An Economic Analysis on Online Game Service

Electronic copy available at: http://ssrn.com/abstract=1335120
An Economic Analysis on Online Game Service
∗
Huhh, Jun-Sok
†,‡
August 28, 2009
Abstract
This paper investigates an economic problem of a frm that provides online
game service. Besides pricing and fne-tuning of its game design, the frm should
consider a virtual economic environment of its service, for the policy on this respect
can infuence its proftability. Among virtual economic issues, Real-money Trading
(RMT) emerges as the most important one in online game business, which is de-
fned by players unofcial transactions between in-game virtual objects such as in-
game currencies, weapons, armors, and money in the real world. This paper ad-
dresses impact of RMT on the proftability of the frm. This paper addresses the-
oretical cases that RMT enhances frms proft. This shows why RMT is likely to
be tolerated by the frm despite the fact that RMT may violate contractual agree-
ments between the frm and players. To keep track of reality in online game busi-
ness, we examine impacts that two variants of RMT have on frms proft addition-
ally. By comparing four diferent regimes to price an online game, conditions that
each regime earns highest proft are identifed.
keywords: online games, network efect, real-money trading, gold farming, mi-
cropayment
JEL classifcations: D21, D62, L12, L86, Z19
1 Introduction
The online game is rapidly rising as a next trend in global video games industry. Since
around 2000, the online game has already occupied absolute market share in South Ko-
rea (henceforth Korea), China, and most of major East Asian countries but Japan. In
case of Korea, one of front-runners in online gaming, it is true that online games created
the culture of video gaming, that online games and its related businesses had around
61% of total video gaming market in 2006 (Korea Game Industry Agency, 2007).
1
In
China, online games have become so popular that the government has started to con-
sider introducing some regulations for securing adults’ productivity and children’s edu-
cation (The Economist, 2008). North America and EU have also joined this new wave
∗
This version is made only for peer review. If you would refer or have any comment on this
article, contact author via below E-mail.
†
The Graduate School of Economics, Seoul National University and Gamestudy.org. Tel: 82-2-10-
4932-9881, E-mail:[email protected].
‡
Thanks to Dr. Sung-Hee Shim of Korea Energy Economics Institute for valuable comments. All
faults in the paper belong to mine.
1
This is not accurate because some part of gambling is included in the estimation. According to
more recent datum in 2007, which is free of this problem, the share goes up to 86.5%.
1
Electronic copy available at: http://ssrn.com/abstract=1335120
in earnest since World of WarCraft, a multi-players online game by Blizzard, gained a
huge success in 2005.
The online game as a service is unique compared to other video games such as con-
sole game or stand-alone PC game. Basically, online games cannot be provided without
network connections, which make a signifcant diference in gaming experience. Broad-
band Internet connections make it possible that more massive and social contents are
delivered to players. All kinds of these full-blown ones are known as the massively multi-
players online game (MMOG). Typical MMOG is concurrently played by a lot of par-
ticipants in a same server of a game, and considerable part of fun is created by players’
diverse and spontaneous interactions. The network of players is a key to understanding
online games.
Two economic aspects of the network are to be concerned. First, like industries such
as software and telecommunications and, more generally, the markets for information
goods, there is network efect or externality where the utility of a consumer from the
purchase of a good or service depends on the number of other consumers doing the
same. The larger population an online game has the higher value it gets. This is direct
network efect where players beneft one another simply by participating. Second, as the
fun of an online game cannot be fxed by the code of software, players’ interactions in
the game as well as its size can exert an infuence on its value. In this respect, one
of the most prominent phenomena is real-money trading (RMT) among players, which
means the unofcial act of trading in-game items, in-game currency, and/or characters
for money of the real world, real-money. It is unofcial since a service does not generally
support RMT in its end-user license agreement (EULA). Roles of players as buyer and
seller in RMT can generate economic gains diferent from direct network efect. In this
case, the value of participating in one side depends crucially on the number of the other.
It is noted that this indirect network efect can be realized via frm’s policy on RMT.
This paper investigates the economic performance of online game service in the pres-
ence of these two kinds of network efect. For this, at frst, a game-theoretic model based
on optimizations of a service provider and players is utilized to build a basic framework.
Later in the paper, this model is extended, incorporating RMT among players and frm’s
strategic choice on RMT, which is related to indirect network efect. To keep track of
reality in online game business, we examine two variant forms of RMT additionally;
gold farming where there exists specialized sellers dedicated to make in-game items for
earning real-money, and micropayment where the service provider directly does RMT
selling done by players in naive RMT. It will be shown that gold farming is tolerated
by a service because it enlarges applicability of RMT. Micropayment works better with
competition among services intensifed, which explains its recent popularity in online
games business.
In the remainder of the paper, we proceed as follows. In Sec. 2, to take a direction
of this paper, economic studies on virtual worlds and those on network efect are shortly
reviewed. In Sec. 3, after briefy defning pricing regimes that we address, a basic model
based on a two-stage game with sequential moves is constructed and optimization of a
frm are analyzed. In Sec. 4, the model is extended to accommodate RMT, and its
efects on behaviors of players and the frm are addressed. In Sec. 5, two variant forms
of pricing regimes infuenced by RMT, gold farming and micropayment, are discussed.
Lastly, Sec. 6 provides a short summary of the paper and agendas for future researches.
2
Electronic copy available at: http://ssrn.com/abstract=1335120
2 Literature Review
Besides its industrial presence, online games have also attracted interests of the aca-
demic world. They are often called, more generally, virtual world studies (de Freitas,
2008). They view virtual worlds where millions of people come to play and socialize
are a new type of social order (Lastowka and Hunter, Forthcoming; Castronova, 2004).
They also stress that virtual worlds would get useful more and more to achieve a variety
of researches and educational goals in the real world (Bloomfeld, 2007). In economics,
Edward Castronova typically shows this direction of interests (Castronova, 2001, 2002,
2003, 2006a,b; The Economist, 2007). He argues that when virtual worlds do become
a large part of the daily life of humans, their development may have an impact on the
macro-economies of the real world (Castronova, 2006a). RMT is one of the clearest evi-
dences that show the power of virtual worlds that stand parallel to the real world. In his
renowned paper on the economy of an online game, EverQuest by Sony Online Enter-
tainment, which has attracted considerable attention among academics and even among
the general public, he claims that Norrath, the name of the world in the game, has a
GDP per capita somewhere between that of Russia and Bulgaria, higher than that of
China and India in 2000 (Castronova, 2001). In spite of his novel perspective, a ba-
sic economic problem of online games has not been under his discussion. How does the
uniqueness of online game afect the real-world structure of a service? What infuence
do strategic choices of a frm have on its virtual world? They are intriguing issues that
economics of virtual worlds can explore, but his researches are less interested in this
kind than in inner problems of virtual worlds.
2
Economic studies on network efect are also closely related to this paper. Since Rohlfs
(1974) frst showed that there exist intriguing economic problems with network size, nu-
merous studies has been done on this account (Shy, 2001; Economides, 1996a). Espe-
cially, exemplifed best by telecommunication service and fax machine market, it pro-
vides a theory that coordination problem related to the issue of critical mass is gener-
ally tied to the presence of network efect. In this paper, by following this theory, frm’s
optimizing problems under network efect diferentiate between critical mass minimiza-
tion and proft maximization. Oren and Smith (1981) and Economides and Himmelberg
(1995) discuss economic features of critical mass which can be infuenced by choices of
economic agents. This paper examines not only the problem of proft maximization, but
also that of critical mass which can be minimized by choosing game design with difer-
ing conditions for a service.
Much of studies on network efect are based on the direct kind where customers
beneft one another simply by joining a network (Economides, 1996b). Economic stud-
ies on two-sided or multi-sided markets highlight roles of platform to create network
efect among two or more distinct groups of customers by making them on the board.
Platform can help these customers get together in a variety of ways and thereby cre-
2
A ground for him to validate virtual worlds, in his researches, RMT is postulated to be a virtual
equivalence of real-world pollution, negative externality. By basic supply-demand model, he contends
that the act of RMT is the case that private cost and social cost diverse. Hence, RMT should be
treated by some kind of regulatory measure to enhance players’ overall welfare. His premise that RMT
can be equated to negative externality that hurts the (virtual) public results from his view that virtual
worlds have a considerable independence from the real world. His argument is that the welfare in a
virtual world has to be evaluated by its own criteria. RMT is understood as an invasion to virtual
worlds from the real world based on monetary power, which causes negative impacts on virtual worlds.
