Fairness in ERC token markets: A Case Study of
Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
No Institute Given
Abstract. Fairness is an important trait of open, free markets. Ethereum
is a platform meant to enable digital, decentralized markets. Though
many researchers debate the market’s fairness, there are few discus-
sions around the fairness of automated markets, such as those hosted
on Ethereum. In this paper, using pilot studies, we consider unfair fac-
tors caused by adding the program. Because CryptoKitties is one of the
major blockchain-based games and has been in operation for an extended
period of time, we focus on its market to examine fairness. As a result,
we concluded that a gene determination algorithm in this game has lit-
tle randomness, and a signiﬁcant advantage to gain proﬁt is given to
players who know its bias over those who do not. We state incomplete-
ness and impact of the algorithm and other factors. Besides, we suppose
countermeasures to reduce CryptoKitties’ unfairness as a market.
Keywords: CryptoKitties ·Smart contracts ·Financial market fairness.
After Bitcoin was proposed, many challenges are conducted to make economic
activities performed autonomously without any trusted party. Bitcoin tries to
realize such a space for a simple application like payment. On the other hand,
with Solidity and another language, Ethereum tries to realize “smart contract”
beyond the payment process. The movement is recently expanding decentral-
ized ﬁnance. When we deal with the simple payment process, requirements on
application-level security are a bit simple, preventing double-spending in the case
of bitcoin. The amount of payment is assumed to be correctly agreed among the
payer and payee. KYC/AML is the other regulatory requirement under debate.
On the other hand, in the case of a smart contract, such requirements become
complicated. Throughout our experience regarding Initial Coin Oﬀering, there is
a potential to scam due to asymmetric knowledge and some unfair situation for
participants. One of the signiﬁcant expectations of permissionless block-chain
mechanism and smart contract as its application is to provide transparency and
fairness of an economic system. It may be true for payment applications like
Bitcoin and cryptocurrency, but it is unknown if we can expect the same fruits
for smart contracts.
arXiv:2102.03721v1 [cs.CR] 7 Feb 2021
2 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
Although there is a lot of research about the ordinary ﬁnancial system’s
fairness, they do not discuss the fairness of markets run autonomously by pro-
gramming code. When we try to discuss the fairness of smart contracts, we need
to consider two aspects, at minimum, addition to the concept of the fairness of
the ordinary ﬁnancial system; (1) eﬀect by autonomous execution, and (2) trust
of the programming code. Autonomous execution may make users diﬃcult to
manage their assets and strategy and understand their ﬁnancial transactions are
executed over a fair setting. The user should trust the programming code of the
smart contract platform. Though the developers claim that the programming
code is disclosed at GitHub for transparency, average users do not have enough
capability to understand the code. As an example of supply chain risks, it is hard
to prove the execution code is the same as the source code at GitHub repository.
At the time of writing of this paper, we do not have good criteria to evaluate
if a speciﬁc smart contract platform/application is fair or not. Though it is
big research to discuss the fairness of smart contracts, it is worth conducting
research on the source of the unfairness of smart contracts. This direction will
be the basis of such evaluation criteria.
1.2 Our Contribution
This research discusses the potential unfairness of a market created by the smart
contract. For example, we analyze CryptoKitties, a blockchain-based game, and
make the most use of smart contracts on Ethereum to evaluate if it is fair or not as
a market. According to , its economic eﬀect is more than forty million dollars.
Thus, the existence of potential unfairness may lead to a question regarding
legitimacy as a place to exchange cryptoasset.
We investigated the internal algorithm of CryptoKitties to determine the
price of each kitty potentially. In particular, we focus on how an ERC-721 token is
created in CryptoKitties. In this game, a kitty is produced as an ERC-721 token.
We assume that each player’s goal at this game is the player earns Ethereum by
exchanging tokens and enjoying the kitty. The characteristics of a newly born
kitty, an ERC-721 token, are determined by this game’s gene algorithm. If this
algorithm is not fair, there is a risk that users will unfairly lose Ethereum. We
also research trading tokens among the owner of kitties. It gives all users a chance
to get kitties.
