unit of Crystallized Shadow rather than buying an Eter-

nal Shadow, converting it, using one of the resulting Crystallized Shadow

for his own and reselling the remaining nines items. On the other side, there

might be no popular recipes that require small amounts of Crystallized Earth.

However, the sheer number of available recipes and professions in World of

Warcraft prevents us from giving an empirical account on exactly why some

interconvertible goods form distinct markets and why others do not. We can

however determine which of these goods are affine.

One method to measure the affinity of two goods is the sample correla-


tion. Highly correlated interconvertible goods form a single market, while

uncorrelated goods form distinct markets. The correlation samples for all in-

terconvertible goods in World of Warcraft are depicted in Table A.8. The p-

Value refers to the null hypothesis that the samples are uncorrelated. About

half of the goods are correlated and thus form a single market. Addition-

ally, I included another class of items: partially interconvertible goods.

These are goods that can be converted one way by all players, and both

ways by players having a specific skill. Their sample correlation is shown

in Figure A.9. Surprisingly most of them are correlated, but it is debatable

whether it can be attributed to partial inter convertibility. Nevertheless, the

sample correlation isn’t a meaningful indicator to undermine the existence

of arbitrage.

Before I design an approach to measure arbitrage, I’d like to generalize

the definition of arbitrage we used in the beginning of this section. Let H be

the very liquid and L the lesser liquid good. They can be converted between

each other at the ratio r so that one unit of H yields r units of L. We assume

that it is possible to sell good H at a price infinitesimally below the lowest

ask price in the market (also called undercutting) without any risk. This

assumption is for simplification, mainly because we cannot observe actual

transaction but merely ask prices. If at any point in time t the ask price of L

is lower than the lowest ask price of H, there isn’t any possibility of arbitrage

because the illiquidity of good L is associated with a risk to sell good L. It

means that the ask price of L must be higher than the lowest ask price of

H, otherwise an arbitrageur could buy good L, convert it to H and realize a

risk free profit. We can write this generalization mathematically:

Proposition 1. Let H and L be two goods interconvertible goods. If:

• Good H is more liquid, i.e. its volume in units of L is higher:

r ∗ V olume(H) > V olume(L) (3.3)

• There is no risk to sell good H by undercutting, i.e. at price P(t)min(H).

This is the risk free sales price.


Then at any given point in time t the lowest ask price of good H must be

lower than all ask prices of good L:

P(t)min(H) < P

(t)i (L) ∀i (3.4)

in order for the market to be arbitrage free.

Now we can define the arbitrage profit as the profit from buying all goods

L below the risk free sales price, converting them to good H and selling H

over the whole observation. This measure is however absolute, and lacks

cross sectional comparability if the goods have observation periods of dif-

ferent lengths. The results are shown in Table A.10 respectively A.11 in

the Appendix. Most of new interconvertible goods introduced on the 13th

of November are arbitrage free, except for Dream Shards and Eternal Life.

Figure A.9 in the Appendix helps to understand the reason why there where

arbitrage possibilities on the Dream Shard market. It depicts the median

price of Dream Shard in gold, the volume in units and the arbitrage profit.

You may see that only during the short period of time after the good was

introduced, there were possible arbitrage profits. This is nothing new in the

real world, where new securities might not be free of arbitrage after their

immediate introduction. The market for Eternal Life (Figure A.10) might

however suggest that arbitrage doesn’t only arise when a good is first intro-

duced, but more or less over the whole period of observation. The key to

the answer is to look at the volume. Arbitrage possibilities disappeared as

soon as the volume reached a critical value (in this case more than 50 units).

We can apply the same reasoning to the market for Dream Shards discussed

before and conclude that arbitrage disappeared as soon as the market volume

went up. The key point here from our observations is that arbitrage in the

Dream Shards market was not linked to the good being new, but to its very

low volume in the first week.

The huge arbitrage profit derived from pre-Expansion goods (i.e. ”old”

ones) infer that our assumption about the risk free price was wrong (see

exemplary Figure A.11 & A.12 in the Appendix). Demand and supply dipped

just before the release of the new expansion on the 13th of November. This


effect is similar to a structural break, although the event was not unexpected.

