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An Analysis of Virtual Currencies in Online Games
Hiroshi YAMAGUCHI
The Japan Center for International Finance
Social Science Research Institute, International Christian University
Abstract
In virtual worlds of MMORPGs (Massively Multiplayer Online Role-Playing Games), we observe that
many players purchase virtual items by using real currencies, which is so-called eBaying. Extending the
model developed by Castronova (2001), I analyze the value of virtual items in the virtual and real markets.
The analysis reveals that incentive for eBaying is inherent to the game design. In addition, I classify the
virtual currencies as a Local Exchange Trading Systems (LETS) because they are used in limited
communities, not under control of money supply by the central banks, and not subject to interest rates.
Since these currencies are not subject to geographical boundaries, they can potentially be global LETS.
The eBaying effectively means that the virtual currencies have exchange rates with real currencies, and
thus have become meaningful for our economy. The online virtual worlds increase its importance for our
life, and so does the virtual currencies.
1. Introduction
This paper aims to analyze the economic and
monetary system of MMORPGs (massively multi-
player online role-playing games), and to discuss its
implications on our real economy.
Economies of virtual worlds in MMORPGs were
first analyzed from academic perspective by Edward
Castronova. [1] analyzed the economic activity in the
virtual world in an online game "Everquest." In the
game, players (avatars) purchase various items
required by using the virtual currency called PP
(platinum piece). Players acquire items by the
activities in the game, or purchase the items by trades
among avatars using PP1. However, some (if not
many) American players, despite the forbid in the
game, trade the items in the real world using real
currency through auction sites of the Internet, such as
eBay.
[1] understood such a phenomenon that there
emerged an exchange rate between real and virtual
currencies based on purchasing power parity. For
example, suppose that an item in Everquest is 100 PP.
1 In some MMORPGs, game companies charges fees based
on items that players purchase. In cases of such item-based
fee system, the prices of the items are directly connected to
real money.
If the same item is traded in the real world at US$1, we
can calculate that 1PP = 1 cent.
2. Economic analysis of virtual worlds
There are dearth of economic research on virtual
worlds, except for [1], [2], and [3] by Castronova, and
[4] by Bartle. To discuss and analyze the currencies in
virtual worlds, we need to clarify what the economic
activities in virtual world are like. I extend Analysis in
[3] by specifying the properties of the utility function,
which were not present in [3].
2.1. “Castronovian” utility function
In ordinary economics, we do not think of Norrath
as if it were a real country. Nevertheless, many
economists have noticed that economic principles were
functional also in this virtual world. In-game virtual
worlds can provide valuable opportunities to observe
economies under somewhat controlled environment.
[3] proposed a new type of utility function that suits
analysis of the virtual worlds. In ordinary utility
functions, as in the panel (a) of the Figure 1, economic
agents maximize their utility by adjusting the
consumption of goods, subject to the corresponding
budget constraint. In contrast, “Castronovian” utility
function assumes that an economic agent is considered
2
as a meta-self who possesses many personalities
(avatars) in many worlds, including the real self in the
real world. The meta-self allocates her time to each of
avatars, and tries to maximize the utility of the meta-
self. In this paper I adopt the idea and extend it to
analysis of the virtual currencies. Assume that an
economic agent (player) has j avatars in i worlds. As
in [3], the Castronovian utility function takes the form
(
)
(
)
(
)
w
wawaawzvxhtuU,,;ΣΣ=K, (1)
where twa is the time spent as
[
]
jja,1,1,0−= L avatar
in
[
]
iiw,1,1,0−= L world, x is the attribute of the
player, wa
v is the attributes of a’s avatar in the w’s
world, w
zis the attributes of w’s world, and
(
)
wwa zvxh,, is the function aggregating these factors.
That is, the function u(twa) represents the utility from
spending time as a’s avatar in the w’th world.
[3] did not provide further detail on the properties
of the utility function. Thus I add constraints with
respect to the time allocation, that is,
,Ttwaaw=ΣΣ and (2)
0000 tt ≥, (3)
where T is the total available time, and t00 is the time
spent as the real world personality, in other words w=0、
a=0, and 00
t is the minimum time that t00 can take. In
ordinary utility function as in the panel (a) of the
Figure 1, utility is generated by consumption of goods.