As a result of the research, we found that CryptoKitties does not satisfy some
fair market conditions. The gene determination algorithm does not have qualiﬁed
randomness, and it has a huge inﬂuence on the determination of characters of
a newborn kitty. It is a source of asymmetry of knowledge. Only a person who
knows the nature of the random function can predict a potential new kitty’s
characteristics. Therefore, it is possible to guess which kitty produces the most
valuable kitty. We found that only users, who know this bias and can buy kitties
that give birth to valuable kitties, can earn more Ethereum. When a player tries
to sell a kitty cheaper than the breeding fee, his revenue will be smaller than
his cost. Thus, the game has an unrealistic assumption on players’ literacy; all
people must have the ability to understand the algorithm. This fact does not
Fairness in ERC token markets: A Case Study of CryptoKitties 3
mean that all players have opportunities to gain proﬁt. Moreover, currently, the
auction format in CryptoKitties has information asymmetry by conspiring with
a seller and a bidder. When the seller tells the bidder when his auction starts, it
is diﬃcult for other players to participate because the bidder makes a successful
bid as soon as it starts. We indicate that CryptoKitties may be providing an
unfair environment for many users.
In this paper, we argue conditions that a fair market should be kept in Section
2. In practice, we compare CryptoKitties and fair market conditions in Section
3. Section 4 mentions countermeasures that may make CryptoKitties fairer. We
consider other vulnerabilities of CryptoKitties in Section 5. Finally, we conclude
our research in Section 6.
1.3 Related Work
Alesja Serada et al. He studied CryptoKitties as a subject to see how blockchain
will shape future game design. He examined the relationship between token own-
ership and the value construction of CryptoKitties. In addition, he showed how
the breeding and market aspects of kitty work concerning maintaining the game
economy. As a result, the authors showed that the kitty’s value is decreasing
because there is no upper limit to the number of kitties that can be bred. The
value of Gen 0 kitties, which cannot be created by breeding, decreased as well.
We also showed that the existence of a transaction fee GAS could hinder the
intervention of new users. He concludes that these are the points that make the
game economy unsustainable .
Charlotte et al. Based on that ”trust without trust,” blockchain has emerged
as a disruptive technology that is considered an alternative to law. The authors
doubt that whether participants can transact with each other without the need
for legally sanctioned trust. The authors speciﬁcally highlight the need for users
to verify that a Dapps (short for decentralized applications) really does fall under
it. He focuses on some Dapps, including CryptoKitties. Since it is possible that
CryptoKitties is not decentralized, it is marketing as a Dapp may be misleading
to users. The reason why kitty is considered immutable and cannot be taken
away from others is the blockchain’s immutability. However, only the market
uses its properties. Charlotte points out that it is a vulnerability, and some can
cheat others to execute a dishonest contract .
2 Considering the Fairness of ﬁnancial services based on
Blockchain Blockchain is a database commonly used as a ledger for cryptocur-
rencies. Satoshi Nakamoto proposed it as a bitcoin ledger in 2008 . Blockchain
has some special characteristics; it enables decentralized systems, immutable
data, transparency, and anonymity.
4 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
A blockchain consists of many blocks. Each block contains transactions, a
timestamp, a previous hash, and a nonce. A transaction has a sender address, a
recipient address, and a value.
There is no administrator in the blockchain. Instead, every member of the
network manages blockchain data. A Peer-to-Peer network connects the partici-
pants as nodes. Each node has blockchain data. If someone creates a new block,
he sends all nodes connecting him to the block. These nodes will send other
nodes when they receive the block. Soon, everyone will have that information.
So, how do users make a new block? First, block creators called miners to
determine a block which they want to connect their block. If they determine the
transactions in that block are legitimate, they will make the previous hash of
their block the hash value of that block. It is called a blockchain because the
blocks are connected like a chain by hashing. If there are six or more blocks con-
nected behind a block, it is considered correct. Next, miners select transactions
which they thought right ones and each transaction fee is high. If a miner creates
a new block, he is rewarded with new coins. In the Ethereum blockchain, the
transaction fee is called ”Gas.” Then, miners calculate ”nonce” so that a block
hash value is less than the threshold. As a block has nonce, if they change its
value, they will also alter the block hash value. This threshold is set so that min-
ers can ﬁnd a nonce in 10 minutes, making it diﬃcult for multiple blocks to be
created simultaneously. If a block is easily created, it is immediately assumed to
be the correct one, and they will approve suspicious transactions. The threshold
prevents this. Finding the nonce is called Proof-of-Work (PoW), and the process
of making the block is called mining. In this way, blockchain is a decentralized
Other properties also meet. Because a block created once will be saved in
every node’s server, he has to attack all nodes if someone tries to tamper with
it. As it is too diﬃcult, all participants can not change blocks. Besides, they can
see all blocks. So, blockchain has transparency, such as seeing which address a
cryptocurrency originated from. By using this, we know an address’ balance. Of
course, other users can not steal its cryptocurrency, thanks to the UTXO system
. However, bitcoin and Ethereum addresses have anonymity so that people
can not ﬁgure out a real person who has the address.