We do not argue upon this independence issue here. Instead, unlike his view, we consider RMT as
incentives that arise among players spontaneously, which can afect frm’s proftability, hence strategic
choice for its service.
3
ate value that might be lost otherwise (Evans et al., 2006). As researches based on this
theory has made good achievements (Evans, 2003; Caillaud and Jullien, 2003; Rysman,
2004; Gabszewicz and Wauthy, 2004; Rochet and Tirole, 2006; Hagui, 2006; Armstrong,
2006; Armstrong and Wright, 2007), online games have not been well discussed by them.
Contrary to console video games where the role of platform can be clearly observed
(Hagui, 2006), online games are considered to have little relevance to this argument.
But, as asserted in virtual world studies, players can enjoy high degree of freedom in
games, which makes the possibility that interactions among them create values invisible
before. Shortly, RMT reveals the potential that online games evolve from a traditional
one-sided service to the multi-sided. Although most of online games do not actively put
themselves as platforms, when a frm tolerates RMT, the logic of platform is implicitly
at work.
3
A theory for online game as an economic platform is not developed here, but
the key for our discussion is that an online game service can have strategic choices sim-
ilar to those of a platform, for example, the policy on RMT.
3 Basic Model
Defning four pricing regimes
Before we start, let’s frst look at pricing regimes used in the paper. The pricing regime
is defned to be the structure in which a frm collects its revenue from players. Regimes
are to be identifed by two categories: what pricing method is applied and whether RMT
is tolerated or not.
There are two kinds of pricing method: fat fee and two-part tarif. In this paper, fat
fee means applying a fxed price unilaterally without regard to each player’s usage level
for a fxed period. This is a generic pricing method for charging one of most popular
genres of online games, massively multi-players online role-playing game (MMOPRG).
Most of fat fee systems for online games have been applied on monthly basis. Two-part
tarif is applying both of entry and usage fee for each player, which is similar to pricing
at amusement parks. By this system, players’ payments can be diferentiated by their
playing behaviors. We consider the case of providing entry for free, which is often called
“free to play”, as a special case of two-part tarif.
The other axis for identifying pricing regimes is frm’s policy on RMT. RMT is to be
discerned into three sorts for our purpose. The frst one is the naive case that players
buy and sell one another in a virtual economy that resembles competitive market. In
this instance, the strategic choice by a frm is about tolerating those economic acts of
players unofcially done. This naive RMT may vary into two other forms, both of which
replace sellers/players in RMT with the specialized. Gold farming is the organized act
gathering in online games exclusively served for earning real-money. The other variant
is the micropayment where a frm merges sellers’ role in RMT into its service. It is
assumed that the fat fee system is automatically excluded for this case.
4
3
Second Life by Linden Lab is a good case for turning online game into an economic platform.
Most of contents in the game are not provided by the frm, but by players themselves (The Economist,
2006a,b). The high degree of technological freedom of the game makes it possible for variety of cre-
ators to provide their unique items in the game. By charging no entry fee, Linden Lab makes incen-
tives for players to trade among them. The considerable part of frm’s revenue comes from commis-
sion for exchanging between Linden Dollar, in-game currency, and real-money.
4
So to speak, two-part tarif is assumed not to be applied without RMT, for usage fee of an online
game is generally charged by selling virtual items, which belongs to RMT in our discussion. Actually,
it is possible to apply this policy by designing other sophisticated pricing systems, for example, fat
fee based on a fner demarcation on pricing period. It is imaginable one, but has not been tried for
4
Without RMT With RMT
Naive Specialized
Flat fee Regime N Regime R Regime G
Two-part tarif Regime M
Table 1: The map of pricing regimes
Four types of pricing regimes that we are to address are : i) regime N (non-RMT)
where fat fee pricing is applied without any RMT; ii) regime R (naive RMT) where fat
fee is applied with naive RMT and without gold farming; iii) regime G (gold farming)
where fat fee is applied with gold farming that replaces sellers/players in regime R;
iv) regime M (micropayment) where two-part tarif is applied with frm’s direct selling
that may replace sellers/players and gold farming. Tab. 1 maps each by two categories.
We also assume that a service can choose the most proftable regime by comparing
its (static) proft in each regime. It is true that this assumption is not realistic in some
cases. If, however, proft maximization is admitted to be the supreme motive for a frm,
putting realization issue aside is not unreasonable for observing frm’s optimal behavior
and economic performance.
U The utility of a game player under the regime without RMT
δ An intrinsic value or monopoly power of a game unrelated to network efect
g
x
The normalized playing time of a player in x. g
x
∈ [0, 1]
h An ex-ante ideal time spending for players set by a frm. h ∈ [0, 1]
β An intensity of network efect. β ∈ (0, 1]
n An actual number of players. By the assumption that x follows uniform
distribution on [0, 1], n ∈ [0, 1] holds, and all kinds of n in the paper are
in [0, 1]
p A fat fee of a game
x The normalized time endowment of a player. x ∈ [0, 1]. This is also the
index of a player, and is assumed to follow uniform distribution
n
c
The critical mass
n
∗
The high level equilibrium
n
c
i
The critical mass by optimization under regime i (i = N, R, G, M)
n
∗
i
The high level equilibrium by optimization under regime i
π
i
The proft function of a frm under regime i
π
∗
i
The maximal proft under regime i
U
b
The utility function of a buyer under regimes with RMT
U
s
The utility function of a seller under regimes with RMT
b
x
A buying quantity of buyer in x
any online game service.
5
s
x
A selling quantity of seller in x
D(p
v
) The demand function of RMT market
S(p
v
) The supply function of RMT market
p
v
The price of RMT market
p
M
v
The optimal choice of p
v
under regime M
w A unit variable cost of organizing gold farming
Table 2: List of key symbols
Two-stage game with sequential moves of a frm and players
We provide our basic model that illuminates strategic interactions between a frm, a ser-
vice provider of online game, and players as a two-stage game in which the two move
sequentially. Key notations used in the paper are provided in Tab. 2 for readers’ con-
venience.
Suppose the timing of the game is: i) frm chooses a price of its service, p ∈ [0, ∞)
and game design, h ∈ [0, 1]; ii) players observe p and h, and then choose their time
input to play, g
x
∈ [0, 1]; iii) by players’ optimal choices, the equilibrium level of partic-
ipation and the proft of the frm are determined. In each stage, choices of g
x
and h are
modeled by Hotelling’s location game (Hotelling, 1929). As this is a model based on se-
quential moves, subgame-perfect Nash equilibrium can be derived by applying backward
induction (Selten, 1965). Namely, to fnd frm’s optimal behavior on h and p, players’
optimization at second stage is to be considered frst.
Players’ optimization under regime N
Players are indexed by x ∈ [0, 1], their endowments on time for playing a game. Suppose
that x is measured relatively among players, and follows some distribution. Without
RMT, the utility of a player in x is given by
U(g
x
) = δ
....
i
−(g
x
−h)
2
. .. .
ii
+βn
e
g
x
. .. .
iii
− p
....
iv
. (1)
Under regime N, the utility of a player consists of four parts: i) The value of playing
game unrelated to network efect; ii) the cost of playing by choosing g
x
; iii) the value
depending on its network size; iv) the price of the game. Exposition for each term is
following:
(i) To attract people to start playing, a game needs an intrinsic value regardless of
network efect. It is noted that δ is not merely determined by content-related ele-
ments, but also by the degree of competition where a frm does its business. Hence
δ is also interpretable as a relative monopoly power that a game has considering
both the quality of the content and the degree of competition in its market.
(ii) Unlike other genres of games, time spending in an online game is evaluated by the
relative intensity among game participants.
5
Hence, social factors play an impor-
tant role in creating the fun of a game. When a player’s time spending is limited
5
In case of stand-alone games, a player can control her game-play by dividing time for playing
6
before reaching h, she will incur some cost by lagging behind other players who
choose longer time spending. The term here captures this reality. The functional
specifcation is assumed to be quadratic to guarantee the existence of equilibria
(Lambertini and Orsini, 2004).
(iii) This is network efect that is frequently observed in this kind of service. Network
efect here is modeled as multiplicative specifcation that allows diferent types of
players to receive difering values from the same network (Economides and Him-
melberg, 1995). β measures the intensity of network efect. It is true that frm’s
game design can afect this value, but β is formed more by emergent interactions
among players. Hence, in this paper, we suppose that β is a parameter out of
frm’s control. Also, it is assumed that β ∈ (0, 1], which means that network efect
cannot exceed n
e
g
x
.
(iv) We start with fat fee pricing for a fxed period. Although fat fee is not frequently
used as before, it still consists of a considerable share in total revenue of online
games industry.
6
Hence, it is not unrealistic to take it as a starting point.
Now, a player with endowment x would maximize U(g
x
) such that g
x
≤ x, and
Lagrange equation for player x is given by L
x
= δ−(g
x
−h)
2
+βn
e
g
x
−p+λ
x
(x−g
x
) where
λ
x
is Lagrange multiplier of the constraint. First-order condition of this constrained
maximization is simply given by
∂L
∂g
x
= −2(g
x
−h) +βn
e
−λ
x
= 0.
If λ
x
= 0, by Kuhn-Tucker Theorem, constraint is not binding, g
∗
x
< x. Optimal
choice for the case is g
∗
x
= h+βn
e
/2. If λ
x
> 0, constraint is binding, and g
∗
x
= x holds.
Let x
H
denote min{h +βn
e
/2, 1}, and optimal choice for the player with x is given by
g
∗
x
=