An economic agent maximizes her utility by selecting
what to consume and how much. In contrast, in the
Castronovian utility function, utility is determined by
allocation of time among different avatars, including
the real personality. If there is no time constraint, the
utility function for the time allocation should look
similar to the ordinary utility function. However, it is
not the case because the available time is limited for us.
Specifically, if the player spends too much time to the
avatar q in the world p, her real life has problems,
physically, financially, or psychologically. This
reduces her utility upq, and results in unique features of
the function. First, the amount of goods for
consumption has no limit in ordinary utility functions,
but in the Castronovian utility function, total available
time that economic agent use is fixed at T, as in the
Equation (2). If a player allocates longer time to an
avatar, the time remaining for other avatars is shorter.
Second, there is a limit on the time that could be
spent for each avatar. An avatar in virtual world is a
derivative of the real personality, and the basic human
needs can not be satisfied in the virtual worlds. To
play game, a player should earn money in the real
world. Therefore, as in the Equation (3), t00 has the
lower limit. Here we define the time that is disposable
for online games as T’ and
00
tTT −≡
′
. (4)
As the time spent in virtual worlds approaches T’,
the life of the player should involve an increasing
degree of difficulty, due to the interaction among
utilities of different avatars2. That is, the function
u(twa) should in fact be constrained by such interactions.
The panel (b) of the Figure 1 shows the utility function
for q’th avatar in p’th world, u(tpq | Kpq), where Kpq
denotes the best possible allocation of time given tpq.
That is, Kpq = [t00, t11, t12, . ., tpq, . . , tij], that satisfies
( )
( )
≡∑∑ pq
wawapq ttuKU|sup . (5)
Then, the constrained Castronovian utility function has
a upward-sloping part for lower value of tpq, but hit its
peak at *
pq
t, and reduces to zero at T’. Thus we have
relationships 0>∂∂ pq
tu *
pqpq tt <,
0=∂∂ pq
tu *
pqpq tt =, (6)
0<∂∂ pq
tu Ttt pqpq ′
<<
*.
As for the second derivative, we have 0
22 <∂∂ pq
tu,
which is the same as in the case of the panel (a).
The Castronovian utility function substantially
differs from ordinary utility functions, but what an
economic agent does in the model is not so different.
In the former, avatars are like goods, and an economic
agent purchases the avatars by spending time instead of
money. The utility maximization through allocation of
time to avatars is in essence the same as that through
2 In Korea, a 24-year-old male died after playing an online
game for consecutive 86 hours (IT Media News, October 9,
2003).
3
allocation of money to goods to consume. In this sense,
we can analyze economic models based on the
Castronovian utility function.
2.2. Why are they eBaying?
Next, I discuss the market of goods in virtual
worlds. The particular focus is put on a question,
“Why players trade virtual items in the real world
auction sites such as eBay?” The real-world trading of
virtual items, often called “eBaying,” has become
popular among players. Since the virtual currency is
used to purchase goods in a virtual world, we need to
model the price mechanism that functions in the virtual
world.
The market mechanism in the virtual world is
somewhat different from that in our real-world
economy. An important feature of this economy is that
no firm exists in the games, and individual players
(avatars) produce items and supply to the market. In
this sense, the virtual world economy is in the “stone
age,” in which people live on hunting and collecting.
Time, the resource to be allocated, is not only a source
of utility but also a source of pain (which means, a
decrease in utility), depending on the shape of utility
function and allocation of time.
Assume that there is only one MMORPG virtual
world, in which each player has only one avatar.
Consider two players, A and B, and assume that A has
higher in-game skills. Denote the level of skills of the
two players as kA and kB (kA > kB), respectively. The
skills affect time required to obtain in-game items.
Define the necessary time for each of them to earn a
newly introduced item as tA and tB (tA < tB),
respectively. For simplicity, I assume here that kAtA =
kBtB. And we denote the income in the virtual world
per unit of time, denoted jA and jB, each of which is
proportional to kA and kB, respectively. In addition,
their real-world income per unit of time are denoted as
hA and hB, respectively.