From then on players didn’t need these obsolete goods, and others stopped

farming for them since they couldn’t sell them anymore. Notice in Figure

A.11 how the theoretical arbitrage profit goes up when the volume drops

beyond a critical value. At the same time, the ask price goes trough the roof

and isn’t meaningful at all. The risk free price assumption in Proposition 1

is wrong in the presence of a degenerated market. In this case the measure

of arbitrage defined before fails.

This section can be concluded with following observations:

1. There is no empirical evidence of arbitrage as long as we have a stable

market. A stable market means its volume is above some critical value

and the risk free price assumption we defined holds.

2. If we face degenerated markets like those of pre-Expansion goods after

the first November week, there is no way to measure arbitrage. This is

due to the nature of our data - we merely observe ask prices and not

actual transactions that took place. When the market degenerates, the

spread between ask and bid prices (the lasts aren’t observable) becomes

so large that ask prices do not reflect a measure of real willingness to

buy or sell.

18 4 CONCLUSION

4 Conclusion

The purpose of this bachelor thesis was to investigate commodity markets

in a virtual world called World of Warcraft. Virtual worlds have idealized

traits otherwise not present in the real world. These traits are however

often assumed in economic theory but not present in the real world. Virtual

worlds such as World of Warcraft offer a possibility to test existing economic

theories. In the field of behavioral economics and finance, virtual worlds can

be seen as an alternative to experiments. The obvious advantage besides

lower costs is that the observed subjects are not in a laboratory setting.

Price dispersion - a violation of the ”price” of one law - has been observed

for decades in the real world. Its existence is attributed to information costs

by the current literature (Baye & Morgan, 2006). In World of Warcraft, price

dispersion is omnipresent despite information costs being inexistent and the

goods totally homogeneous. Cheap goods have a significantly higher price

gap than expensive goods. Price dispersion is independent of the number of

sellers contrary to real world empirical results. The price gap shows as well

a cyclical pattern, which suggests that it results from elements varying over

time like the competitiveness between sellers. A topic of further research

would be to model cyclical price dispersion.

The second empirical part questioned the existence of arbitrage in World

of Warcraft. There is no empirical evidence of arbitrage as long as we face

stable markets, i.e. markets in which there are enough buyers and sellers.

It is not possible to establish empirical evidence for goods that are no ac-

tively gathered by players. This is due to unavailability of data for actual

transactions - it is only possible to observe ask prices and volume in World

of Warcraft.

As a conclusion, Blizzard needs to provide actual transactions data to

allow more economic research about their game.

19 A APPENDIX

A Appendix

A.1 Data

Figure A.1: Auction house in the player’s perspective

Figure A.2: Auctions saved in a textfile

20 A APPENDIX

Figure A.3: Auctions in the SQL database

Table A.1: Descriptive statistic for the most popular items

Item Mean Median Std Skewness Kurtosis

Greater Cosmic Essence 29.89 28.00 7.77 1.83 8.15Frozen Orb 174.79 100.02 206.06 4.18 34.01Eternal Fire 49.78 45.00 21.10 5.03 43.93Frost Lotus 23.94 18.50 13.60 2.03 7.49Eternal Life 39.61 40.00 18.54 0.70 3.36Eternal Earth 14.47 12.00 9.23 2.86 14.70Eternal Shadow 19.37 18.00 6.30 0.83 3.09Borean Leather 1.43 1.20 2.26 11.93 150.34Saronite Ore 3.91 2.90 3.43 8.47 107.44Infinite Dust 8.62 8.00 5.27 14.83 253.51Frostweave Cloth 2.03 1.60 3.88 17.24 361.71Adder’s Tongue 2.89 2.15 2.75 4.57 25.56Saronite Bar 4.82 3.75 2.85 7.54 118.52Netherweave Cloth 0.36 0.20 0.81 15.30 302.34Runecloth 0.47 0.36 0.73 23.34 751.46Mageweave Cloth 0.58 0.45 0.76 7.43 61.84Silk Cloth 0.27 0.10 0.82 15.33 686.40Wool Cloth 0.35 0.33 0.38 19.28 494.79Linen Cloth 0.12 0.04 0.37 6.84 60.38