x for x ∈ [0, x
H
)
x
H
for x ∈ [x
H
, 1].
This shows that players at x ∈ [0, x
H
) will exhaust all of their endowments, but
those at x ∈ [x
H
, 1] will just choose the optimal time, x
H
. Player will participate in the
game as long as
U(g
x
) ≥ U, (2)
where U is the reservation utility, the best from other alternatives.
Now, to simplify our analysis, we make following three assumptions: i) U is normal-
ized as 0; ii) x follows uniform distribution on [0, 1]; iii) players have a perfect foresight,
in her own way. When she plugs of the machine/device, the game does not progress anymore. Con-
trastingly, an online game player cannot totally control its gaming experience because the consequence
of playing cannot depend exclusively on her act. In a typical MMOG, players should consider the
situation and the context of other players in the game. For example, if a player do not play for the
time being, she cannot but be left behind, which may constrain her game-play and the quality of
experience.
6
In case of Korean online games market in 2006, fat fee pricing had 7.2% among pricing methods,
but about 30% of total revenues (Korea Game Industry Agency, 2007). Especially, for MMORPG,
the most popular genre in online games, fat fee is still a natural solution for pricing.
7
formally, n
e
= n where n is actual number of player.
7
Let ˆ x denote the location that
satisfes (2) as an equality. As (2) is naturally satisfed for x ∈ [ˆ x, 1], the level of par-
ticipation is given by n = 1 − ˆ x. When ˆ x ∈ [0, x
H
],
δ −(ˆ x −h)
2
+β(1 − ˆ x)ˆ x −p ≡ 0. (3)
From (3), two values of x that are important to our analysis are given by
x
c
= min{1,
2h +β +

4(1 +β)(δ −p) +β(4h(1 −h) +β)
2(1 +β)
}
x
∗
= max{0,
2h +β −

4(1 +β)(δ −p) +β(4h(1 −h) +β)
2(1 +β)
}.
The interpretation for them is that for given parameters there can be two levels of
demand: a low level, n
c
= 1−x
c
, that is associated with a small number of players where
a very few enthusiastic players keep playing. n
c
is also called critical mass. In addition,
there can be a high demand measured by n
∗
= 1−x
∗
, implying that casual players also
participate in the game. It is to be noted that only n
∗
is a stable equilibrium, since at
n
c
, a small increase in the number of players would make participation more desirable,
thereby causing all of players on [n
c
, n
∗
] to get on board. Hence, the low demand n
c
has
a unique characteristic that determines the minimal number of players needed to ensure
that at least this number of players will beneft from participating in the service.
8
From the condition that ensures n
c
, n
∗
∈ R, it should hold that β(4h(1−h)+β)/4(1+
β) ≥ p −δ. Let V
N
(h, β) denote LHS of the inequality, and n
c
and n
∗
are also given by
n
c
(p, h, β, δ) = max{0, 1 −
2h +β
2(1 +β)
−