Players earn in-game skills based on experience in
the game. The Figure 2 shows the patterns of skill
accumulation in virtual and real worlds. To attract
customers, as shown in the panel (a), the game
company designs the game so that the players can
accumulate new skills much faster than the players can
accumulate real world skills in the real world. Some
skills may be more difficult to obtain, but in many
cases majority of players can reach the highest level by
spending long enough hours to play. In contrast, as
shown in the panel (b), we earn skills in the real world
much more slowly, and many of us can not reach the
“highest” level. In this sense, the remuneration scheme
in virtual worlds is similar to that of so-called seniority
system (a typical characteristic of post-war Japanese-
style management), rather than performance-pay
system.
The assumption that player A has higher in-game
skills leads us to another assumption that B has higher
real-world income (hA < hB). That is, player A has
higher in-game skill because she had already allocated
a higher proportion of available time to the game than
player B had. Player A could do so because the
opportunity cost of time denominated by real-world
income is lower than B. In contrast, due to the higher
real-world income, player B put a higher priority to the
real-world life, and allocate shorter time for game-play.
Each player has her own utility function for the
time spent as the avatar. Up to now, they have
allocated time period sA and sB for their respective
avatars. Changes in utility when they allocate
additional time for the avatar to obtain the new item
depend on the current time allocation and the
additional time requirement. When the player A
increases her utility by playing the game by tA longer,
while the player B decreases her utility by spending
additional tB, both players would have incentive to
trade items. When there is a relationship
(
)
(
)
(
)
(
)
BBBAAA sutsusutsu−+>−+ , (7)
then player B would purchase the item from A.
The transaction price of the item in this simplified
virtual world is determined by the opportunity costs of
obtaining the item for both players in the virtual world.
By assumption, these opportunity costs are identical;
that is, jAtA = jBtB.
4
Limited virtual-world income of player B relative
to that of real world provides her with incentive to
purchase the item in the real world. In particular, since
player B has a short history of game play and allocates
longer time for real-time job, it is likely that she owns
less amount of virtual money and earns lower income,
while earning higher real-world income. Therefore,
player B has higher opportunity cost in the real world
than player A does , in other words,
hAtA < hBtB. (8)
This means, both players A and B have incentive to
trade the new item in the real world at the price
between hAtA and hBtB. If the item is rare, which is
typically the case for newly introduced items, player B
would be willing to pay up to her reservation price,
hBtB. Then the exchange rate between virtual and real
currencies is determined by hB/jB. As the supply of the
item increases in the virtual world, the exchange rate
would gradually decline to hA/jA.
The incentive for eBaying is affected by the
differences in shape of the utility function and the real-
world income. In the Equation (7), as the difference
between the left and right hand sides widens, both
players are to a greater extent better off by trading the
new item. That is, the incentive for trading of the
items in the game is accelerated. Likewise, in the
Equation (8), as the real-world income of player B
rises relative to that of player A, the incentive to trade
the item in the real world is enhanced.
The above analysis reveals that the incentive for
eBaying among players is inherent to the game design.
In many MMORPGs, players earn skills and higher
status based on in-game experiences. To make players
feel achievement and fun, game developers tend to
exaggerate the improvement of skills, and design the
game so that the accumulation of skills occurs more
rapidly than in the real world. This enhances relative
difficulty of obtaining items for less experienced
players. In addition, unlike in the real world, the skill
accumulation basically does not depend on player’s
talent but on the time allocated to the game. Any
player can reach the highest level as long as she
allocates enough time to the game. Then for those
players who are more constrained in terms of time
allocation but less constrained in real-world income, it
is rational to trade the virtual items by using the real
currency. Player A, to maximize her utility, exploits
her comparative advantage in the available time for the
game. Likewise, player B exploits her comparative
advantage in the holding of the real currency.
3. Analysis of virtual currencies
Next, I analyze the currencies in virtual worlds, the
main theme of this paper. Although [4] provided in-
depth discussion on virtual currencies, its scope was
limited to the boundary of the virtual world. Here I
discuss the issue including its implications to the real
world.