Smart Contract Nick Szabo proposed smart contracts in the 1990s . We
deﬁne a contract in advance. Everybody can not change it once deﬁned. When a
person agrees with its deﬁnition, the contract is executed. His and the contrac-
tor’s settlement will be run automatically. We need no third party to run this
contract. Take a vending machine, for example; the pre-deﬁnition is the prod-
uct’s price and pictures displayed. By selecting a juice, it is correctly executed
until settlement. If the input is the same, smart contracts must have the same
output. For a given contract, if the input is the same, the result must be the
same regardless of who performs it. If this is not the case, then diﬀerent people
can buy the same juice at diﬀerent prices. This would make smart contracts
unreliable and diﬀerent from the concept.
Fairness in ERC token markets: A Case Study of CryptoKitties 5
Ethereum has implemented smart contracts for the ﬁrst time. With writing
pre-deﬁnition on blockchain, all users do not re-write it. After pre-deﬁnition, pro-
gramming code Solidity runs contracts. Thanks to this system, we can exchange
CryptoKitties CryptoKitties is one of the most famous blockchain-based games
. Axiom Zen created this game in 2017 . We show CryptoKitties’ overview
in Fig 1. In this game, users exchange Ethereum and ERC-721 tokens. ERC-721
is a non-fungible token(NFT) transferred on the Ethereum blockchain. Unlike
cryptocurrency tokens, NFTs are unique tokens, with speciﬁc parameters. Each
ERC-721 token diﬀers in its value. In CryptoKitties, an ERC-721 token is a kitty.
Again, players exchange kitties and Ethereum. These kitties have an ID, gene,
and generation. A kitty’s ID is assigned in the order of birth, and the algorithm
written in Solidity determines the gene that determines the appearance of the
kitty. The generation of a child kitty is one greater than the generation of the
parent kitties. By birthing and trading kitties, users aim to earn Ethereum. This
game’s source code is written in Solidity. So, all trades and breeding in this game
are executed by smart contracts. Not only transactions but kitties’ data are on
Fig. 1. CryptoKitties’ Overview
There are two ways to obtain a kitty. One is winning an auction. The auction
of CryptoKitties is the dutch system that the exhibited kitty’s price goes down
as time passes. There are two types of auctions; standard and rental. When a
user wins a standard auction, he can get a kitty. In case of rental, a winner has
to return the kitty after breeding, another way to get a kitty.
6 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
A user can get a new kitty created by the gene determine algorithm. To make
a kitty, he needs to choose two parent kitties that are inputs of the algorithm.
Parent kitties can be chosen from his own kitties, or one of them can be a kitty
he won at a rental auction. After selecting parent kitties, he can get a baby kitty.
Thus, this process is called breeding. A player has to pay 0.008 Eth when he lets
two kitties breed. Since a kitty has no gender, it can be either a matron or a sire.
The breeding deﬁnes a baby kitty’s gene and generation. A kitty’s generation
settles its breeding period  . It has 14 kinds; the longest is two weeks,
and the shortest is one minute. When a kitty is created, the cooldown period is
determined by its generation, and from that point on, each time it is bred, the
period increases by one kind. After breeding, until this period of time has passed,
a matron kitty cannot reproduce. Through this kind of trading and breeding,
players can get expensive kitties and sell them for a proﬁt.
2.2 Fairness in CryptoKitties Market
In terms of economics, a fair market should keep the following criteria . Ac-
cording to , every player has opportunities to proﬁt and take risks equally.
It must also be impossible to cheat to earn money. The information asymmetry,
where some people know information about making a proﬁt, must remain rel-
atively small. The trading environment must also be equal for all participants.
Finally, fairness includes adopting some measures to protect the weak.