δ −p +V
N
(h, β)
1 +β
}
n
∗
(p, h, β, δ) = min{1, 1 −
2h +β
2(1 +β)
+

δ −p +V
N
(h, β)
1 +β
},
with δ ∈ [p −V
N
, ∞).
Firm’ optimization under regime N
To fnd subgame-perfect Nash equilibrium, let’s go back to the frst stage in which a
frm’s optimization problem lies. In our model, besides the price of service, game design,
h, can be used for frm’s optimization. For example, if the frm chooses h = 0, there
is no barrier in playing. This, however, also lowers optimal choice of g
x
, thereby the
value of a game. At the other extreme, If h = 1, the maximum ideal level would reduce
participation of players. But this raises players’ optimal choices of g
x
and the value
of a game. For a frm, h incorporates a trade-of in game design of its service. If a
7
The frst is only matter of measurement. The second is not restrictive in that considerable re-
searches in industrial organizations take this for granted. Actually, assuming of uniform distribution
keeps analysis simple without causing many unnecessary complications. The third is made because of
static nature of our problems. As equilibrium states are to be observed, it is acceptable to assume
that players will attempt to obtain the correct information anyway.
8
Mathematically, U
′
(n) > 0 at n
c
and U
′
(n) < 0 at n
∗
for non-boundary equilibrium case. As
n ≡ 1 −x, the sign of U
′
(n) is opposite to that of U
′
(x).
8
frm increases h, it puts more weight on loyalty from the incumbent at the expense of
openness of newcomers. In case that h decreases, it is the other way around.
In our model, a service has two kinds of optimization. As n
c
afects the probabil-
ity for a game to reach higher state of participation, when a frm starts its service, it
should minimize n
c
frst to make more favorable condition for achieving high level equi-
librium.
9
There are two simplifed paths of pricing strategy for critical mass: i) Firm
would introduce initial price to be zero for reaching critical mass faster, and increase it
after the number of player goes beyond some level. ii) Firm would apply optimal price
from the start by taking a risk of lower chance to overcome critical mass. Firm’s choice
here is a kind of dynamic question, and the frst path can be reasonably rationalized.
10
For the remainder of the paper, the condition for this is assumed, which makes mini-
mizing critical mass interesting (Oren and Smith, 1981; Lambertini and Orsini, 2004).
Critical mass minimization
A frm would get smaller n
c
as possible by choosing h and p.
Proposition 1 (frm’s critical mass minimization under regime N). For a frm to min-
imize critical mass, i) optimal choice of p is given by p
c
N
= 0; ii) if δ ∈ [0, ∞), optimal
choice of h is given by h
c
N
= 1, and the critical mass by optimization is given by n
c
N
= 0;
iii) if δ ∈ [−V, 0), optimal choice of h is given by h
c
N
= (1+

4δ/β + 1)/2 , and n
c
N
> 0
occurs.
Proof of Proposition 1. Proof is provided in Appendix A.
According to Proposition 1, for δ > 0, there is no problem of critical mass because
n
c
N
= 0 is obtained by setting h
c
N
= 1. For the case of δ ∈ [−V, 0), frm’s minimization
on critical mass results in positive n
c
N
. It is to be noted that frm cannot get positive
proft at high level equilibrium if δ < 0 because p ≤ δ holds at high level equilibrium
as we shall see. Firm can earn positive proft only for the case of δ > 0 where n
c
N
= 0
(Lambertini and Orsini, 2004). So to speak, for games of δ < 0, the efort to minimize
critical mass may be futile unless δ turns positive before reaching n
∗
.
In online games, it is often observed that a frm ofers players some period free of
charge.
11
This period may come from the nature of online games as experience goods,
which means that the value of a good is to be revealed only after it is tested. But
9
Let ρ ∈ (0, 1) be the common probability for each player to experience a game by chance. Suppos-
ing statistical independence among players, a frm need at least n
c
–level simultaneous infow of players
to reach higher level equilibrium. The probability to attain n
∗
is P =
R
1
n
c
ρ
x
dx = (ρ −ρ
n
c
)/ln ρ, and
dP/dn
c
= −ρ
n
c
< 0 means that smaller n
c
is better for the frm.
10
Let n
c
is the critical mass with p
∗
which is chosen by proft maximization at high level equi-
librium. Denoting d(n
c
) ∈ (0, 1] the probability to overcome n
c
, expected time before reaching n
c
is
(1−d)/d. Hence, assuming discrete infnite horizon and sufciently fast adjustment to n
∗
after reach-
ing n
c
, the expected proft by path i) is [r
(1/d)
/(1 −r)]p
∗
n
∗
where r ∈ (0, 1) is a discount factor, for
the frst revenue would be expectedly obtained at the period of 1/d+1. The maximum expected proft
by path ii) is d · (p
∗
n
∗
) + (1 −d)(p
∗
n
c
). It is noted that this value is the maximum in that realized
revenue in case of not overcoming n
c
cannot exceed p
∗
n
c
. When the frst is greater than the second,
the frm would ofer initial price of zero to minimize critical mass. It can be shown numerically that
this case holds for sufciently large r and small d.
11
In North America and EU, client programs of popular online games are often sold by CD/DVD
packages from the start. For this case, no free-playing period is ofered to players. In Korea, owing to
high penetration rate of broad-band Internet access, clients of online games are generally distributed
free by downloading. It is natural that publishers provide free period for this case. In Korea, this
period is called “Open-Beta” service. Ofcially, it is a period for massive testing before launching its
service, but this is a kind of marketing that ofers players free games.
9
this period can be also understood as a strategic move for a frm to get smaller n
c
.
Proposition 1 implies that δ determines the duration of free period for each service.
According to a survey done by Korea Game Industry Agency (2007), on the average, an
online game in Korea provides 4.5 months for free during four years from 2000 to 2004.
Lineage II by NC Soft, one of the most popular online games in Korean gaming history,
ended this free ofering within two months in 2003. In 2005, World of WarCraft by
Blizzard, followed the case in Korea by almost immediately launching its ofcial service.
This diference cannot be explained by the characteristic of online games as experienced
goods. With our model, when a game has δ > 0 where it gains a little of monopoly
power, it is natural for it to focus on proft maximization with short free experiencing.
Proft maximization at high level equilibrium
For maximizing proft at n
∗
, supposing production takes place at constant returns to
scale, frm’s objective function is given by π
N
= (p − c) · n
∗
(p, h) − F, where c is a
unit cost, and F is a fxed cost of the service. Optimal choice of a frm at high level
equilibrium is following:
Proposition 2 (frm’s proft maximization under regime N). Supposing c = F = 0,
optimal h and p, the strategy by subgame-perfect Nash equilibrium, are given by
h
∗
N
= max{0,
2
3
−
1
3

3δ/β + 1}
p
∗
N
=

6δ +β +

β(3δ +β)

