Axie Infinity’s Unsustainable Design
This article is a work in progress. I will continuously improve the analysis based on feedback from the community. Of course, all insights will always be completely free. If you appreciate the article follow me on Twitter.
Introduction
Axie Infinity recently made headlines due to its explosive growth. The blockchain-based game has grown its user base from less than 100’000 users in May 2021 to over 1’000’000 as of today. In addition to that, the revenue generated by the game has exploded along its user base. At the current rate, the protocol itself is generating around15 million in revenue on a daily basis. This is similar to the entire fees generated by Ethereum.
The “Play-to-earn” game is rewarding players by giving them newly issued tokens when playing successfully. The idea of rewarding players is radically different compared to traditional game-related business models where typically users pay the game creators to play. Or alternatively, users purchase in-game items as is the case for Fortnite.
Such a radical new business model brings up many questions. How is the distribution of rewards sustainable? Who pays for the rewards? And most importantly;
Where is the value creation?
I will begin this article by explaining roughly how the game works and then dig deeper into the design of the economic incentives. If you already know how the game works please skip the first two chapters and continue with “Breeding and Population Growth”.
Gameplay
Axie Infinity runs on the Ronin Sidechain of Ethereum. On the website the game is described as follows:
Axie Infinity is a Pokémon-inspired universe where anyone can earn tokens through skilled gameplay and contributions to the ecosystem. Players can battle, collect, raise, and build a land-based kingdom for their pets.
The game consists of unique digital monsters called “Axies”, all of which are NFTs. Owning a team of at least 3 Axies allows a player to battle other players or play on adventure mode.
When winning battles, players earn a token that is called “Smooth Love Potion”, short “SLP”. The supply of SLP is expanded automatically by the smart contracts of the game to ensure that rewards can always be paid.
Existing Axies can be bought and sold on the official Axie Infinity Marketplace using ETH as a currency. To play the game for the first time, one has to acquire at least 3 Axies.
To allow more people to play the game, Axies can be created by mating two existing Axies. This process is referred to as “breeding”. More on that in the chapter “Breeding and Population Growth”.
Assumptions
The game itself is more complex than has been outlined so far. However, many aspects that are relevant for the gameplay are much less relevant for an economic evaluation.
For example, Axies themselves have different classes. Similar to how Pokémon works, each Axie class has an advantage against specific other classes during battles. This is, however, mostly a gamification element that averages out over different Axie teams. Additionally, the quality of a player just determines if he/she wins more battles but does not determine the amount of newly issued SLPs that are given out as rewards.
Besides that, Axies have different gene types; dominant, recessive, and minor recessive, which are passed on to their children with specific probabilities. However, these probabilities also average out over the long run which means there should not be a significant dilution of the strength of Axies over time. In my view, this is also simply a gamification element and not relevant for the economic analysis.
These are examples of many more elements that mostly exist to make the game more entertaining. Amongst others, there are the following gamification elements that I think average out over many games and won’t be further discussed:
- Body Parts
- Mystic parts
- Abilities
- Pureness
- MEO and MEO 2
- Mutations
- Cards
In case you think I left out important aspects of the game or if you think I should pay more attention to these elements, please let me know in the comments section!!!
My core assumption is that there is a hypothetical “average Axie” which is priced based on how well it can be used to generate rewards and breed other Axies. I will ignore the existence of rare Axies as well such as “origin” Axies or Axies with a low ID. I think their role is negligible in an exponentially growing Axie population.
What is much more important is how the game is rewarding players and the process of breeding new Axies. Let’s have a closer look at that.
Breeding and Population Growth
To breed new Axies players need a specific amount of the SLP token that gets burned during the process. As stated before SLP can be earned by winning battles in the game. Generally, the SLPs used to reward players are newly issued. In addition to SLP, breeding requires 4 AXS tokens. The AXS token is the official future governance token of the game and cannot be earned in the game but has to be acquired on an exchange. Decentralized governance has not yet been introduced though.
AXS derives its value from being burned during the breeding process and by governing the protocols treasury. Additionally, a 4.25% fee on any sales on the Axie marketplace is being charged by the protocol.
A couple of Axies can only have a total of 7 offspring until they become infertile. The number of offspring is being tracked by what is called the “breed count”. If two Axies each have a breeding count of 0 (neither of them having a child), both will end up having a breed count of 1 after giving birth to one child. The breeding count is capped at 7, which means the number of offspring per existing Axie is capped at 3.5.
Breeding cost in SLP is over-proportionally rising in the breeding counts of the parents:
That cost has to be paid for both parent Axies. That means if both parents have a breeding count of 0 the total cost will be 300 SLP (150*2) and 4 AXS that are just paid per breeding. If the breeding count of one parent is 0 and 1 for the other, the SLP cost would be 450 SLP plus the 4 AXS.