21 A APPENDIX

Table A.2: Descriptive statistic for the most popular items, clear from outliers

Item Mean Median Std Skewness Kurtosis

Greater Cosmic Essence 28.70 27.50 5.52 0.56 2.61Frozen Orb 130.09 100.00 96.99 1.93 7.00Eternal Fire 46.96 45.00 12.14 1.16 4.11Frost Lotus 20.99 17.90 8.18 0.99 2.95Eternal Life 37.99 40.00 16.46 0.34 2.23Eternal Earth 12.75 11.20 5.36 1.50 5.36Eternal Shadow 18.63 18.00 5.48 0.62 2.41Netherweave Bag 7.65 7.50 0.94 0.21 2.72Borean Leather 1.26 1.20 0.51 3.05 20.27Saronite Bar 4.48 3.75 1.58 0.95 3.17Infinite Dust 8.29 8.00 1.63 0.93 4.57Frostweave Cloth 1.77 1.60 0.75 2.08 9.45Adder’s Tongue 2.32 2.10 0.79 2.72 12.21Saronite Ore 3.71 2.85 2.02 1.28 3.63Netherweave Cloth 0.29 0.20 0.30 3.16 12.29Runecloth 0.43 0.36 0.26 2.45 10.22Mageweave Cloth 0.50 0.45 0.24 1.72 6.32Silk Cloth 0.16 0.10 0.20 3.65 18.76Wool Cloth 0.33 0.33 0.11 2.43 15.90Linen Cloth 0.07 0.04 0.09 4.25 27.84

22 A APPENDIX

Table A.3: p-Values of statistical tests for returns

Item QLBa QML

b Tc Sd Pe

Greater Cosmic Essence 0.8270 0.3685 0.3880 0.3657 0.6971Frozen Orb 0.7336 0.7307 0.0649 0.7290 0.7284Eternal Fire 0.1188 0.8207 0.3880 0.7630 0.5814Frost Lotus 0.8331 0.0509 0.0571 0.5403 0.7211Eternal Life 0.6561 0.2680 0.7658 0.7557 0.9006Eternal Earth 0.2055 0.1578 0.7658 0.7557 0.3092Eternal Shadow 0.0905 0.9282 0.2973 0.7557 0.7617Netherweave Bag 0.9447 0.5247 0.2418 0.1724 0.8257Borean Leather 0.4518 0.6076 0.5773 0.3798 0.3353Saronite Bar 0.7357 0.9569 0.6064 0.0339 0.8121Infinite Dust 0.0964 0.1967 0.1953 0.7630 0.2993Frostweave Cloth 0.6856 0.6672 0.7805 0.7697 0.5433Adder’s Tongue 0.5395 0.5711 0.6492 0.2059 0.5483Saronite Ore 0.5451 0.5550 0.7658 0.3507 0.0971Netherweave Cloth 0.0528 0.3830 0.4828 0.8299 0.2812Runecloth 0.1700 0.7710 0.1605 0.5192 0.9630Mageweave Cloth 0.3508 0.7404 0.6162 0.8299 0.7022Silk Cloth 0.1676 0.7100 0.4225 0.8299 0.8438Wool Cloth 0.0072 0.5413 0.6810 0.3789 0.6363Linen Cloth 0.0131 0.9850 0.4225 0.8299 0.8077

a Ljunx-Box-testb McLeod-Li testc Turning point testd Difference-sign teste Rank test

23 A APPENDIX

A.2 Price dispersion

Table A.4: Price gaps of the most popular goods

Item Relative gapa Absolute gapb Median Price

Expensive Items (>10g)Greater Cosmic Essence 0%-20% 0c - 6.67g 27.50gFrozen Orb 0%-36.36% 0c - 40g 100gEternal Fire 0%-43.63% 0c- 24g 40gFrost Lotus 0%-47.62% 1c - 5.12g 17.90gEternal Life 0%-74.19% 0c - 23g 45gEternal Earth 0%-81.81% 1c - 4.50g 11.20gEternal Shadow 0%-97.67% 1c- 14g 18g

Medium Items (1-10g)Netherweave Bag 0%-25.22% 0c - 1.4g 7.5gBorean Leather 0%-30.60% 0c - 0.34g 1.2gSaronite Bar 0%-35% 0c - 1.24g 3.75gInfinite Dust 0%-43.75% 1c - 1.75g 8gFrostweave Cloth 0%-44.44% 0c - 0.44g 1.60gAdder’s Tongue 0%-50% 0c - 1g 2.10gSaronite Ore 0%-61.36% 0c - 3.42g 2.85g