/9.
Proof of Proposition 2. Proof is provided in Appendix B.
From Proposition 2, four comparative statics are obtained as
∂h
∗
N
∂β
≥ 0,
∂h
∗
N
∂δ
≤ 0,
∂p
∗
N
∂β
> 0,
∂p
∗
N
∂δ
> 0 (4)
The last two of (4) fts intuition. That is, higher value of a game supports higher
pricing by the frm. Intriguing results are the frst two, which are completely opposite
to the case of n
c
minimization.
We often observe the increase of δ when a game being successfully serviced is re-
inforced by newly introduced contents like “expansion package.” With the launch of
new expansion package, game design tends to be relaxed by ofering temporary extra-
efciency for in-game hunting/gathering by players. This kind of marketing campaign is
well explained by the second of (4). By Proposition 2, when δ is sufciently high such
that δ > β(≥ 0), frm would take full openness policy, h = 0, to maximize its proft.
Considering the frm sets h = 1 to make n
c
N
= 0, our model predicts that as the number
of players grows, h get smaller from 1 to 0 under regime N. This does not match the
reality of online game service. Players often complain about overly harsh game design
of popular games. To address this issue, in next section, we will introduce RMT which
can change frm’s choice on h.
4 Real-money Trading and Firm’s Choice of Regimes
RMT is one of key economic behaviors that can be observed in online games. RMT
emerged as one of hot issues in online gaming for its huge size. Although it does not
10
seem to be possible to estimate the world-wide volume of RMT precisely, it is widely
admitted that its volume cannot be ignored.
12
Dibbell (2007) speculated that world-
wide volume of RMT was around US Dollar 1.8 billion, which is not trivial at all con-
sidering that the world-wide volume of online games was estimated to be around US
Dollar 6.47 billion in 2007 (DFC Intelligence, 2007). The focus here is to investigate
its efects on the proftability of a service, which determines frm’s policy on RMT. We
start discussion by modeling RMT among players.
13
Setup of RMT
Players can choose three positions in RMT market: buyer, seller, and player without
RMT. At frst, suppose that the price of RMT, p
v
, is given to players. So to speak, in
RMT market, players behave as price-takers. RMT position can be determined econom-
ically by considering two choices. A player would i) optimize her buying/selling quan-
tity according to each utility, ii) choose the highest position comparing three indirect
utilities, maximal utility by buyer, by seller, and without RMT.
U
b
(g
x
, b
x
) = δ −(g
x
+b
x
−h)
2
. .. .
i
+βng
x
−p −p
v
b
x
....
ii
s.t. g
x
≤ x (5)
U
s
(g
x
, s
x
) = δ −(g
x
+s
x
−h)
2
. .. .
i
+βng
x
−p +p
v
s
x
....
ii
s.t. g
x
+s
x
≤ x. (6)
Supposing a unit technological converting rate between item and playing time is 1,
in (5) and (6), players choose b
x
or s
x
considering i) its impact on cost of playing ii) ad-
ditional monetary expense/compensation.
14
The incentive in purchasing items or, more
precisely, playing time embedded in items (b
x
), is to lessen cost in playing in expense of
paying real-money (p
v
b
x
). In the model introduced in previous section, buyers originate
from players with endowments constrained for reducing cost in playing. For the case,
b
x
would be added to the cost term, g
x
−h, in (1). Conversely, the incentive in selling,
positive s
x
, is to earn real-money (p
v
s
x
) by sacrifcing some utility from gaming and/or
12
In 2006, Korea Game Industry Agency committed a research for estimating the size of RMT in
Korea. According to Jang (2006), in Korea, the total size of RMT in 2005 including transactions
by mediation and those by direct exchange among players was US Dollar 923 million by the average
exchange rate of 2005.
13
For the clarity of following discussion, I would like to discern two kinds of RMT. The one is based
on the pure scarcity of items that players have. This can be called ‘market for virtual valuables.’ In
online games, some of items and characters that depend heavily on luck are extremely rare. Naturally,
these valuable items are priced high, and tend to be directly traded with real-money. A part of RMT
is stem from this kind, but this is not our interest. The other kind of RMT is from diference in leisure
time among players as we modeled previously. This can be called ‘market for virtual labor.’ By this,
players generally trade in-game currency with real-money. Actually, it is reported that most of RMT
activities are composed of this kind (Robischon, 2007), which is more important in our discussion.
Even though I will call in-game objects for RMT “items”, in most cases, this is embedded playing
time spent by sellers/players.
14
It is debatable that only cost of playing is afected. What if RMT afect network efect term?
At frst, our modifed specifcation of utilities with RMT is based on two ofcial surveys on players
of online games, which are done in US (Robischon, 2007) and in Korea (Jang, 2006). Two clearly
show that reducing time input, often called ‘grinding’ in online games community, is the top motive
for RMT. Moreover, alternative specifcations may not change our implications, but cause unnecessary
complications in later analysis.
11
by incurring the cost from supplying additional gaming hours.
15
For x ∈ [x
H
, 1] who
have no reason to choose more than x
H
in regime N, if monetary gains from selling
item exceed their costs, they would divert their endowments to RMT purpose. It is to
be noted that selling quantity should come from players’ endowments x, which means
g
x
+s
x
≤ x in (6).
Now, three conditions that make a player in x ∈ [0, 1] to be buyer are given by
U
∗
b
(x) ≥ U
∗
(x) (BIC I)
U
∗
b
(x) ≥ U
∗
s
(x) (BIC II)
U
∗
b
(x) ≥ 0, (BIR)
where indirect utility of buyer is denoted by U
∗
b
(x) ≡ U
b
(b
∗
x
, g
∗
x
), that of seller by U
∗
s
(x) ≡
U
s
(s
∗
x
, g
∗
x
), and that without RMT by U
∗
(x) ≡ U(g
∗
x
) denoting optimal choices by b
∗
x
,
s
∗
x
and g
∗
x
. Those for seller are given by
U
∗
s
(x) ≥ U
∗
(x) (SIC I)
U
∗
s
(x) ≥ U
∗
b
(x) (SIC II)
U
∗
s
(x) ≥ 0. (SIR)
Buyers’ optimization
Lagrange equation of buyer in x is denoted by L
b
x
= U
b
+ λ
x
(x − g
x
), and frst-order
conditions for g
x
and b
x
are given by
∂L
b
x
∂g
x
= −2(g
x
+b
x
−h) +βn −λ
x
= 0 (7)
∂L
b
x
∂b
x
= −2(g
x
+b
x
−h) −p
v
= 0 (8)
When constraint is binding, by Kuhn-Tucker Theorem, g
∗
x
= x with λ
x
> 0. (7) and
(8) cannot hold at once unless (λ
x
−βn) = p
v
. Hence, for buyer, only one that ensures
higher utility is to hold. By checking each condition, it can be shown that holding (8)
is always better for player x.
16
When constraint is not binding, x > g
∗
x
, λ
x
= 0 holds.
But this case can be excluded because the utility by non-binding case is always smaller
than that by binding case. Intuitively, as ∂U
b
/∂g
x
> 0 for proper range of g
x
, a player
has no reason to save her endowment. Considering all of cases, optimal choice of b
x
is
given by b
∗
x
= h − p
v
/2 − x. As b
∗
x
is to be positive, buyer x should be in [0, b] where
b ≡ h −p
v
/2.
Next, let’s check three conditions for a player to be buyer. (BIC I) is redundant if
buyer choose positive b
x
when she could choose b
x
= 0 where the utility is indiferent
to that without RMT. Namely, by revealed preference, positive b
x
satisfes (BIC I). To
check (BIC II), it is to be shown that player could not get more utility by selling than
by buying for x ∈ [0, b]. For this range, seller’s optimal choice is inputting all of her
15
When g
x
= x holds in regime N, by choosing positive s
x
, g
x
decreases in regime R. When g
x
< x
holds, positive s
x
incurs additional costs in playing as long as total spending time (g
x
+s
x
) of regime
R is larger than that (g
x
) of regime N.
16
Extracting indirect utility of holding (7) from that of doing (8) is
(nβ+p
v
−λ)
2
4
≥ 0.
12
endowment into selling, s
∗
x
= x and g
∗
x
= 0. By some calculation, U
∗
b
(x) ≥ U
∗
s
(x) can be
shown for x ∈ [0, b]. When
ˆ
b is minimum x that satisfes (BIR), let b denote max{0,
ˆ
b}.
The range for buyers is [b, b]. For buyer side to exist, two constraints satisfed are given
by
b ≤ b (RC I)
b ≥ 0. (RC II)
In sum, for x ∈ [b, b], optimal choice of purchasing is given by b
∗
x
when (RC I) and
(RC II) hold.
Sellers’ optimization
When Lagrange equation of seller at x is denoted by L
s
x
= U
s
+ λ
x
(x − g
x
− s
x
), frst-
order conditions for sellers are given by
∂L
s
x
∂g
x
= −2(g
x
+s
x
−h) +βn −λ
x
= 0 (9)
∂L
s
x
∂s
x
= −2(g
x
+s
x
−h) +p
v
−λ
x
= 0 (10)
When constraint is binding, by Kuhn-Tucker Theorem again, x = g
x
+s
x
with λ
x
> 0.
Although (9) and (10) cannot hold at once, the binding case comes to same conclusion
as long as p
v
≥ βn that is a necessary condition for sellers to exist. Intuitively, this
condition shows that players get inclined to sell her items when marginal compensation
by real-money is larger than marginal cost of extra toiling incurred by selling. When
min{h + p
v
/2, 1} is denoted by ˆ s, seller x ∈ [0, ˆ s] would sell out all of her endowment,
x, and optimal choice is s
∗
x
= x and g
∗
x
= 0. Extracting the range of x for buyer, seller’s
range where s
∗
x
= x and g
∗
x
= 0 is in [b, ˆ s]. As for the non-binding case where x ∈ [ˆ s, 1],
optimal choice of seller is s
∗
x
= min{h +p
v
/2, 1} = ˆ s and g
∗
x
= 0 for p
v
≥ βn.
Like (BIC I), (SIC I) can be excluded when sellers choose positive s
x
by revealed
preference of seller. For x ∈ [b, 1], U
∗
s
≥ U
∗
b
can be easily shown, thereby (SIC II) is
also satisfed. (SIR) holds for x ∈ [b, 1] as long p ≤ δ.
17
For seller side to exist, one
constraint satisfed is given by
p
v
≥ βn. (RC III)
The range of x that buyers and sellers occupy is given by Fig. 1. To save notations,
let B denote the set of x ∈ [b, b], S
1
that of x ∈ [b, ˆ s], and S
2
that of x ∈ [ˆ s, 1].
Equilibrium in RMT market
Demand and supply of in-game items are given by
17
This condition crowds out players without RMT in regime R. For the case of regime N, p ≤ δ
is easily confrmed. This seems arbitrary for regime R. But as is shown in numerical simulations and
a simplifed model, a frm would not choose its price where p > δ. Intuitively, pricing over δ may
harm benefts from network efect, which cannot be proftable for frm.
13
b
b
ˆ s 1
B

S
1

S
2

Figure 1: The range of x for players’ RMT
D(p
v
, h, p) =

B
(h −x −
p
v
2
) dx, S(p
v
, h, p) =

S
1
xdx +

S
2
ˆ s dx.
Equilibrium p
v
is given by the condition of equilibrium in RMT market, D(p
∗
v
) =
S(p
∗
v
), when three constraint (RC I), (RC II) and (RC III) hold. p
∗
v
is the function of
given h, p, and other parameters, that is, p
∗
v
= p
∗
v
(h, p, β, δ). In addition, we can put
following two more constraints for stability of equilibrium in RMT market.
D
′
(p
∗
v
) ≤ 0 (RC IV)
S
′
(p
∗
v
) ≥ 0 (RC V)
Firm’s optimization under regime R
Like the previous case of regime N, frm chooses h and p to minimize critical mass and
to maximize proft. Now, players’ choices of RMT and decisions for joining a game are
afected by p
∗
v
, which plays a role in frm’s optimization and regime choice.
Critical mass minimization
It is not possible to discuss critical mass minimization with RMT because no proper
incentive among players exists with frm’s optimal choice of h and p as we shall see. But
what if RMT market exists anyway? For the time being, let’s assume that there exists
some buying power that purchases in-game items from players at the outset. This may
come from irrational buyers in RMT, or outside buyers who do not directly participate
in a game. Firm would choose h and p to minimize critical mass which is given by
n
c
= max{0,
1
2
−
p
∗
v
(h, p, β, δ)
2β
−

δ −p +V
R
(h, p
∗
v
(h, p, β, δ), δ)
β
},
where V
R
(h, β, p
∗
v
) =

2(1 −2h)p
∗
v
+p
∗
v
2
(1 + 1/β) +β

/4 with δ ∈ [p −V
R
, ∞). Like the
previous case of regime N, for δ ≥ 0, there is no problem of critical mass. For δ < 0,
RMT market plays a role in decreasing n
c
.
Proposition 3 (frm’s critical mass minimization under regime R). Supposing RMT
market is established, i) optimal choice of p and h is given by p
c
R
= 0 and h
c
R
= 0; ii) for
δ ∈ [−V
R
(0, β, p
∗
v
), −(p
∗
v
2
+ 4p
∗
v
)/4), n
c
R
> 0, and for δ ∈ [−(p
∗
v
2
+ 4p
∗
v
)/4, ∞), n
c
R
= 0;
iii) minimized critical mass with RMT is at least as small as that without RMT, for-
mally, n
c
R
≤ n
c
N
.
14
Proof of Proposition 3. Proof is provided in Appendix C.
From Proposition 3, it is clear that RMT can help the frm to make critical mass
smaller. With RMT, even for some range of negative δ, n
c
R
= 0 is realized, which is
diferent from the result in Proposition 1. When positive critical mass exists, n
c
R
≤ n
c
N
holds. This means that a game with RMT has better chance to succeed in attaining
high level equilibrium.
18
Like regime N, this advantage by RMT is also limited one in
that this is relevant for the case of δ < 0.
Discussion here explains partly why some publishers of online games are eager to
emphasize their RMT feature at their early stages. Project Entropia, now renamed as
Entropia Universe, was targeting all of its marketing on players’ RMT from the begin-
ning (BBC News, 2004, 2005; Marketwire.com, 2007). In case of Korea, it is not uncom-
mon that publishers of online games start their services in alliances with RMT-related
companies that specialize in mediating and backing up players’ RMT outside the game.
RMT market at early stage can emerge only when buying power comes to exist as is
shown. Hence, it is not impossible to imagine that this may come from the frm itself
as long as this outside buying in RMT market pays. An intriguing example on this ac-
count is ZT Online serviced by a NASDAQ-listed company in China, Giant. From its
early years, the publisher has paid real-money to players just for their playing hours and
activities (Martinsen, 2007). Despite tough competition in Chinese online games market
when it launched in 2004, the game was recorded as one of the fastest growing online
games in there.
Maximization of high level equilibrium
High level equilibrium with players’ RMT is given by
n
∗
= min{1,
1
2
−
p
∗
v
(h, p, β, δ)
2β
+