We apply these requirements to CryptoKitties. We consider CryptoKitties’
opportunities and information to gain proﬁt, cheating, trading, and the infe-
rior. To begin with, getting and selling a high-value kitty is the way to make
Ethereum. So, an equal chance in this game means that all players can get high-
value kitties. If you get a valuable kitty, you can sell this kitty and earn a lot
of Ethereum. Then, we assume CryptoKitties’ cheating. It is earning Ethereum
unfairly. Since players need to get kitties to earn, we focus on the way to obtain
a kitty. Now, there are two methods to get a kitty: winning an auction or breed-
ing. So, cheating could be winning the kitty without following the rules at the
auction or obtaining it by tampering with the breeding algorithm. CryptoKitties
must not allow either action.
Information about kitties is essential for players to maintain a relatively
symmetric market. For example, what kind of kitty is being sold and at what
price? How is a new kitty created? CryptoKitties should make all such informa-
tion available. Next, we check the trading environment. Again, players can get
a kitty by auction or breeding. It is the only auction that a player trades his
kitty with other players. Therefore, there should be a rule of auction so that no
one has a disadvantage. Finally, we deﬁne the weak. According to , it takes
players who do not have enough information, ability to negotiate and judge as
examples. We have already deﬁned information as about a kitty. Then, a player’s
bargaining power has to do with how valuable kitties he can get to gain proﬁt. If
he has a lot of Ethereum, he will get many kitties and valuable ones. Thus, this
ability is related to ﬁnancial resources. Besides, as mentioned in Section 2.1, the
Fairness in ERC token markets: A Case Study of CryptoKitties 7
gene determination algorithm expresses how it creates a kitty. If a player under-
stands this game’s algorithm, he knows and can judge which kitty he should get
and how kitties he should select as parents to gain proﬁt. With understanding
this game’s algorithm and making the right decisions, he can make money, so
judgment is aﬀected by how well he understands this game. He will try to un-
derstand the algorithm written in Solidity to obtain an expensive kitty. Hence,
the ability to judge is related to the ability to read Solidity. Therefore, we deﬁne
the weak as players who have little Ethereum and can not read Solidity.
We found that CryptoKitties does not meet some of condition that we show
below. Condition No.1 and No.2 are rules for protecting the socially vulnerable.
Other states provide opportunities to gain proﬁt for all users. We point out that
this game does not meet all conditions except for No.4 in Section 3. In Section
5, we mention that CryptoKitties may not be satisﬁed with Condition No.1, 3,
and 4 as a future work.
1. There is a rule that avoids disadvantages for those who do not have large
amounts of Ethereum.
2. There is a rule that avoids disadvantages for those who can not understand
3. Information about the prices that are available in the market for each digital
kitty is communicated instantaneously and costlessly to all users so that they
know what trading opportunities exist.
4. The users are suﬃciently small compared to the size of the market that their
supply and demand behavior does not have enough inﬂuence on the market
to be recognized as such.
5. The possibility of realizing proﬁt opportunities is equally open to all users.
3 Analysis on CryptoKitties and its impact to fairness
3.1 Analysis on Gene Determination Algorithm
Gene, one of a kitty’s parameters, is a 240-bits number and depends on Gene
Determine Algorithm, as shown in Algorithm 1. Again, gene deﬁnes a kitty’s
appearance. In detail, each of the ﬁve bits determines an element of appearance.
For example, the ninth ﬁve bits correspond to the kitty’s eyes’ color. This al-
gorithm is a smart contract and determined by the mixGenes function deﬁned
in GeneScience.sol . In this algorithm, a gene array is used. Its length is 48,
and each cell corresponds to an element of the kitty’s appearance. The ﬁrst cell
is the last 5 bits of gene value. The second cell is the second last 5 bits of gene
value. In the same way, determine all of the cells of the gene array. We elucidate
whether the gene determination algorithm that builds the value of tokens to be
traded in the market makes the market unfair.