Cheap Items (<1g)Netherweave Cloth 0%-60% 0c - 0.18g 0.20gRunecloth 0.07%-233.33% 1c - 0.54g 0.36gMageweave Cloth 0%-500% 0c - 0.25g 0.45gSilk Cloth 0.20%-376% 1c - 0.08g 0.10gWool Cloth 0%-1804.76% 0c - 0.37g 0.33gLinen Cloth 0%-1233.33% 0c - 0.09g 0.04g

a G(t) = p(t)2 −p

(t)min

p(t)min

b g(t) = p(t)2 − p

(t)min

24 A APPENDIX

Table A.5: Regression results between price gaps and number of sellers

Item R2 R2 F-Stat p-Value

Expensive Items (>10g)Greater Cosmic Essence 0.0007 -0.0315 0.0219 0.8832Frozen Orb 0.0001 -0.0434 0.0017 0.9671Eternal Fire 0.0017 -0.0305 0.0534 0.8187Frost Lotus 0.0297 -0.0027 0.9175 0.3458Eternal Life 0.0685 0.0364 2.1324 0.1550Eternal Earth 0.0537 0.0211 1.6458 0.2097Eternal Shadow 0.0866 0.0551 2.7494 0.1081

Medium Items (1-10g)Netherweave Bag 0.0491 0.0321 2.8910 0.0946Borean Leather 0.0160 -0.0138 0.5380 0.4684Saronite Bar 0.0003 -0.0452 0.0059 0.9397Infinite Dust 0.0153 -0.0164 0.4830 0.4923Frostweave Cloth 0.0104 -0.0196 0.3467 0.5600Adder’s Tongue 0.0757 0.0427 2.2935 0.1411Saronite Ore 0.0103 -0.0238 0.3019 0.5869

Cheap Items (<1g)Netherweave Cloth 0.0000 -0.0159 0.0006 0.9797Runecloth 0.0581 0.0431 3.8852 0.0531Mageweave Cloth 0.0093 -0.0064 0.5905 0.4451Silk Cloth 0.0208 0.0053 1.3397 0.2515Wool Cloth 0.0001 -0.0166 0.0066 0.9354Linen Cloth 0.0202 0.0047 1.3010 0.2584

25 A APPENDIX

Table A.6: Regression results between price gaps and logarithmic number ofsellers

Item R2 R2 F-Stat p-Value

Expensive Items (>10g)Greater Cosmic Essence 0.0046 -0.0275 0.1438 0.7072Frozen Orb 0.0039 -0.0395 0.0889 0.7683Eternal Fire 0.0074 -0.0246 0.2312 0.6340Frost Lotus 0.0520 0.0204 1.6461 0.2093Eternal Life 0.0399 0.0068 1.2067 0.2810Eternal Earth 0.0436 0.0106 1.3212 0.2598Eternal Shadow 0.1431 0.1135 4.8420 0.0359

Medium Items (1-10g)Netherweave Bag 0.0820 0.0656 5.0038 0.0293Borean Leather 0.0039 -0.0263 0.1289 0.7218Saronite Bar 0.0184 -0.0262 0.4121 0.5275Infinite Dust 0.0275 -0.0039 0.8750 0.3568Frostweave Cloth 0.0000 -0.0303 0.00 0.9947Adder’s Tongue 0.0578 0.0241 1.7163 0.2008Saronite Ore 0.0026 -0.0318 0.0747 0.7865

Cheap Items (<1g)Netherweave Cloth 0.0004 -0.0156 0.0140 0.9063Runecloth 0.0867 0.0722 5.9786 0.0173Mageweave Cloth 0.0000 -0.0158 0.0024 0.9608Silk Cloth 0.0064 -0.0094 0.4033 0.5277Wool Cloth 0.0032 -0.0134 0.1905 0.6640Linen Cloth 0.0058 -0.0099 0.3703 0.5450