3.1. What is a “currency?”
In ordinary economics, we do not classify in-game
currencies as real. For example, Monopoly, one of the
most popular board games, has a currency called
“dollar.” However, this is only a part of the game, and
the Monopoly dollar can not be a real currency. Then,
what are the differences between virtual currencies of
MMORPGs and those of ordinary games?
In general, money has the following three
functions: (i) medium of exchange, (ii) measure of
value, and (iii) mean of storage. For an object to
function as money, its value should be assured in some
way because money is money because people believe it
as money. In this sense, we must admit that many
virtual currencies, including Monopoly dollar and PP
in Everquest, have these three functions in the
respective virtual world of games. For example,
Monopoly dollar is the medium of exchange, the
measure of value and the mean of storage of value in
the game world.
A virtual currency is valid only in the
corresponding virtual world. But this is not a problem
for the virtual currency to be a currency. Any real
currencies in the world are used within some
geographical boundaries. For example, we can not
5
purchase goods in Japan with Zimbabwe dollar. But
this does not contradict with the fact that Zimbabwe
dollar is the legitimate currency in Zimbabwe.
The goods in the virtual world are only imaginary
and have no physical substance, different from real-
world goods like bread or automobiles. But this is not
a problem, too. In the real world, we have goods that
do not have physical substance, for example, brands
and information. An online game is a kind of
information service provided through the Internet.
There is no reason for us to distinguish an in-game
item, a piece of information, from other piece of
information such as news articles or recipes provided
at other websites. These virtual goods are “rare” in
economic sense in the virtual world, and have value for
the dwellers there.
Although the government does not assure the value
of virtual currencies, this is not a problem, too. The
assurance of value by the government is not necessary
if the value is assured in other ways. For example,
Sony, the creator and the ultimate authority of the
world of Norrath, assures PP as the legitimate currency.
Players have no concern about the value of PP in the
game. And this is the same for Monopoly dollar. In
this sense, in-game virtual currencies are the same as
the real currencies.
Therefore, it is only a preoccupation (“virtual
worlds are not the object of economic analysis”) that
has divided the virtual and real currencies. When we
adopt the basic idea in [3] and take human activities in
virtual worlds into consideration, the distinction has
lost its reasoning. Virtual currencies are currencies.
3.2. A “meaningful” virtual currency
However, we cannot conclude that the Monopoly
dollar is identical to the real currency. As Adam Smith
told, demand for money is determined by what we
purchase by using the money. That is, the virtual
currency in a MMORPG is used for consumption in
the virtual world. Both a building in Monopoly and an
item in Everquest are imaginary goods. However, it is
quite different that many Everquest players are willing
to purchase the in-game items by using the real
currency; in contrast, no one would buy an imaginary
building in Monopoly by paying real money. PP is
distinguished from other game money as a
“meaningful” currency, which can be exchanged for
the real money. This effectively means that we have
the exchange rate between PP and real currency. The
existence of exchange rate is the condition for an in-
game money to become a “meaningful” currency.
4. Virtual currency as “LETS”
Despite the similarity of virtual currencies to real
currencies, the former is significantly different from
the latter in some important ways. This leads us to a
hypothesis that we should view these virtual currencies
as so-called Local Exchange Trading System (LETS).
4.1. Differences between virtual and real currencies
The major differences between virtual and real
currencies are twofold. First, players themselves issue
virtual currencies. In many MMOROGs, players earn
money by selling items that hunted monsters drop.
There is no central bank that issues currency, and there
is no banking system that lends us money, too. Thus
the virtual world has no measure to control money
supply. The balance between goods and money is
determined by collective consumption/saving decisions
by players.
The absence of the monetary control has a
significant meaning when we analyze the virtual
economy. Since players earn in-game skills faster than
they do in the real world, the total wealth of avatars,
the sum of virtual items and money, is increased
rapidly. Therefore, as time passes, the scarcity of
virtual items and money relative to those in the real
world declines. What makes PP as a “meaningful”
currency is the existence of the items that players are
willing to buy by using US dollar. Thus this decreases
the value of PP compared to that of real currencies. In
other words, virtual money is destined to depreciate
against the real money.