The ﬁrst step in this algorithm between lines 6 and 21 is a swap for parents’
genes. Before the swap, the gene value is divided into twelve groups. Each group
has four cells; the ﬁrst four cells are group 0, the second four cells are group 1,
and so on. Within each group, the swap operation is to change the order of the
8 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
Algorithm 1 Gene determination algorithm
1: matron := matron gene array
2: sire := sire gene array
3: child := child gene array
4: hash := SHA-256(target block), hash[i] means i-th bit of hash
5: k= 0, k uses for hash
6: for i= 0 . . . 11 do
7: for j= 2 . . . 0do
8: if hash[k:k+ 2] == 0 then
9: swap(matron[i∗4 + j], matron[i∗4 + j+ 1])
10: end if
11: k+ = 2
12: end for
13: end for
14: for i= 0 . . . 11 do
15: for j= 2 . . . 0do
16: if hash[k:k+ 2] == 0 then
17: swap(sire[i∗4 + j], sire[i∗4 + j+ 1])
18: end if
19: k+ = 2
20: end for
21: end for
22: for i= 0 . . . 47 do
23: mutated =false
24: if i%4 == 0 then
25: if abs(matron[i]−sire[i]) == 1 and min(matron[i], sir e[i])%2 == 0 then
26: if hash[k:k+ 3] <= 1 then
27: child[i] = smallT /2 +16
28: k+ = 3
29: mutated =true
30: end if
31: end if
32: end if
33: if !mutated then
34: if hash[k] == 1 then
35: child[i] = matron[i]
37: child[i] = sire[i]
38: end if
39: k+ = 1
40: end if
41: end for
42: return child
Fairness in ERC token markets: A Case Study of CryptoKitties 9
gene array. Next, the SHA-256 hash value of a block on the Ethereum blockchain,
called the ”target block,” is involved in the algorithm. Six bits of the hash value
of the target block are used for the swap in one group. Group 0 uses the last
six bits, and group 1 uses the second last six bits and same as below. Let us
say the four cells in the group are a0,a1,a2, and, a3starting with the one with
the smallest index. If the last two bits among six bits are both zero, a2and a3
are swapped. Then, if the next two bits are both zero, a1and a2are swapped.
Finally, if the remaining two bits are both zero, a0and a1are swapped.
The next operation between lines 22 and 41 is to ﬁll the cells of the gene array
of the kitty to be born one by one (for i= 0 to 47). There are two methods for
genetic determination in a new kitty; inheritance and mutation. The ﬁrst action
executed in this operation is checking to see if cell iof the parents meets the
requirements for mutation. If two cells are satisﬁed with 1, 2, and either 3-a or
3-b in below, the formula (1) determines the child gene’s cell i. In that formula,
smallT means the smaller of the two parents’ cell i.
1iis multiple of 4
2the absolute value of matron cell iand sire cell iis 1, and smaller one is even
3-a the smaller cell value is less than 22, and the lower three bits of the unused
bits in the hash value of the target block are 001 or 000
3-b the smaller cell value is not less than 22, and the three bits of the unused
bits in the hash value of the target block are 000.
cell =smallT /2 + 16 (1)
When any of the conditions are not met, a baby inherits either parent’s cell. If
the lowest bit of the unused bits in the hash value of the target block is 1, cell
iof a child gene will inherit from the matron’s gene. If not, it inherits from the
In short, a baby gene is dependent on its parents’ gene and target block hash.
All kitties’ genes are on the blockchain. By using Etherscan, a block explorer,
we can check any kitty’s genes. Then, what is the target block? We can predict
a breeding result if we know the hash value. If it means randomly choosing one
of all the blocks on the blockchain, we can not infer the outcome. However, the
target block is somewhat limited and predictable. The target block is a block
that will be issued when a matron kitty becomes fertile again. Speciﬁcally, there
is a variable that stores the frequency of block creation. The product of that
value and the matron kitty’s breeding period corresponds to the blocks issued
when she can breed again. We can ﬁnd out the breeding period of the kitty from
CryptoKitties’ oﬃcial page. Therefore, we know when the breeding period ends,
and the block issued at that time or thereabouts becomes the target block. By
calculating the hash value of the target block, we can predict a baby gene.
The fact that the results are predictable means that CryptoKitties has not
satisﬁed conditions 1 and 5 of fairness, as deﬁned in Section 2. First, the blockchain’s
transparency allows us to see what kitties are traded at a high price. Since we
can expect breeding results, it is also possible to predict parent kitties to produce
10 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
ones that match these trends. If we can make a successful bid to them, we will
get a good kitty and earn Ethereum.
However, in this kind of competition, well-ﬁnanced users will have an im-
mense advantage. We prove this by setting up a simple environment for Cryp-
toKitties. First of all, we use ”Cattribute,” which means the attribute of kitty.