There is one further constraint other than the breeding fees;
Siblings cannot breed together and Parents cannot breed with their offspring.
This is somewhat intuitive as it would simply feel weird to mate siblings or children with their parents. Every other family constellation is possible though. So a child can for example mate with its uncle.
Breeding will result in an egg that will hatch into an adult after 5 days. As soon as the egg has hatched the newly created Axie can again be used for breeding.
Remember that each Axie can generate SLP over time within the game. It is crucial to understand that if no breeding occurs, there won’t be enough Axies for new players to join the game. If we assume that more and more people want to join the game, per definition the number of Axies has to be expanded, thus breeding has to occur. Axies generally live forever, they don’t die or become weaker over time. That means one Axie could be used for playing potentially indefinitely.
The reader might have noticed that the SLP cost is rising over-proportionally with the breed count. That might give the impression that the total population of Axies is limited in size. However, when we take a closer look that is not the case.
We can make a simple analogy to humans to understand the growth rate of the Axie population. With humans, if every couple in the world would have 2 children and if we assume everyone finds a partner, the population would roughly stay constant over time. Of course, this is the case because old people regularly die off and each person is essentially creating another person.
In the Axie world, the old Axies don’t die off. If we assume that each Axie creates one offspring (a couple creates two children) then the population is growing over time. As old Axies don’t die out, the total population of Axies is constantly increasing. However, only a constant number of Axies stays fertile with a total number of Axies ever increasing. This essentially means the population is growing linearly in absolute terms with a relative decreasing growth rate. In this example, the 10 new Axies are the ones that breed 10 more every cycle.
The chart below shows an example of such an Axie society beginning with just 10 eggs. As soon as these 10 eggs hatch they will become fertile. Each of these Axies will then produce one more Axie resulting in a total population of 20, 10 of which are eggs. Once these 10 eggs hatch they will again produce 10 offspring. In the meantime, the Axies that have produced offspring already are here assumed to become infertile. So there would be 10 infertile Axies, 10 Axies that directly create new eggs, and their 10 eggs. This will repeat over and over again which implies a population growing linearly.
On the other hand, if each Axie is creating more than one offspring the population will be increasing exponentially with a constant growth rate. Please note that on the chart below the growth rate will eventually converge towards 1.5. The more Axies are being bred per Axie the higher the growth rate of the population.
It is important to understand that this growth rate is not a yearly growth rate but a rate of growth for 5 days!
If there are 4 Axies bred for each couple of Axies, so 2 Axies per one parent, the population would double every 5 days.
What determines the growth rate of the Axie population?
The answer to that question is which level of the breed count still leads to a profit. People will breed as much as they can as long as it is profitable. That means as long as they get more rewards over time than they had to spend on breeding fees. Breeding 7 children for a couple with both having a breed count of 0 would mean that the seventh child costs 6300 SLP in addition to the 4 AXS. If the discounted amount of SLP that the 7th child is generating over time is higher than that and a similar USD price of SLP is assumed over time people would breed 7 children. Of course, a skilled investor would fear that the SLP price could go down over time or would simply demand a risk premium for investing and playing a game that is highly experimental. So when I say profitable I mean profitable considering all the risks involved and thus, applying an adequate discount rate of future rewards. Discounted payments over time are referred to as “present value” (PV) in economics.
The reward side of the equation that determines breeding behavior could be described in the following way:
Discounted USD value of SLP rewards
On the cost side of the equation, there is simply the USD value of the breeding fees. Note that the term depends on the Breeding Count of the parents.
USD value ( SLP( Breeding Count ) +4AX )
The profitability calculation of an investor would therefore be the following:
USD value ( SLP ( Breeding Count ) +4AX ) < PV USD value of SLP rewards
One has to understand that for a higher breed count the equation might not hold depending on how high the rewards are or how high the discount rate of the investor is. It implies that certain investors might choose to only breed lower breed counts. The profitability of breeding essentially determines the growth rate of the system.
If a breed count of 7 is still profitable the total Axie population will grow 3.5X every 5 days. If only a lower Breed Count of let’s say 3 is profitable the growth rate will be 1.5X every 5 days. Of course, the profitable breed count could also be a number such as 2.2, as individual investors potentially apply different discount rates which would imply a 10% growth rate every 5 days.
Analysis Structure
The following chapters will focus on the Axie economy which depends a lot on the prices of SLP and AXS. I will, therefore, separate the analysis into different parts. I will start by going to the origins of the game where both the SLP and the AXS token had a value of 0. There I will explain how both tokens became valuable and how that lead to the beginning of an unsustainable economic incentive scheme. I will then, discuss how a hypothetical economy could behave in which only the SLP token has value. Finally, I will discuss the role of the AXS token and show why its existence is crucial for the economy.