Figure A.4: Absolute price gap over time of Greater Cosmic Essence

11/14/08 11/30/08 12/16/080

0.05

0.1

0.15

0.2

Gap

26 A APPENDIX

Figure A.5: Absolute price gap over time of Infinite Dust

11/15/08 12/01/08 12/17/08

0.1

0.2

0.3

0.4

Gap

Figure A.6: Absolute price gap over time of Netherweave Cloth

10/14/08 11/13/08 12/13/080

0.2

0.4

0.6

Gap

A.3 Arbitrage

Figure A.7: Price and volume of Greater Cosmic Essence (GCE) & 3 x LesserCosmic Essence (LCE)

11/16/08 11/23/08 11/30/08 12/07/080

20

40

Pri

ce,

[gol

d] gce

lce x 3

11/16/08 11/23/08 11/30/08 12/07/080

200

400

600

Adj.

vol

27 A APPENDIX

Figure A.8: Price and volume of Dream Shard (DS) & 3 x Small DreamShard (SDS)

11/16/08 11/23/08 11/30/08 12/07/080

20

40

Pri

ce,

[gol

d] ds

sds x 3

11/16/08 11/23/08 11/30/08 12/07/080

200

400

Adj.

vol

28 A APPENDIX

Table A.7: Volumes of interconvertible goods over the observation period

Liquid Good Illiquid Good V (H)a V (L)b

Greater Cosmic Essence Lesser Cosmic Essence 7689 1415Dream Shard Small Dream Shard 4794 643Eternal Air Crystallized Air 10760 1485Eternal Earth Crystallized Earth 30260 3589Eternal Fire Crystallized Fire 14800 1115Eternal Shadow Crystallized Shadow 18740 1775Eternal Life Crystallized Life 9980 1259Eternal Water Crystallized Water 14520 3258Greater Astral Essence Lesser Astral Essence 11238 2376Greater Eternal Essence Lesser Eternal Essence 9144 1550Greater Magic Essence Lesser Magic Essence 11259 2942Greater Mystic Essence Lesser Mystic Essence 11787 1546Greater Nether Essence Lesser Nether Essence 4515 337Greater Planar Essence Lesser Planar Essence 12720 1277Primal Air Mote of Air 25050 1552Primal Earth Mote of Earth 42600 4988Primal Life Mote of Life 37460 4938Primal Fire Mote of Fire 22130 3312Primal Mana Mote of Mana 30540 3887Primal Shadow Mote of Shadow 19480 4323Primal Water Mote of Water 20650 2844

a Volume of the liquid goodb Volume of the illiquid good

29 A APPENDIX

Table A.8: Correlations of interconvertible goods

Liquid Good Illiquid Good Correlation p-Value

Greater Cosmic Essence Lesser Cosmic Essence 0.6060 0.0002Dream Shard Small Dream Shard 0.7947 0.0000Eternal Air Crystallized Air -0.1103 0.5477Eternal Earth Crystallized Earth 0.7308 0.0000Eternal Fire Crystallized Fire 0.1845 0.3120Eternal Shadow Crystallized Shadow 0.3893 0.0406Eternal Life Crystallized Life 0.7259 0.0000Eternal Water Crystallized Water 0.4666 0.0071Greater Astral Essence Lesser Astral Essence 0.1658 0.1869Greater Eternal Essence Lesser Eternal Essence -0.0581 0.6459Greater Magic Essence Lesser Magic Essence 0.5001 0.0000Greater Mystic Essence Lesser Mystic Essence -0.0621 0.6229Greater Nether Essence Lesser Nether Essence 0.3944 0.0013Greater Planar Essence Lesser Planar Essence 0.4093 0.0008

Table A.9: Correlations of partially interconvertible goods

Liquid Good Illiquid Good Correlation p-Value

Primal Air Mote of Air 0.4489 0.0002Primal Earth Mote of Earth 0.1195 0.3507Primal Life Mote of Life 0.3340 0.0066Primal Fire Mote of Fire 0.3931 0.0012Primal Mana Mote of Mana 0.8412 0.0000Primal Shadow Mote of Shadow 0.7317 0.0000Primal Water Mote of Water 0.6702 0.0000

30 A APPENDIX

Table A.10: Arbitrage profits of interconvertible goods over the observationperiod