In this market, there are 324 kinds of Cattribute. Let us take ”driver” one of the
Cattribute as an example. As of Jan. 13, there were 24 ”driver” kitties in the
market, and when we checked the gene sequences of all of them, we found that
No.0 is 15 and No.36 is 23 in common. Therefore, we expect that the kitty that
satisﬁes these two points has a ”driver.” In case of other Cattribute, ”domina-
tor,” we found that No.0 is 28 and No.28 is 23 in common. Also, for a Cattribute,
the ﬁrst kitty to belong to that it gets Diamond. The ﬁrst 10 kitties to belong
to it will get Gilded, and the ﬁrst 100 kitties will get Amethyst. From then on,
these jewels are called ”Family Jewels,” as shown in Fig 2 . According to
, the minimum price for each Jewel 5, 0.5, 0.07, 0.009 Eth, in order of rarity.
Since these prices are positively correlated with rarity, the environment we set
up should be like that. So, our environment will adopt these prices. In other
words, all kitties with Diamonds are assumed to be 5 Eth. For the other kitties,
we take those kitties that can produce XEth will be sold for X/2 Eth. For
example, a kitty that can reliably give birth to a Diamond kitty would be priced
at 2.5 Eth. Also, the minimum price of kitty to be sold in the market shall be
0.004 Eth. This amount is the minimum in the market as of Jan. 13.
Fig. 2. Family Jewels
The key is a kitty who has Diamond, which represents the pioneer of that
Cattribute. Assuming that the value remains the same as more kitties of the
same Cattribute, if a player gets a Diamond kitty, his earnings will be greater.
Speciﬁcally, he gives birth to 499 kitties so that all of them inherit Diamond
kitty’s Cattribute and gets family jewels. He will get 9 Gilded, 90 Amethyst,
and 400 Lapis kitties. Selling all kitties, his earnings will be 14.4 Eth. (0.5∗9 +
0.07 ∗90 + 0.009 ∗400) Thus, the player who has a Diamond kitty will gain a
lot of proﬁt. Then, in order for this to happen, you need to win the auction or
mutate and give birth to the Diamond kitty.
This algorithm will make it easy to know which kitty to get to make money.
Such kitty is in high demand, and users with ﬁnancial resources are more likely
to win its competition. Alice, who has little Ethereum, can not buy Diamond
kitty because it is expensive. So, to get these kitties, she has to birth them from
other kitties. She can expect which kitties will give birth to a Diamond kitty.
Fairness in ERC token markets: A Case Study of CryptoKitties 11
However, it is diﬃcult for her to get these parent kitties because they are also in
high demand. Since we can predict what kind of kitty will be born, some players
may repeatedly give birth to make a parent kitty. But, Alice can not do a lot
of births because a fee of 0.008 Eth is charged for breeding, and again she has
little Ethereum. For Alice to make a proﬁt, she needs to do things diﬀerently. It
is a way of making a lot of small gains. However, since the birth fee is 0.008 Eth,
selling a normal kitty will negatively aﬀect revenue. So, she ought to sell kitties
that have family jewels. As with the Diamond kitty, they are in high demand, and
Alice will be hard to get them. Therefore, since the proﬁt opportunity for players
who do not have a lot of Ethereum is small, CryptoKitties violates Condition
No.1 and No.5.
3.2 The readability of Solidity source code
Based on the previous section, rich players can make money, but is it really
possible for everyone? Next is focusing on the actions they will take. The most
important thing is understanding the gene determination algorithm. When they
try to give birth to a Diamond kitty, they must ﬁnd a Cattribute that has not
been found yet. Besides, they have to choose parent kitties so that a Diamond
kitty is created. In other cases, when trying to produce other kitties with family
jewels from a Diamond kitty, they also have to select parent kitties so that the
child inherits a parent’s Cattribute. So, to make money, they need to understand
the algorithm’s behavior.
However, not everyone will be able to understand this algorithm. The main
reason is that it is only written in Solidity. People who lack this Solidity knowl-
edge will ﬁnd it almost impossible to understand the algorithm. There is a con-
siderable gap between those who can understand Solidity and those who can
not, which signiﬁcantly aﬀects proﬁt opportunities. Therefore, the results are
contrary to Condition No.2 and No.5.