δ −p +V
R
(h, p
∗
v
(h, p, β, δ), β))
β
}.
Firm’s objective function is π
R
= (p − c) · n
∗
(h, p, p
∗
v
(h, p)) − F. Now, frm should
check the efect of its decision of h and p on p
∗
v
which is a part of determining π
∗
R
. As
the decision of the frm cannot be derived analytically, numerical simulations are gen-
erated. The procedure of simulation consists of following: (i) With players’ RMT, we
generate profts for diferent (h, p) with small step for each term. (ii) Simulated results
are checked by fve constraints from (RC I) to (RC V). If any constraint is not satis-
fed, RMT market cannot exist. (iii) Even if RMT market can be established, when the
maximal proft of the frm with RMT is smaller than that without RMT, frm would
ban RMT to gain higher proft. Hence, among results generated by each (h, p), only
proft that is higher than that without RMT is to be selected by the frm adopting the
policy of tolerating RMT.
A computer program by Mathematica of version 7 is built for undertaking the frst
two. Supposing that c = F = 0, (a) of Fig. 2 shows a visualization of frm’s optimiza-
tion with RMT. To perform comparative statics, optimal choices of frm are observed
18
Rochet and Tirole (2003) points out that there may be certain customers on one side of the
market, referred as “marquee buyers” who are extremely valuable to customers on the other side of
the market. They argue that marquee customers who create strong network efect tend to reduce the
price to all on the same side of the market and increase it to customers on the other side. In our
discussion, the marquee side is sellers who can play a role in making critical mass smaller. Supposing
the frm subsidizes sellers implicitly by buying their items, the burden in playing for sellers is lighter
than that for buyers.
15
0
1
1
0
1
0
h
p
π
∗
N
(h
∗
N
, p
∗
N
)
π
R
(h, p)
(a) Visualization of frm’s proft maximization pro-
cess under regime R. For given β = 0.5 and δ = 1,
this is generated with each step of 0.01 for p and
h. Positive π
R
is obtained when RMT can be es-
tablished. Also, the choice of our interests is the
case that π
∗
R
> π
∗
N
where the top of the mountain
of π
R
is higher than the plane of maximal proft
without RMT.
0.1 0.48
0.75
1
0.1
β
p
∗
R
p
∗
v
h
∗
R
n
∗
R
(b) Numerical simulation of RMT by β.
For given β and δ, (h, p) plane is searched
by 0.05 step for each variable to get
the maximal proft under regime R. β is
moved with the step of 0.01 from 0.01 for
given δ = 1, and no RMT can be estab-
lished for β ≥ 0.49.
0.42 1.5
0.1
1
0.9
δ
p
∗
R
p
∗
v
h
∗
R
n
∗
R
(c) Numerical simulation of RMT by δ.
Simulation is done by the same condition
of (b) except for β and δ. δ is moved
with the step of 0.01 from 0.01 for given
β = 0.5, and no RMT can be established
for δ ≤ 0.41.
Figure 2: Numerical simulations of RMT.
repeatedly with varying parameters, β and δ individually, for small step. (b) and (c) of
Fig. 2 shows an example of comparative statics by simulation.
Key results of simulations are summarized as following: i) There exists β
R
such that
RMT cannot be established for β ∈ [β
R
, 1]; ii) for β ∈ (0, β
R
), as β get larger, frm’s
proft get smaller; iii) under regime R, higher h is chosen than under regime N, formally,
h
∗
R
> h
∗
N
.
i) and ii) show that as β increases, p
∗
v
should increase to give sellers sufcient in-
centives, which results in higher h. Meanwhile, as p
∗
v
increases, p
∗
R
get smaller. This
simply squeezes frm’s maximal proft. This result is paradoxical in that the increase
of β makes a game more valuable, but the frm cannot beneft from this. It is to be
noted that this happens only in the setup of regime R. Actually, higher p
∗
v
can provide
new incentives for another kind of sellers who have diferent objective from naive sell-
ers/players. iii) shows that the frm would create the condition for promoting players’
RMT by choosing harsher game design than that chosen without RMT.
16
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
β
R
R
N
Figure 3: Regime choice between N and R. For each shaded area where π
∗
i
> π
∗
j
(i ̸=
j, i, j ∈ {N, R} assuming n
∗
R
= 1), i is assigned to be most proftable regime for that
area.
Generally, for a frm, it is desirable to discriminate players by their willingness to
pay. At a glance, there seems little chance of accomplishing this under fat fee pricing.
Our results, however, imply that RMT can create two economic consequences of price
discrimination: i) Players’ monetary burden to play an online game is diferentiated by
their sides in RMT market. In our model, a player in x ∈ B costs p +p
∗
v
(h −p
∗
v
/2 −x)
that is larger than p. Contrastingly, a player in x ∈ S
1
∪S
2
costs p−p
∗
v
· min{x, h+p
∗
v
/2}
that is smaller than p. ii) There exist cases that a frm can get larger proft with RMT.
In this respect, RMT serves as a device for price discrimination without any apparent
discrimination by the service.
19
Maximization supposing n
∗
R
= 1
Our model of RMT cannot be observed in analytic way. But, if we put a restriction of
n
∗
R
= 1 that the efect of RMT is realized at its full scale, the model can be simplifed
enough to be treated in analytic manner. This assumption can be justifed in two way:
i) For the relevant range of parameters where π
∗
R
≥ π
∗
N
holds, it is true that n
∗
R
≈ 1.
ii) In qualitative sense, behaviors of optimal choice by simulations is also similar to those
by assuming n
∗
R
= 1. Proposition 4 shows the result supposing n
∗
R
= 1.
Proposition 4 (frm’s optimal choices under regime R when n
∗
R
= 1). Supposing that
n
∗
R
= 1, a frm’s optimal choice of h and p is given by h
∗
R
= max{(2+
√
2)/4, (β+
√
2)/2}
and p
∗
R
= 1/2 −h
∗
R
+δ, and equilibrium RMT price is (2h
∗
R
−
√
2).
Proof of Proposition 4. Proof is provided in Appendix D.
Proposition 4 well illuminates one reality in online games. When there is no RMT,
h is set high at frst, and get lower as the number of players approaches n
∗
N
. This con-
tradicts considerable cases where players, especially newcomers, often complain about
19
The fundamental economic logic underlying an economic platform is to do price discrimination
among its participating groups by designing elaborating price mechanisms (Armstrong, 2006). It is
intriguing that frm’s decision to tolerate RMT may be rather from this proft motive by making
players divided into buyers and sellers than from the inability to sort RMT out.
17
overly harsh game design of popular online games. In the case of regime N, for δ > 0,
h
∗
N
< 1/3 holds. But, under regime R, h
∗
R
> 3/4 holds for the same condition. With
RMT, frm would set high h to get additional beneft from side economic activities
among players. For all players’ discontents, high h is hard to be lowered because this
is proftable.
Fig. 3 illustrates frm’s choice of regime supposing n
∗
R
= 1, which is provided to
perform comparative statics for regime choice by a service. Regime R is better than
N only for the range of high δ and β < β
R
. This shows that the support of RMT
is meaningful for such a game that already enjoys a considerable monopoly power in
its market, which is the case of high δ. This implies that RMT may make a positive
feedback that bolsters direct network efect in online games business. Namely, compared
to regime N, regime R can consolidate ‘winner-takes-it-all’ tendency in the business.
5 Two Variants of RMT
Once RMT comes to exist, economic incentives behind can bring forth other forms
of RMT. Among what can be watched, gold farming and micropayment are most fre-
quently observed and interesting.
Gold farming
Gold farming is the act of repetitive gathering in online games exclusively served for
earning real-money. Most of gold farmers are employed by entrepreneurs who run sweat-
shops or something for making in-game items. The purpose of gaming for gold farmers
is not enjoying but earning their wages in online games. Hence, the level of wage is one
of key determinants of the efectiveness gold faming has in a game.
20
It is to be noted
that this wage level also refects the overall condition of gold farming in a game. When
gold farming in a game get more strictly regulated, operators in there need to purchase
more accounts to secure the same amount of in-game items as before, which raises vari-
able costs. Hence, in our model, a unit variable cost of gold farming, w, is to be used
as a proxy for this wage level.
Critical mass minimization can be set aside, for it is not likely that gold farming
starts at the early stage of a game. Let’s check proft maximization directly. Previously,
p
∗
v
≥ βn is necessary for RMT to be established, for this provides sellers incentives. But,
to a worker/player in gold farming business, this constraint is not applied anymore. She
is not to optimize her utility, but just to do tasks assigned by her employer. Imagine
an entrepreneur that operates a sweatshop for gold farming. Proft function of her is
given by p
∗
v
v − wv − F where v is selling quantity, w is the unit cost of producing in-
game items, and F is fxed cost. Supposing F = 0 as before, as long as p
∗
v
≥ w, she
has an incentive to go on her business. So to speak, if gold farming comes to exist with
βn > w, the lower bound of p
∗
v
under regime N, βn, is to be replaced by w under regime
G. On the other hand, when βn ≤ w(≤ p
∗
v
), sellers/players can undercut gold farmers,
20
This also tends to determine where gold farming is organized. Most of gold farming is done in
emerging economies like China, Vietnam and Indonesia where low-wage workers exist with convenient
Internet access. Especially, it is estimated that China has around 80–85% of employment and output
in this business (Heeks, 2008). There are few reliable data on gold farmers yet, according to data
gathered by Heeks (2008), chronological estimates of employment are between 100,000 and 500,000,
and an average wage of individual gold farmer in China is around Chinese Yuan 1,000/US Dollar 145
per month, which is fairly low compared to salaries of low-paid workers in developed countries.
18
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
R
N
N
G
(a) For w = 0.1
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
R
N
G
G
(b) For w = 0.2
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
R
N
G
(c) For w = 0.3
Figure 4: Regime choice among N, R and G. For each shaded area where π
∗
i
> π
∗
j
(i ̸= j, i, j ∈ {N, R, G} assuming n
∗
k
= 1 for k = R, G), i is assigned to be the most
proftable regime for that area.
and gold farming vanishes for the case. Hence, w < βn is the proper condition for gold
farming to persist.
Another stylized fact is that gold farming makes the slope of RMT supply curve
virtually fat at nearly w (Lee, 2005; Wang, 2008). Most of popular games where RMT
emerges tend to experience consecutive drops of RMT price, which is thought to be
caused mostly by massive infux of gold farmers. After gold farming is settled in a game,
the upward moving trend of RMT price is hard to be watched. So to speak, with gold
farming, RMT price of a game is not determined by demand and supply originated
from naive players, but by gold farmers. As long as p
∗
v
< βn holds in regime G, all
of sellers/players would disappear. Contrastingly, the fall of p
∗
v
is an opportunity for
buyers. In short, gold farming kills seller side of, and makes buyer side grow. Diferent
from the former case of regime R, gold farming can make a number of players without
RMT.
With gold farming, frm’s proft function is π
G
= p · n
∗
(h, p, w) + pqD(w) where
n
∗
(h, p, w) is high level equilibrium under regime G, and q ∈ [0, 1] is a coefcient that
represents the ratio of accounts run by gold farmers to RMT demand. Now, the equi-
librium price of RMT market is not p
∗
v
but w. The assumption of n
∗
G
= 1 is also ac-
ceptable for the same reason for regime R. Proposition 5 shows the optimization of a
frm under regime G.
Proposition 5 (frm’s optimal choices under regime G when n
∗
G
= 1). Supposing n
∗
G
=
1, with gold farming existing where w < β, frm’s optimal choice of h and p is given by
i) h
∗
G
= 1 and p
∗
G
= δ − w(4 − w)/4 for q > 0; ii) h
∗
G
= w/2 and p
∗
G
= δ − w
2
/4 for
q = 0.
Proof of Proposition 5. Proof is provided in Appendix E.
(a)-(c) of Fig. 4 shows regime choices among regime N, R and G by w. The re-
sults shows that i) regime G erodes regime N even for low δ where regime R is less
proftable than N when w is sufciently low, ii) the erosion is more efective as w get
lower, iii) regime G is also applicable for the case of β > β
R
.
It is generally admitted that the shift of place for gold farming from the domestic
to low-wage countries makes RMT more prevalent among online games players, which
is well illustrated by Fig. 4. Meanwhile, as the history of a game goes, β tends to get
19
0.139
0.3
1.6
1
q/w
p
∗
G
π
∗
G
n
∗
G
h
∗
G
Figure 5: Simulation result of gold farming by q/w. For given β = 0.7 and δ = 1.5,
(h, p) plane is searched by 0.01 step for each variable to get the maximal proft under
regime G. q/w is moved with the step of 0.01 from 0.01.
larger because players have accumulated diverse communication with one another. In
contrast to regime R, regime G can be utilized for the case where a game has long
history of service. Although it is not possible to discern naive RMT from gold farming,
there is partial evidence that gold farming thrives commonly in relatively old games. At
IGE (http://www.ige.com), the largest RMT mediation service in North America and
EU where gold farmers can enter, eight games being featured have average 4.3 years for
their periods of service. Especially, for four games considered to have most active gold
farming, the number goes up to six years.
21
Another point raised by Proposition 5 is the major contributing part that gold farm-
ing has to a service. Results by simulation exemplifed in Fig. 5 shows that there are
two kinds of equilibrium states. One is that frm choose low h, and most of players are
without RMT. The other is that frm choose high h, and most of players are buyer. q/w
decides which equilibrium state appears. In Proposition 5, this situation is investigated
by discerning q = 0 and q > 0 case respectively. When q = 0, frm would ignore the
direct contribution of gold farmers to its revenue. When q > 0, frm would consider it in
choosing its strategy. If q = 0 case be true, paradoxically, RMT would be marginalized
with the help of gold farmers. Firm could set a loose game design, low h, the experience
of RMT in regime G would be much rarer than regime R. But, if it is true that gold
farming makes RMT more prevalent, the case of q > 0 may be closer to the reality.
Micropayment
In online games, micropayment or micro-transaction is typically accepted as a pricing
mechanism that ofers players alternative way of purchasing in-game currency or items
instead of paying a fat fee. This is often called “free-to-play”, for no entry fee exists
21
At ItemBay (http://www.itembay.com) and ItemMania (http://www.itemmania.com), two major
middlemen of RMT in Korea, and that permit gold farmers to enter, the situation is similar. In these
two markets, detail specifcation of RMT transactions can be observed on real-time basis. It is easily
observed that the share in RMT considered to be from gold farmers has high correlation with the
service periods. As there is no rigorous statistical observation yet, this has been accepted as a fact
at least in Korea. To observe this point, selling ofers were recorded for fve oldest games with active
RMT by two hour interval on December 12 2008 in these two Korean places for RMT. The share of
gold farming by this casual sampling is 89.7%.
20
in some cases. The rationale of micropayment results from in-game diferences among
players by their paying. Items purchased by players are often more powerful than those
that can be obtained by players without paying, or ofer an advantage or feature oth-
erwise unavailable.
22
On minimizing critical mass, the role of RMT in lowering critical mass is not likely
to be played under regime M because selling by players may not be approved. But,
when p
v
= 0 where players can enjoy in-game items without charging, critical mass is
0 without regard to the choice of h. So to speak, games based on micropayment can
eliminate this problem easily by setting p
v
= 0.
For proft maximization under regime M, two points are to be frst considered for
a service: i) A frm would never want to tolerate gold farming because gold farming
generally determines the RMT price. This makes a service lose its control over a source
of its proft. ii) A frm can choose whether sellers/players exist or not, by choosing p
v
.
When p
v
≥ nβ, there is a band for sellers in x ∈ [h −p
v
/2, 1]. Otherwise, the frm kills
sellers of. Firm’s objective function under micropayment is given by
π
M
=