Liquid Good Illiquid Good Total Arbitrage Profits

Greater Cosmic Essence Lesser Cosmic Essence 0Dream Shard Small Dream Shard 222.52Eternal Air Crystallized Air 0Eternal Earth Crystallized Earth 0Eternal Fire Crystallized Fire 0Eternal Shadow Crystallized Shadow 0Eternal Life Crystallized Life 3208.40Eternal Water Crystallized Water 0Greater Astral Essence Lesser Astral Essence 1.71Greater Eternal Essence Lesser Eternal Essence 2759.60Greater Magic Essence Lesser Magic Essence 1587.30Greater Mystic Essence Lesser Mystic Essence 52.45Greater Nether Essence Lesser Nether Essence 66.74Greater Planar Essence Lesser Planar Essence 3869.60

Table A.11: Arbitrage profits of partially interconvertible goods over theobservation period

Liquid Good Illiquid Good Total Arbitrage Profits

Primal Air Mote of Air 1586.50Primal Earth Mote of Earth 1031.10Primal Life Mote of Life 3532.80Primal Fire Mote of Fire 1031.50Primal Mana Mote of Mana 1929.80Primal Shadow Mote of Shadow 3024.40Primal Water Mote of Water 0

31 A APPENDIX

Figure A.9: Arbitrage profits of Dream Shards & Small Dream Shards

11/16/08 12/02/0810

20

30

40M

edia

npri

ce

11/16/08 12/02/08

20406080

100120

Vol

um

e

11/16/08 12/02/080

20

40

Arb

itra

ge

32 A APPENDIX

Figure A.10: Arbitrage profits of Eternal Life & Crystallized Life

11/16/08 12/02/08

20

40

60

80M

edia

npri

ce

11/16/08 12/02/080

50

100

Vol

um

e

11/16/08 12/02/080

200

400

600

800

Arb

itra

ge

33 A APPENDIX

Figure A.11: Arbitrage profits of Greater Eternal Essence & Lesser EternalEssence

10/14/08 11/13/08 12/13/0810

15

20

25

Med

ian

pri

ce

10/14/08 11/13/08 12/13/080

50

100

150

Vol

um

e

10/14/08 11/13/08 12/13/080

100

200

300

Arb

itra

ge

34 A APPENDIX

Figure A.12: Arbitrage profits of Greater Magic Essence & Lesser MagicEssence

10/14/08 11/13/08 12/13/08

0.5

1

1.5

2

Med

ian

pri

ce

10/14/08 11/13/08 12/13/080

100

200

Vol

um

e

10/14/08 11/13/08 12/13/080

50

100

150

Arb

itra

ge

35 References

References

Baye, M. R., & Morgan, J. (2006). Information, Search, and Price Disper-

sion. http://www.nash-equilibrium.com/baye/Handbook.pdf.

Blizzard. (2008). WORLD OF WARCRAFT SUBSCRIBER BASE

REACHES 11.5 MILLION WORLDWIDE. http://eu.blizzard

.com/en/press/081223.html.

Blizzard. (2009). Auction Houses. http://www.worldofwarcraft.com/

info/basics/auctionhouses.html.

Castronova, E. (2001). Virtual Worlds: A First-Hand Account of Market

and Society on the Cyberian Frontier [Working Paper Series]. SSRN

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Farming”: Real-World Production in Developing Countries for the Vir-

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Lehdonvirta, V. (2005). Virtual Economics: Applying economics to the

study of game worlds. In Proceedings of Future Play. http://virtual

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Lehtiniemi, T. (2008). Macroeconomic Indicators in a Virtual Econ-

omy. Unpublished master’s thesis, University of Helsinki. https://

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Nash, J., & Scheneyer, E. (2004). Virtual Economies: An In-Depth Look at

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Sandmann, K. (2001). Einfuhrung in die Stochastik der Finanzmarkte.

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36 References

Eigenstandigkeitserklarung

Ich erklare hiermit,

- dass ich die vorliegende Arbeit ohne fremde Hilfe und ohne Verwendung

anderer als der angegebenen Hilfsmittel verfasst habe,

- dass ich samtliche verwendeten Quellen erwahnt und gemass gangigen

wissenschaftlichen Zitierregeln nach bestem Wissen und Gewissen kor-

rekt zitiert habe.

markets in virtual worlds

Economy & Finance