3.3 Auction in CryptoKitties
In this game, trading kitty is always done through auctions. So, users can only
get kitties from the auction market. In this auction, a seller decides the starting
and ending price of a kitty and auction. He can then start the auction with his
intentions. According to condition No.3, a fair market should provide information
about a trade for all players. It needs an environment where they know what
kind of transactions exist. In this sense, information on what type of kitty is on
sale and what price must be shared with all users.
However, when an exhibitor, Alice, and a user, Bob, are colluding, other
players, Charlie, have little chance to get Alice’s kitty. Alice tells when her
auction tries to start Bob. As soon as her auction starts, Bob bids for her kitty,
and Charlie can not see its trading. For example, Alice gives Bob a Diamond
kitty in this way. Other players can not get her kitty, and Bob can get it and
its child kitties. They have the same Cattribute as their parent’s one and with
12 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
family jewels. As a result, only Bob can gain proﬁts. It contradicts condition
No.3 and also enhances to expand information asymmetry.
4 Enhancement of fairness
4.1 Gene Determination Algorithm
As mentioned in Section 3.1, we state that it is diﬃcult for not rich players to gain
proﬁt in CryptoKitties. To earn Ethereum, players need to sell a valuable kitty.
Users with ﬁnancial resources have the advantage of getting that kitty at auction.
The method of giving birth and getting a kitty is also easier for wealthy users
than ordinary ones. Because the outcome of the gene determination algorithm
is predictable, so the demand for parent cats is high, and only rich people can
If the gene determination algorithm’s output is unpredictable, everyone may
have a chance to gain proﬁt. With that algorithm, no one would know which
parent kitties would produce a valuable kitty. All players do not know which
kitties as parent kitties will make a proﬁtable kitty. As a result, the value of the
parent kitties that produced a valuable kitty is unknown. Therefore, there is a
possibility that even a cheap kitty can give birth. If kitties are reasonable, many
users can bid on them, so we think the game will be fairer than it is now.
However, there is a problem with introducing an unpredictable system in
CryptoKitties. Again, this algorithm is written in Solidity and a smart contract.
Smart contracts should output the same result if the input is the same. So, smart
contracts cannot use a random number generator. Therefore, we have to consider
the system without a random number.
To add an external randomness source in deciding the gene, we suggest that
the users jointly create a random number as an input to a hash function (e.g.,
SHA-256) instead of creating value from a block on the blockchain. For instance,
when someone does breeding, everyone chooses a random number. The sum of
them which users submit will be the input to a secure hash function. As all users
cannot predict the input, its output is also unpredictable. This game’s usability
will not be compromised if a tool automatically generates and sends a random
number every time requested. It provides fairness to the market since every user
can have a chance to get a high-value ERC-721 token and trade it to Ethereum.
We show this system’s overview in Fig 3.
4.2 The readability of Solidity source code
We explained that if a player does not understand the gene determination al-
gorithm, he may not get a valuable kitty from kitties he has in Section 3.2. For
example, though he has a Diamond kitty, he could not inherit its Cattribute to
its kitties. He will not make Ethereum because the kitty without Family Jew-
els is expected not popular. On the other hand, if another player understands
the algorithm, he will create expensive kitties. We expect that there are sig-
niﬁcant gaps to opportunities to gain proﬁt between knowledgable players and
Fairness in ERC token markets: A Case Study of CryptoKitties 13
Fig. 3. Countermeasure’s Overview
not. In order to make CryptoKitties fair, this game should ﬁx so that all users
can understand its gene algorithm. However, we insist that CryptoKitties does
not achieve it. The readability of a programming language is not high, and it is
estimated that more people cannot read it than those who can.
We assert that CryptoKitties needs a system so that more people can ﬁgure
it out. These game managers should prepare not only to source code but also a
diagram, ﬂowchart, language description, and so on. It is expected that a variety
of explanatory methods will reduce the information asymmetry about the gene
determination algorithm, and this game will be satisﬁed with Condition No.2.
4.3 Auction in CryptoKitties
We show that when a seller and a bidder are colluding, it is diﬃcult for other
players to get the seller’s kitty in Section 3.3. Though other players will not
create this kitty’s children, the bidder can. The seller gains proﬁt by selling the
kitty, and the bidder also earns Ethereum by selling child kitties of his kitty. But,
other players have no opportunities to gain proﬁt from the kitty. We argue that
CryptoKitties does not provide an environment that every user has a chance to
gain proﬁt equally. This problem stems from the fact that the time between the
auction starts and the winning bid is too short.