6
Second difference is that there are no interest rates
in virtual worlds in general. The absence of interest
rates, ceteris paribus, reduces incentive for saving and
raises that for consumption. Since many virtual worlds
do not have inflation of the general price level, we can
not say in general that consumption is preferred in
virtual worlds relative to the real world. Nevertheless,
still there should be greater incentive for consumption
compared to the case in which there are interest rates.
4.2. History and Current Status of LETS
The above differences can be better understood if
we view the virtual currencies as local currencies
rather than ordinary currencies. Many of local
currencies that we see today in the world are similar to
the Local Exchange Trading System (LETS) proposed
by Michael Linton. A LETS is defined as “a trading
network supported by its own internal currency; it is
self-regulating and allows its users to manage and issue
their own money supply within the boundaries of the
network3.”
Notice here that the LETS is issued by the
participants. A participant receives LETS credits from
other participants in exchange for the services that she
provided. In addition, the absence of interest rate
intends to enhance consumption of goods and services.
LETS often involves administration cost that is
subtracted from the accounts, and the cost effectively
means negative interest rates. These characteristics are
shared by many virtual currencies. That is, the virtual
currencies in MMORPGs are local currencies in online
cyber-communities.
The greatest difference between virtual currencies
and real world LETS is that the virtual currencies are
not subject to geographical boundaries. An ordinary
LETS is geographically bounded because
implementing the system requires implicit binding
power of community. Any existing LETS are valid
only in some relatively small communities in small
areas. Therefore, the values of the LETS, by which
3 http://www.gmlets.u-net.com/home.html
people can purchase goods and services, link with
specific real currencies, such as yen or dollar. Thus
they do not need to worry about exchange rates. In
case of MMORPGs, a community can consist of
members from all over the world, irrespective of
physical and social boundaries. In fact, Everquest has
approximately 100,000 out of 450,000 subscribers
living outside the U.S. In this sense, I understand the
emergence of “meaningful” virtual currencies as an
early sign of a “global LETS4.”
5. What does the virtual currencies bring us?
Next, I discussed the implication of the emergence
of the “meaningful” in-game virtual currencies. A
virtual currency is considered as an important part of
the economy of the virtual world. And the analysis of
virtual worlds is often useful in improving game design.
In addition, if we broaden our view to the entire fields
of Internet, we can see a potential impact of the global
LETS on our real economy. Here I focus on the latter.
Global LETS can potentially be a numeraire of the
value of information and services in the Internet, where
there are emergence of non-monetary-based activities.
5.1. Implications to the real worlds
In recent years, we have been observing an
expansion of activities of people in online networks.
However, human activity in virtual worlds does not
reflect in the existing economic indicators. As [3]
argued, MMORPG players enjoy utility from activities
as avatars in the games. The satisfaction of the players
affects their behavior seeking for utility maximization.
Similarly, people’s activities in cyberworld other than
games increase the importance in their lives. But the
importance of these activities is not fully understood.
Enhanced activities in virtual worlds mean that people
allocate longer time for the virtual worlds. Given that
the total amount of human activities is the same, this
effectively means shrinkage of our real-world economy.
4 We should put some reservation on this point because in
reality many MMORPGs, game companies set up different
servers from region to region.
7
However, this is not necessarily our worse off; taking
the virtual-world activities into account, we may be in
fact better off by increased total utility from the “off-
account” virtual economies.
At least a part of the activities in the Internet clearly
has more than negligible importance in terms of quality,
too. In many fields of cyberworld, the boundary for
professionals and amateurs has become increasingly
ambiguous. As in the case of the development of
Linux, contributions by individuals or groups of people
not for monetary compensation are now equally
important to those by profit-seeking professionals.
Many engineers provided spontaneous contributions
for improvement without monetary compensation.