p · n
∗
(h, p, p
v
) +p
v
· (D(p
v
) −S(p
v
)) −c · n
∗
−F, for p
v
≥ n
∗
β
p · n
∗
(h, p, p
v
) +p
v
· D(p
v
) −c · n
∗
−F, for p
v
< n
∗
β,
where n
∗
(h, p, p
v
) is the high level of equilibrium under regime M. Supposing c = F = 0
as before, frm will choose h, p and p
v
to maximize its proft. By numerical simulations,
it can be shown that n
∗
M
≈ 1 holds by optimal choices of the frm for all relevant param-
eters with p ≤ δ. Intuitively, it is desirable to make full participation because players
are dual sources of revenue in regime M. Like former cases, the assumption of n
∗
M
= 1
is proper for regime M.
Proposition 6 (frm’s optimal choices under regime M when n
∗
M
= 1). Supposing n
∗
M
=
1, with micropayment, frm’s optimal choice of h and p is given by h
∗
M
= 1 and p
∗
M
=
max{0, δ −p
M
v
(4 −p
M
v
)/4}, and optimal p
v
is given by
p
M
v
=











p
L
v
, for β ∈ (0, β
1
] and δ ∈ [0, δ
β
]
β −ϵ, for β ∈ (0, β
1
] and δ ∈ (δ
β
, ∞)
β −ϵ, for β ∈ (β
1
, β
2
) and δ ∈ [0, ∞)
p
H
v
, for β ∈ [β
2
, 1] and δ ∈ [0, ∞),
where p
L
v
= (4 −
√
10)/3, p
H
v
= 2/3, β
1
= 0.15822, β
2
= p
H
v
, δ
β
= β(4 − β)/4, and ϵ is
an arbitrary small positive amount.
Proof of Proposition 6. Proof is provided in Appendix F.
Fig. 6 shows regime choice by a frm with adding regime M: i) When δ is sufciently
low, regime M is the most proftable among the four. Especially, for this case, regime
M is more likely to take free-to-play (M
F
region in Fig. 6). ii) For low β where gold
farming cannot be established, regime M fully erodes regime N. iii) For sufciently high
22
For recent years, this model has been gain a notable success in East-Asia countries. A survey
shows that 49.9% of total revenue made by Korean online games industry in 2006 was from micro-
payment (Korea Game Industry Agency, 2007). In case of Japan where considerable online games are
from Korea, the share of online games based on micropayment increased to 81.9% in 2007 from only
22.2% in 2004 (Japan Online Game Association, 2008).
21
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
M
NF
M
F
N
G
(a) For w = 0.1
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
M
NF
M
F
N
G
G
(b) For w = 0.2
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.5
1.0
1.5
2.0
2.5
β
δ
M
NF
M
F
N
G
(c) For w = 0.3
Figure 6: Regime choice among N, R, G and M. For each shaded area where π
∗
i
> π
∗
j
(i ̸= j, i, j ∈ {N, R, G, M} assuming n
∗
k
= 1 for k = R, G, M), i is assigned to be the
most proftable regime for that area. M
NF
denotes the case of p
∗
M
> 0, and N
F
does
that of p
∗
M
= 0.
w, regime M erodes gold farming for some area of β > w where gold farming reigns if
regime M is not available. iv) For sufciently low β where regime M is chosen, as δ
grows, entry fee is charged (M
NF
region in Fig. 6).
Proposition 6 illuminates a question of genre matching, that is, where micropayment
does work better. As β gets higher, economic performance of regime M get worse com-
pared with those of regime G and N. Hence, regime M would be less observed in gen-
res of high β than low one. Considering MMORPG has generally higher β than other
genres, Proposition 6 shows why micropayment is less watched in there. Contrastingly,
the genre based on arcade-style action games, called “casual games” in Korea, generally
have low β, which fts micropayment. In Korean market, as of 2008, 87.2% of games
based on some kind of micropayment can be categorized into these casual games (Korea
Game Industry Agency, 2007).
Proposition 6 tells that regime M would charge some entry fee for the region of high
δ. But, considering there is no entry fee in most of games based on micropayment, how
can a service provider charge players? In case of Sudden Attack, one of the most popu-
lar online games in Korea, most of core in-game items purchasable have time limitation
in using. Among seven items categorized as “package items”, fve have thirty days lim-
itation, which are priced at from Korean Won 17,500/US Dollar 17.5 to 8,300/8.3 by
the average exchange rate of 2008. This serves as the very entry fee charged without
regard to player’s usage in the model.
23
Regime M has an implication on the idea of winner-takes-it-all destiny of online
games industry. It is true that a few games like World of WarCraft and Lineage have
huge subscriptions that other games cannot take over readily. But, it is not true that
online game service shall converge to very few, either. The experience of Korean online
game industry may be helpful to exemplify this point. Lineage series were the over-
whelming top by revenue and subscription from 1998 to 2003, but Nexon’s Kart Rider,
23
Top ffty games popular in Korea during 2008 are investigated for checking this point. According
to the data collected by Gametrics (http://www.gametrics.com), a Korean research company collect-
ing usage data of online games played in the PC bang, dedicated places for online gaming, thirty
seven among them were based on micropayment models. Interesting fact is that the average number
of time-limited items for top ten of them is 5.8, that for next ten is 2.6, and that for the rest is only
0.8. If the popularity of a game can be translated into the amount of δ, this matches the theoretical
discussion here.
22
an arcade-style racing game based on micropayment, quickly took over this winner in
2004. Since micropayment has been introduced and widely applied in Korean industry,
the genre and the share of revenue among online games have more variety compared to
those in the former era of MMORPG led by Lineage series. In short, the evolution of
business model into micropayment partly invalidates the logic of winner-takes-it-all in
favor of more complex one.
6 Concluding Remarks
Results of optimization hitherto are summarized in Tab. 3. Key fnding and implication
are following:
(i) In minimizing critical mass, harsh game design, high h, is chosen for non-RMT
case. Contrastingly, for the case of naive RMT and gold farming, low h is chosen
to entice sellers into starting a game. When a positive critical mass exists, RMT
at the early stage of a service makes it smaller than obtained without RMT. This
can help a frm to reach high level equilibrium faster.
(ii) In maximizing proft, it can be shown that RMT can enhance the proftability of
an online game service. For the case of naive RMT, however, this efect cannot be
realized for high β. For all regimes with RMT, frm’ profts are higher than that
without RMT for sufciently high δ. This implies that RMT can help games that
have already a monopoly power in competition.
(iii) The proftability of gold farming depends on the wage level in its business. When
it is sufciently low, gold farming replaces non-RMT even for lower δ where naive
RMT cannot erode. For high β where naive RMT cannot be established, gold
farming is applicable. In those cases, gold farming enhances the proftability of
a service.
(iv) When a game do not have enough monopoly power, δ is low, frm’s pricing is
likely to take micropayment. For low δ, micropayment is the most proftable among
four regimes, which shows the reason why it becomes popular as competition gets
tougher. As the wage level for gold farming gets unfavorable, micropayment erodes
gold farming. As the monopoly power of a service gets stronger in the area where
micropayment reigns, in addition to usage fee, a service would try to charge play-
ers for entry.
Finally, two future agendas for research are shortly addressed. First, this paper is
based on static maximization. But, as another name for online game, “persistent world”,
reveals itself, there are interesting issues analyzed better by dynamic framework. For
instance, one of sellers’ motives for RMT may be from their leaving a game. They do
not want to give up the valuable accumulated during their playing. Hence, selling items
tends to occur when players leave the game. The overall structure of players’ staying as
well as leisure endowment can afect RMT behaviors, and strategies of a service. Gold
farming, one of debatable issues in online gaming, can be also more fully addressed by
integrating its dynamic efects. Especially, welfare issues around gold farming can be
interestingly treated by this consideration. Second, discussion of RMT in the paper is
based on the positive side of network efect, which is generally considered as negative in
some studies of virtual worlds. More unifed and balanced works may illuminate richer
economic meaning that online games have. For example, when players without RMT
23
V
a
r
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a
b
l
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s
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g
i
m
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M
T
t
o
l
o
w
e
r
c
r
i
t
i
c
a
l
m
a
s
s
24
regard RMT as negative, the transaction between buyers and sellers could be viewed as
pollution to some of players. In this case, interesting questions about governance and
business of virtual worlds are to be explored.
Appendix A Proof of Proposition 1
Proof. Proof is given by each part: i) As ∂n
c
N
/∂p > 0 always hold, p is set to be 0
for minimizing n
c
. ii) The frm would minimize n
c
with respect to h with p = 0. 2’nd-
order condition holds because ∂
2
n
c
/∂h
2
> 0. If δ ≥ 0, h
c
N
is bounded to be 1, and
some calculation shows that n
c
= 0. iii) When δ ∈ [−V, 0), by the frst-order condition,
h
c
N
∈ (0, 1] is obtained as in the proposition, and n
c
N
> 0.
Appendix B Proof of Proposition 2
Proof. First-order conditions are given by
∂π
N
∂h
= 2 −
2β(1 −2h)β
2
√
1 +β

δ −p +V
N
(h, β)
= 0
∂π
N
∂p
= 1 −
p
2
√
1 +β

δ −p +V
N
(h, β)
−
2h +β −
√
1 +β

δ −p +V
N
(h, β)
2(1 +β)
= 0.
Sets of (h, p) to satisfy frst-order conditions except p
∗
N
= 0 cases are given by
s
1
=

min{1,
1
3

2 +

3δ/β + 1

},
1
9

β + 6δ −

β(β + 3δ)


s
2
=

max{0,
1
3

2 −

3δ/β + 1

},
1
9

β + 6δ +

β(β + 3δ)


.
For h ∈ [0, 1], 2’nd-order conditions are given by
∂
2
π
N
∂h
2
< 0,
∂
2
π
N
∂p
2
< 0,
∂
2
π
N
∂h
2
∂
2
π
N
∂p
2
−(
∂
2
π
N
∂h∂p
)
2
> 0.
As only s
2
satisfes second-order conditions, optimal choice for h and p is uniquely
given by s
2
.
Appendix C Proof of Proposition 3
Proof. Proof is given by each part: i) As it always holds that ∂n
c
R
/∂p > 0 and ∂n
c
R
/∂h >
0, frm’s optimal choice for h and p to minimize n
c
is given by h
c
R
= p
c
R
= 0. ii) Some
calculation shows that when δ ≥ −(p
∗
v
2
+ 4p
∗
v
)/4, n
c
R
= 0, and −V
R
(0, β, p
∗
v
) ≤ −(p
∗
v
2
+
4p
∗
v
)/4 holds for all relevant cases. It can be shown that n
c
R
> 0 for δ ∈ [V
R
(0, β, p
∗
v
), −(p
∗
v
2
+
4p
∗
v
)/4). iii) Critical masses between regimes where minimized values of n
c
are positive
are more easily compared by investigating two conditions that produce each critical mass
with frm’s optimal choice.
25
(1 −x)xβ +
p
∗
v
2
4
+p
∗
v
x +δ = 0 (C.1)
(1 −x)xβ −(x −(

4δ/β + 1 + 1)/2)
2
+δ = 0 (C.2)
As both of conditions have the same functional form of quadratic inverted U-shape,
if LHS of (C.1) of regime R is larger than that of (C.2) of regime N, n
c
R
≤ n
c
N
should
hold, which is trivially shown.
Appendix D Proof of Proposition 4
Proof. RMT demand is given by
D(p
v
) =

B
(h −p
v
/2 −x) dx =
(2h −p
v
)
2
8
, where b = 0.
RMT supply can be diferent if ˆ s ≡ h+p
v
/2 ≥ 1 or not. First, supposing that ˆ s ≥ 1,
and RMT supply is given by
S(p
v
) =

S
1
xdx =
1
2
−
(p
v
−2h)
2
8
.
From the equilibrium condition of RMT market, equilibrium RMT price is simply
given by p
∗
v
= (2h −
√
2).
With n
∗
R
= 1, frm’s proft with RMT is π
R
= p·n
∗
R
= p. To satisfy n
∗
R
= 1, U
∗
b
(0) ≥ 0
should holds, which is p ≤ 1/2 − h
2
+ δ. The frm would choose p
∗
R
= 1/2 − h
∗
R
2
+ δ
that is the highest, and h is to be chosen as small as possible. On the choice of h, fve
constraints for RMT are to be checked. i) D
′
≤ 0 and S
′
≥ 0 that is (RC IV) and (RC
V) respectively; ii) h−p
∗
v
/2 ≥ 0 that is (RC I) and (RC II); iii) p
∗
v
≥ β that is (RC III).
(RC I), (RC II), (RC IV) and (RC V) are trivially satisfed. h+p
∗
v
/2 ≥ 1 and (RC III)
are relevant constraints for h. h
∗
∈ (0, 1) that maximizes proft of the frm is given by
h
∗
R
= max{(2 +
√
2)/4, (β +
√
2)/2} where β ∈ (0, β
R
) with β
R
= 2 −
√
2.
The other case of h+p
∗
v
/2 < 1 can be safely excluded because it can be shown that
there is no optimal h ∈ (0, 1) that satisfes the condition by similar steps above.
Appendix E Proof of Proposition 5
Proof of Proposition 5. When n
∗
G
= 1, RMT demand is given by (2h −w)
2
/8, and frm’s
proft is π
G
= 1 · p
G
+q