CryptoKitties should create an auction where everyone has an opportunity
to trade. One countermeasure is that supposing it allows a certain amount of
time, one hour, for example, between when a player puts up an item and when
it becomes available for bidding. During this period, many people will be able
to grasp the kitty the seller exhibits and think whether each of them should bid
or not. We hope that it enhances to give all users a chance to get the kitty and
14 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
5 Future Work
5.1 Proof of Stake
In the Ethereum environment, there is an assumption that no user has a large
enough Ethereum to impact the market signiﬁcantly. The symbol of this is Proof-
of-Stake (PoS). Suppose hypothetically; some users had a substantial amount of
Ethereum that could change the market value signiﬁcantly. This situation is not
satisﬁed with Condition No.4. In that case, it is quite likely that those users
would be able to get the right to create blocks many times. There is no bias
towards users’ chance in terms of a decentralized system, which means to have
the right to create. However, there is no countermeasure to prevent this from
happening, and playability could be lost considerably.
5.2 Secret trading
We state that transactions can only be conducted through the auction market.
However, is this really the case? We ﬁnd some suspicious transactions, as shown
in Fig.4 . They traded kitties for nothing and without going through an
auction possibly. We can not ﬁgure out how they traded. If they really sold
using other methods, this game does not meet condition 3 and will be reversed.
This game should also take measures for such cases.
Fig. 4. One example of suspicious transactions
5.3 Blockchain anonymity
Ethereum’s blockchain is guaranteed to be anonymous. The blockchain address
cannot be tied to who the actual user. However, there is one problem that arises
from this. That is insider trading. Insider trading is that a person who has
inside information about a company buys or sells shares before the information
Fairness in ERC token markets: A Case Study of CryptoKitties 15
about the material fact is made public. Or, this company’s employees trade
them. In order to discover these transactions, it is necessary to know who made
them. Unfortunately, it is so diﬃcult to ﬁnd them in the blockchain environment
because of blockchain anonymity. If its developer takes part in this game and
earns a large Ethereum, we will not see his illegal activity. Thus, CryptoKitties
should prove that they are not doing this.
5.4 Fee of transaction and breeding
We argue that Gas and breeding fee are an obstacle to the motivation to trade for
the average user. Transaction fee, GAS, is a miner’s motivation because if he has
a right to create a block, all GAS in the block will be his income. Miners tend to
select transactions whose GAS are high. Therefore, wealthy users’ transactions
are apt to be approved since they pay high GAS. Besides, the Breed fee, currently
0.008 ETH, is CryptoKitties managers’ income. When a player tries to breed his
kitties, he pays Ethereum in exchange for a new kitty. Users who can aﬀord
Ethereum can breed or exchange kitty without hesitation. In contrast, for other
players, their action count is limited. So, they have fewer opportunities to get
good kitties and gain proﬁt than rich people. In other words, these fees do not
help conditions No.1 and No.5. One countermeasure we think is decreasing the
breeding fee so that more players give birth to baby kitties many times.
We found that CryptoKitties is not satisﬁed with four conditions that fair mar-
kets should keep. The gene determination algorithm which aﬀects the ERC-721
token value is not satisﬁed with two conditions. We show that we can predict we
will produce a token. In the environment we set, a player can not gain proﬁt when
he creates and sells a cheap token because of the breeding fee. So, he needs to
sell a token whose value is more than the breeding fee. Since we can know which
token we will make, we know tokens that can produce high-value ones. Thus,
rich players are more easily to get lucrative limited tokens. Besides, people who
can understand this algorithm are limited because the only Solidity expresses
this algorithm. Users who know this bias have a signiﬁcant advantage in play-
ing CryptoKitties. Also, there is a problem with its trading market. When two
players are colluding, it will be possible to attack them by not allowing others
to trade with them.
We also mention the countermeasures of these problems. In the case of the
gene algorithm, it needs an unpredictable system. Since this problem stems from
seeing the input of the hash value it is using; we propose that all users determine
its input. Moreover, describing these mechanisms in other than a programming
language will reduce the information asymmetry. Finally, as one cause is that
from the auction starts to the winning bid is too short, one method would be
noticing what kitties have been put up for auction and allow a certain amount
of time before the bidding starts. We propose these improvements, but there are
other problems in CryptoKitties.
16 Kentaro Sako, Shin’ichiro Matsuo, and Sachin Meier
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