Axie Economy: SLP = 0 | AXS = 0
Let’s start as early as possible. Imagine the Axie team just hacked together the game and started running the code on a blockchain. We are in an economy where both the SLP token and the AXS token don’t hold any value.
We assume that the rules of the game have been designed and the game is fun to play. Each of the team members has the minimum number of Axies to play against each other. So basically just a bunch of dudes playing a game.
Now imagine other people would want to play the game as well. The blockchain-enforced rules do not allow for it unless someone breeds new Axies. In addition to that, breeding a new Axie takes 5 days and requires some SLP.
As the game seems really fun and quite a lot of crypto gaming nerds would like to test it out, one of them offers 1$ to be the first in line to get an Axie. The team agrees. However, none of the team members themselves have the required SLP amount for breeding. Yet together they have enough. So one of the members buys the SLP tokens of the others for a bit less than the new guy had offered for the Axie. He then breeds and sells the Axie to the new guy. That is essentially how both the SLP token and the Axies themselves have started to have a monetary value. It’s important to understand that SLP and Axies themselves are nearly identical things. An Axie is an asset that generates SLP over time. SLP is a token that is both, needed to create the asset but also what the asset pays over time. You can imagine that the demand for Axies and the demand for SLP are tightly related.
As soon as the SLP token has value, people realize they cannot only play a fun game but also make a profit when doing so. Of course, that sounds even better! People who wanted to test the game now want to play, even more, offering more money to be the first in line to do so. This causes more demand which drives up the value of SLP further.
This essentially means that as soon as the SLP token has any value, investors want to start playing the game to exponentially increase their capital. So at the heart of the whole scheme lies a game that is indeed fun. However, as soon as the SLP token has value, new entrants are attracted mostly to increase their capital.
Axie Economy: SLP > 0 | AXS = 0
Now let’s further dig into the economics of an Axie economy in which the SLP token is valuable. In this chapter, we still assume that AXS does not hold any value.
As we saw earlier the following equation needs to hold so that breeding occurs:
USD value ( SLP ( Breeding Count ) +4AX ) < PV USD value of SLP rewards
We assume here that people form their expectations on the SLP price in the future based on the SLP price today. We also assume for simplicity that a Breed Count of 3 is still profitable. Furthermore, discounting future rewards is strictly decreasing the value of these future rewards. That means discounting just decreases the right side of the equation. Out of these assumptions, the following equation must hold true as well:
SLP breeding fee < SLP over time
That means for breeding to occur people need to get more SLP over time than they pay for breeding.
Generally one can imagine an investor growing an ever-increasing Axie herd when a breed count above 2 is profitable. He/she can earn a profit by either always selling old, infertile, Axies or by keeping all of them and use them to generate SLP rewards. If you're curious how an investor can manage hundreds of Axies and play the game with all of them at the same time? The answer is scholarships. However, I will dig into that in another article.
It’s interesting to understand that both the reward and the breeding fee are denominated in SLP. For new entrants, the price of SLP in dollar terms is, therefore, a direct indication of their profit per Axie. Consequently, if there is a high demand to enter the game, the SLP price will not be able to clear the market, as both the cost to enter the game and the reward of entering the game increase.
it is even more interesting to observe that the incentives to enter the game require MORE SLP to be generated over time than get destroyed during breeding. This is implying that every newly created Axie is a promise on MORE SLP over time. That means breeding INCREASES the supply of SLP over time but DECREASES it in the short run.
Every exponentially newly created Axie is however a promise on more newly created SLP over time than was needed for breeding. So as long as SLP holds its value investors are making an exponential profit.
The issuance of new SLP however is going exponential as well, so why does it not lose its value?
Breeding can happen to such a large extent that the supply of SLP is very scarce in the short term which is how its value is maintained. On the following chart, we can see the SLP supply dropping to 0 with an exponential increase in outstanding promises on SLP in the future.
It essentially means even though the SLP supply will grow to infinity eventually the short-term supply is being absorbed by more and more people breeding. It’s a vicious cycle that attracts more and more capital that eats up the supply of SLP but eventually leads to an even bigger supply.
As long as the growth rate of new entrants is high enough to absorb the higher and higher rate of newly issued SLP the price could even go up instead of down.
When does it collapse?
Once a natural limit of new investors is reached, the scheme turns the other way. In theory that could be once all the capital in the world is used for breeding. More realistically, once investors start to question the legitimacy of their returns. Doubts about the future value of SLP could lead investors to stop buying into the scheme which would lead to a decreasing SLP price. As soon as there aren’t enough new investors entering the game there is not enough SLP burning to absorb the supply increase. The amount of SLP in existence flooding the market explodes based on the number of Axies that have previously been created. SLP essentially becomes worthless.