(2h −w)
2
/8

p
G
.
∂π
G
∂h
=
1
2
pq(2h −w). (E.1)
∂π
G
∂p
= 1 +q(2h −w)
2
/8 (E.2)
As (E.2) is positive, frm would set p as high as possible. U
∗
b
(0) ≥ 0 should hold to
satisfy n
∗
G
= 1, which is p ≤ (w
2
− 4wh + 4δ)/4. With the condition of p ≤ δ, frm’s
optimal choice of p
G
is given by p
∗
G
= (w
2
−4w + 4δ)/4 for w < β ≤ 1.
26
Let’s check q > 0 case frst. For (E.1), no frst-order condition exists for maximiza-
tion. Hence, h is chosen to be 0 or 1 by the sign of (E.1). When h < w/2, the op-
timal choice of h is h
∗
G
= 0, which means frm kills players’ buying and gold farming
of. This case can be excluded because this is exactly regime N. Otherwise, the opti-
mal choice of h is h
∗
G
= 1, which is proper case for our purpose. It can be easily shown
that relevant RMT constraints are all satisfed at this optimum. Optimal p is given by
p
∗
G
= (w
2
−4w + 4δ)/4.
For q = 0 case, (E.1) is not relevant. As p ≤ (w
2
−4wh + 4δ)/4, frm would choose
small h as possible. (RC I), (RC II), and (RC IV) are all amount to h ≥ w/2. Hence,
the proft with h = w/2 is the maximal proft for this case. It can be easily shown that
relevant RMT constraints are all satisfed at this optimum.
Appendix F Proof of Proposition 6
Proof. Now, a frm can choose whether seller side exists or not by choosing p
v
. If p
v
> β,
sellers exist. Otherwise, do not. By this choice, frm has diferent objective function. By
comparing proft in each choice, frm’s optimal choices on h, p, and p
v
are to be deter-
mined. At frst, let’s check maximization with seller and that without seller individually.
First, suppose that frm chooses to make sellers exist. First derivatives with respect to
h, p
v
, and p are given by
∂π
M
∂h
= p
v
(2h −p
v
) (F.1)
∂π
M
∂p
= 1 (F.2)
∂π
M
∂p
v
= h
2
−2hp
v
+
3p
v
2
4
−
1
2
. (F.3)
When (F.1) is positive, 0 < p
v
≤ 2h, optimal h under micropayment is chosen by
h
∗
M
= 1. When p
v
> 2h, h
∗
M
= 0, which can be excluded as irrelevant case. (F.2) shows
that p is chosen as high as possible. From the condition of participation, U
∗
b
(0) ≥ 0,
p ≤ max{0, δ − p
v
(4 − p
v
)/4}. With the condition of p ≤ δ, optimal p under regime
M is given by p
∗
M
= min{δ, max{0, δ −p
v
(4 −p
v
)/4}}. From (F.3), optimal p
v
is given
by p
L
v
= (4 −
√
10)/3 by frst-order and second-order conditions. By p
v
= p
L
v
, p
∗
M
=
max{0, δ − p
L
v
(4 − p
L
v
)/4}. It can be shown that fve RMT constraints are all satisfed
at this optimum. Let π
L
M
denote π
M
(h
∗
M
, p
∗
M
, p
L
v
).
Second, supposing that the frm chooses to make sellers extinct, optimal choices can
be derived by h
∗
M
= 1, p ≤ min{δ, max{0, δ − p
v
(4 − p
v
)/4}}, and p
H
v
= 2/3. By p
H
v
,
p
∗
M
= max{0, δ −p
H
v
(4 −p
H
v
)/4}. Let π
H
M
denote π
M
(h
∗
M
, p
∗
M
, p
H
v
).
Firm’s choice on seller’s existence depends on β. For given β, frm can make sellers
alive by choosing p
v
= β + ϵ, and extinct by doing p
v
= β − ϵ where ϵ is an arbitrary
small positive. Let π
+
M
denote π
M
(h
∗
M
, p
∗
M
, β +ϵ), and π
−
M
do π
M
(h
∗
M
, p
∗
M
, β −ϵ).
For β ∈ (0, p
L
v
], frm’s proft is chosen between π
L
M
that is the maximal proft with
sellers and π
−
M
is the approximated highest proft without seller for an arbitrary small ϵ.
Firm would choose π
L
M
for β ∈ (0, β
1
], δ ∈ [0, δ
β
] where β
1
= 0.15822 that is numerically
calculated, and δ
β
= β(4 − β)/4 because it is not possible to fnd positive real ϵ that
makes π
L
M
< π
−
M
for this range of β and δ. For β ∈ (0, β
1
] and δ ∈ [δ
β
, ∞), it possible
to fnd ϵ that satisfes π
−
M
> π
L
M
, hence p
M
v
= β − ϵ. For β ∈ (β
1
, β
2
) δ ∈ [0, ∞) where
β
2
= p
H
v
, frm’s choice is between π
+
M
, the approximated highest proft with sellers and
27
π
−
M
, that wihout seller. For β ∈ (β
1
, p
L
v
], frm can choose p
L
v
, but it is shown that there
exists a proper ϵ such that π
L
M
< π
−
M
. For β ∈ (p
L
v
, p
H
v
), frm cannot choose p
L
v
, as there
is no seller by p
v
= p
L
v
, which violates the condition for deriving p
L
v
. By similar reason,
p
H
v
cannot be chosen. Also, for β ∈ (β
1
, β
2
), it can be shown that π
+
M
< π
−
M
for all
positive ϵ. Finally, for β ∈ [β
2
, 1] and δ ∈ [0, ∞), frm’s choice is between π
H
M
and π
+
M
,
and it is shown that there is no proper ϵ that π
+
M
> π
H
M
for β ∈ [β
2
, 1]. Hence, for this
region, p
M
v
= p
H
v
.
28
Bibliography
Armstrong, Mark, “Competition in Two-Sided Markets,” RAND Journal of Eco-
nomics, 2006, 37 (3), 668–691.
and Julian Wright, “Two-Sided Markets, Competitive Bottlenecks, and Exclusive
Contracts,” Economic Theory, 2007, 32 (2), 353–380.
BBC News, “Gamer Buys $26,500 Virtual Land,” December 17 2004. http://news.
bbc.co.uk/2/hi/technology/4104731.stm.
, “Virtual Property Market Booming,” November 11 2005. http://news.bbc.co.uk/
2/hi/technology/4421496.stm.
Bloomfeld, Robert J., “Worlds for Study: Invitation - Virtual Worlds for Studying
Real-World Business (and Law, and Politics, and Sociology, and....),” Social Science
Research Network Working Paper Series May 2007. http://ssrn.com/abstract=
988984.
Caillaud, Bernard and Bruno Jullien, “Chicken & Egg: Competition among Inter-
mediation Service Providers,” The RAND Journal of Economics, 2003, 34 (2), 309–
328.
Castronova, Edward, “Virtual Worlds: A First-Hand Account of Market and Society
on the Cyberian Frontier,” CESifo Working Paper Series No. 618 December 2001.
http://ssrn.com/paper=294828.
, “On Virtual Economies,” CESifo Working Paper Series No. 752 July 2002. http:
//ssrn.com/abstract=338500.
, “The Price of ‘Man’ and ‘Woman’: A Hedonic Pricing Model of Avatar Attributes
in a Synthethic World,” Social Science Research Network Working Paper Series June
2003. http://ssrn.com/abstract=415043.
, “The Right to Play,” New York Law School Law Review, June 2004, 49 (1), 185–210.
http://ssrn.com/abstract=733486.
, “A Cost-Beneft Analysis of Real-Money Trade in the Products of Synthetic
Economies,” Info, 2006, 8 (6), 51–68. http://ssrn.com/paper=917124.
, Synthetic Worlds: The Business and Culture of Online Games, University Of
Chicago Press, October 2006.
de Freitas, Sara, “Serious Virtual Worlds,” November 2008. http://www.jisc.ac.
uk/media/documents/publications/seriousvirtualworldsv1.pdf.
DFC Intelligence, “The Online Game Market,” 2007.
Dibbell, Julian, “The Life of the Chinese Gold Farmer,” New York Times June 17
2007. http://www.nytimes.com/2007/06/17/magazine/17lootfarmers-t.html.
Economides, Nicholas, “The Economics of Networks,” International Journal of In-
dustrial Organization, March 1996, 14 (2), 673–699.
, “Special Issue on Network Economics: Business Conduct and Market Structure,”
International Journal of Industrial Organization, October 1996, 14 (6), 669–671.
29
and Charles Himmelberg, “Critical Mass and Network Evolution in Telecommu-
nications,” in “Toward a Competitive Telecommunications Industry: Selected Papers
from the 1994 Telecommunications Policy Research Conference” 1995, pp. 47–63.
Evans, David S., “The Antitrust Economics of Multi-Sided Platform Markets,” Yale
Journal on Regulation, 2003, 20 (2), 325–382.
, Andrei Hagiu, and Richard Schmalensee, Invisible Engines: How Software Plat-
forms Drive Innovation and Transform Industries, The MIT Press, October 2006.
Gabszewicz, Jean J. and Xavier Y. Wauthy, “Two-Sided Markets and Price Com-
petition with Multi-homing,” CORE Discussion Paper May 2004.
Hagui, Andrei, “Pricing and Commitment by Two-Sided Platforms,” RAND Journal
of Economics, 2006, 37 (3), 720–737.
Heeks, Richard, “Current Analysis and Future Research Agenda on “Gold Farming”,”
IDPM Working papers 2008. http://www.sed.manchester.ac.uk/idpm/research/
publications/wp/di/documents/di_wp32.pdf.
Hotelling, Harold, “Stability in Competition,” Economic Journal, March 1929, 39,
41–57.
Jang, Yong-Ho, “The Survey on Real Money Trading of Online Game Items [written
in Korean],” Korea Game Industry Agency Research Report 2006.
Japan Online Game Association, “Japanese Online Game Market Report [written
in Japanese],” 2008.
Korea Game Industry Agency, “The Rise of Korean Games 2007,” June 2007.
Lambertini, Luca and Raimondello Orsini, “Network Externality and the Coordi-
nation Problem,” Journal of Economics, June 2004, 82 (2), 123–136.
Lastowka, Greg and Dan Hunter, “The Laws of the Virtual Worlds,” California Law
Review Forthcoming. http://ssrn.com/abstract=402860.
Lee, James, “Wage Slaves,” 1Up.com July 5 2005. http://www.1up.com/do/feature?
cId=3141815.
Marketwire.com, “Entropia Universe Enters 2008 Guinness World Records Book
for “Most Expensive Virtual World Object”,” September 18 2007. http://www.
marketwire.com/press-release/Entropia-Universe-770780.html.
Martinsen, Joel, “Gamble Your Life Away in ZT Online,” DANWEI December 26
2007. http://www.danwei.org/electronic_games/gambling_your_life_away_in_
zt.php.
Oren, Shmuel S. and Stephen A. Smith, “Critical Mass and Tarif Structure in
Electronic Communications Markets,” The Bell Journal of Economics, 1981, 12 (2),
467–487.
Robischon, Noah, “Station Exchange: Year One,” 2007. http://www.gamasutra.
com/features/20070207/SOE%20Station%20Exchange%20White%20Paper%201.19.
doc.
30
Rochet, Jean C. and Jean Tirole, “Platform Competition in Two-Sided Markets,”
Journal of European Economic Association, 2003, 1 (4), 990–1029.
and , “Two-Sided Markets: a Progessive Report,” RAND Journal of Economics,
2006, 37 (3), 645–667.
Rohlfs, Jefrey, “A Theory of Interdependent Demand for a Communications Service,”
The Bell Journal of Economics and Management Science, 1974, 5 (1), 16–37.
Rysman, Marc, “Competition Between Networks: A Study of the Market for Yellow
Pages,” Review of Economic Studies, 2004, 71 (2), 483–512.
Selten, Reinhard, “Spieltheoretische Behandlung eines Oligopolmodells mit Nachfra-
gentragheit,” Zeitschrift f¨ ur die gesamte Staatswissenschaft, 1965, 12, 201–324.
Shy, Oz, The Economics of Network Industries, Cambridge University Press, 2001.
The Economist, “Living a Second Life,” September 26 2006.
, “Wonders of the Metaverse,” April 20 2006.
, “Getting serious,” December 6 2007.
, “Alternative Reality,” January 31 2008.
Wang, Ryan, “The Truth Behind Gold Farmers,” WowMine.com January 14 2008.
http://www.wowmine.com/WoWmine_The_Truth_Behind_Gold_Farmers.php.
31