When we think of the virtual world economy, we
should be aware that the value system in cyberworld is
not necessarily compatible with that of our existing
real-world economic principles. In principle, the
Internet is based on participation of spontaneous
participants. Exchanges of information and services
there involve reciprocity. In other words, the values of
the information and services that are exchanged in the
cyberworld, as long as the two parties agree, are not
necessarily consistent with the value system of the real
world. It is less likely that arbitrage trading occurs in
virtual economies. Notice that this characteristic is
similar to that of a LETS, which is effective in a small
community consisting of people with shared value
system and interest. In case of the virtual currency, the
community exists in the cyberworld, irrespective of
physical distance.
Virtual worlds have become meaningful to our lives.
However, we have not yet known fully on what is the
mechanism of exchanges of information and services
in these worlds. Virtual currencies in MMORPGs first
showed us that a LETS can exist within cyber-
communities, which by its nature involve no
geographical limitation. The above observation leads
us to a generalized idea that a LETS-like instrument
can potentially become a system that enhances
people’s interactions through the Internet.
In addition, for those opponents against government
intervention on the Internet, the concept of virtual
currencies has further importance. As people’s
activities in the Internet expand, governments may
become interested in taxation on items and transactions
in the cyberworld. When we denominate values in
virtual worlds into real currencies, it is more difficult
to defend these values from taxation. In this sense, we
had better denominate values in virtual worlds in a unit
that is unique to the virtual world.
5.2. Lessons from virtual worlds
Our observation of virtual worlds of MMORPGs
has become increasingly important opportunities to
improve our real society. Recall that the virtual world
can be a laboratory for experiments in economics.
Although online games are for fun rather than research,
the cyberworld provide important opportunities on how
we design and operate our economy.
Lessons learned from the experience of running
virtual worlds are useful to run our real economy
because our economy has turned into “fun-based”
economy. In many advanced economies, people
become less concerned about threat against their lives.
They basically own everything they need for their
everyday lives, and become less interested in further
improvement of living standard. We have been
steadily losing the centripetal force that has united our
society as a group.
In such an environment, policymakers should
become more concerned about how to motivate people
toward socially meaningful activities. And some
people focus on “fun” element of the economy. In
conventional economics, job is only a pain. People try
to minimize labor. But we know that many people in
advanced economies are in fact willing to work longer
and harder, not because of monetary income, but of fun.
Notice that the reason for those people to work is the
same as that for the players to play MMORPGs. That
is, self-fulfillment. Game companies try their best to
attract customers by designing the “quests ” or jobs in
the games more enjoyable. Why don’t we utilize the
8
know-how of these firms to design our real-world
economy?
6. Concluding remarks
Many people might think that the virtual worlds are
different from the real world. Yes, they are, for the
time being. But remember the situation 20 years ago.
How many of us could imagine such a rapid expansion
of the Internet, and resulting changes in our lives? Our
current situation has gone far beyond our imagination
in those days. What we observe today may be a sign
of our own future. Virtual worlds can potentially be
our new frontier. Some of us have already let their
avatars “migrate” there, and are building new
communities. Understanding the virtual worlds and
their economy is beneficial for both of the (real)
society and ourselves.
7. References
[1] Castronova, E., “Virtual worlds: a first-hand
account of market and society on the cyberian frontier”,
CESifo Working Paper 752, California State Univ.
Fullerton, 2001.
[2] Castronova, E., “On virtual economics”, CESifo
Working Paper 752, California State Univ. Fullerton,
2002.
[3] Castronova, E., “Theory of the Avatar”, CESifo
Working Paper 863, California State Univ. Fullerton,
2003.
[4] Bartle, Richard A. Designing Virtual Worlds. New
Riders 2004.
Figure 2: Accumulation of Skills
(a) Virtual World
Highest
Level of
Skill
Time
Spent
BA
(b) Real World
Time
Spent
AB
Highest
Level of
Income
Consumption (C)
Utility
U(C)
(a)An Ordinary Utility Function
Marginal utility is
always positive.
Time Spent as p’s avatar in q’th world (tpq)
Utility
u(tpq)
(b)Castronovian Utility Function
of An Avatar in A Virtual World
T’
Marginal utility is
partially negative.
T
Figure 1: Ordinary and Castronovian Utility Functions
t*pq