As there is a lack of incentives to breed (assuming some transaction costs) the growth rate of the Axie population will also go to 0.
How quickly would that whole thing happen?
It would happen fairly quickly. One could imagine a quick bubble as we have seen in other Ponzi-like crypto schemes. If the SLP cost and reward were chosen in a way to make a breed count of 7 profitable, the system would be exploding, basically growing 3.5x every 5 days. One has to understand that is neither an exact science nor static.
The true system is designed to be more resilient and in my opinion more dangerous. A natural reducing force of the growth rate is needed to make the system more sustainable.
In fact, there is a mechanism that achieves exactly that, namely the AXS tokens that are required for breeding.
Axie Economy: SLP > 0 | AXS > 0
In this chapter, we are assuming both the SLP and the AXS token having value. Of course, this is the case in reality. The AXS token is currently traded at 73$ and the SLP token at around 0.2$.
As stated before the value of the AXS token is derived from the amount of breeding going on and the fees that are charged on the Axie marketplace.
In return, the USD value of the AXS token is a determining factor of the breeding profitability. The higher the value of the AXS token is relative to the SLP token the fewer incentives people have to breed new Axies.
During the build-up of that scheme discussed in the last chapter, the AXS holders earn fees on every breeding that occurs. As there are exponentially more Axies created the AXS token holders will be able to extract an ever-increasing amount of fees.
As a result, the market will price in more revenue over time and will thus mark up the price of AXS. This of course slows down the system as it makes breeding more expensive.
I stated before that the whole system is not an exact science but the AXS price offers an entirely market-driven way of adjusting the growth rate of the scheme.
In contrast to the SLP token, the AXS token only profits from the scheme and is not diluted by an ever-increasing amount of tokens.
I’d argue that the AXS token does not only allow the token holders to profit from the dynamic but it is necessary to eventually grow it bigger. In my opinion, three things are achieved by introducing the AXS token:
- The SLP supply growth is slowed down which leads to increased confidence by investors that the SLP token will preserve its value.
- Without the AXS token, the supply of SLP would drop to near 0 in the short term along with a rapidly increasing price. The volatility and rapid price increase would reduce the confidence of investors about the stability of the system.
- The slower growth rate gives the system more time to propagate in the real world.
On the following chart, we can see an example of an economy that grows at a lower rate initially but can avoid a quick death. As a result, it will eventually outgrow the economy that is not slowed down by the AXS token.
When will it collapse?
Theoretically, the AXS token could go up in value faster (no dilution) than the SLP token up to a point where breeding is completely unprofitable. At that point obviously breeding would come to a halt which would eradicate the fees generated for the AXS token holders. In that scenario, it is not entirely clear which token would drop more in value. In case the AXS token would drop more, breeding would become profitable again and the system would start to grow once more. On the other side, if the SLP token value would drop more, the economy would be in a death spiral in which both tokens would lose value but breeding never becomes profitable again.
However, it is crucial to understand that the team behind Axie Infinity is in control of the entire economy. In fact, the AXS token is not yet a real governance token meaning the team alone can dictate the economic policies.
Conclusion
The whole Axie economy is fairly fragile and not sustainable. A Ponzi scheme has been built on top of a legit game. While the team could have let the game grow organically they have chosen to implement the described incentives.
I’ve been asked by people in the community to propose solutions instead of only applying criticism. In my view, the only moral solution is to stop giving out SLP rewards and thus, ending the unsustainable incentives that are not backed by real value creation.
The team seems to think that they will be able to build further services on top of the game to eventually reduce the amount of Axies in existence and thus, preserve the value of SLP.
While there is a certain POSSIBILITY for that scenario to play out, it does not by any means justify running an unsustainable scheme in the first place. The people that invest in the Axies economy could be the ones that eventually have to pay for that risky endeavor.
Another argument the team has frequently brought up is the possibility to sell in-game items and subsequently buy back existing Axies with that revenue. In my opinion that is also far from likely to succeed. In contrast to Fortnite, Axie Infinity will end up in a situation where 99% of players are paid to play the game. By the use of scholarships, the people who play the game will most likely have a low purchasing power and will be more focused on making a living than buying in-game items.
To conclude, the sheer HOPE of building a valuable service on top of a Ponzi does not justify running it.
It’s mindblowing to me that either I am missing something obvious or that every credible crypto investor is not paying attention to how Axie Infinity really works, blinded by the scenario of NFTs going “mainstream”.
I’d like to end with one further question that nobody has brought up so far and is not on me to answer;
Is this legal?
If you appreciate the article follow me on Twitter.
