Dave White proposes new NFT primitive Mortys: composites representing fractional ownership of NFT classes

summarize

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summarize

This article introduces a new NFT primitive: Martingale shares, or "Mortys". (Note: Martingale, martingale, this is a concept in probability theory.)

Mortys are synthetics that represent fractional ownership of NFT categories.

They do not require buyouts or oracles, but instead rely on a randomized martingale settlement process.

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motivation

Imagine that Alice owns an Ocelot (an ocelot) from the Awful Hot Ocelots series.

When she bought the ocelot, it wasn't worth much. However, the project has been live since then, and she hopes to gain some liquidity and reduce her price exposure.

She didn't want to just sell her ocelot and set it as her Twitter profile picture, very attached to it. Ideally, she would only want to sell half of them.

Challenges Facing NFT Fragmentation

If she wanted to sell half of a plate of cookies, she could sell half. If she wants to sell 50% of a business, she can sell shares representing 50% of the cash flow it generates.

However, her Ocelot NFT is not naturally divisible and does not generate any cash flow. How can it be partitioned in an economically meaningful way?

Fractional

fractional.art will let Alice split her ocelots by selling tokens and extract 50% of the proceeds from their eventual future sales. This means Fractional has to ensure that future sales will be fair and actually happen. Therefore, the agreement implements a buyout mechanism, allowing interested buyers to open auctions for this ocelot at any time.

This works great for famous and unique NFTs that have a lot of market interest. However, for more generic NFTs, such as Alice's Ocelot, the situation is a bit more difficult.

A fraction of her Ocelot shares would be a brand new token, and Alice would have to carve out a new market for them somewhere on Uniswap or something. With many ocelots already split, she suspects it will be difficult to attract enough attention to sell her stake at a reasonable price.

Likewise, if someone later initiates a buyout auction for her ocelot, it may not attract as much attention or liquidity, potentially resulting in a sale at a price that is not favorable to Alice.

Floor Perps

Alice can also use her Ocelot to mint some Floor Perps, and these derivative synths use a funding rate mechanism and an oracle of floor prices to track the price of Ocelot's floors.

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In theory, she could create a floor perp to just track the reserve price of Wizard Hat Ocelots, but this would require defining an oracle for the Wizard Hat Ocelot floor. Since there are only 200 ocelots with the wizard hat attribute, any such oracle is likely to be inaccurate and susceptible to manipulation.

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Lottery Fragmentation

In a recent blog post, Vitalik Buterin offered a possible solution: Alice could sell shards in a lottery.

For example, let's say Alice's Ocelot is worth 10 ETH.

If she sells Bob half of the ocelots as a lottery ticket, he will give her 5 ETH and she will give him a 50% chance of winning the ocelot by flipping a coin. If the name is corrected, Alice will take the leopard cat back. If tails, Bob gets the ocelot.

Likewise, if Alice sells 10% of her ocelot to Bob, Bob can give her 1 ETH and they can roll a 10-sided die. If 1 comes up, Bob gets Ocelot, if 2 to 9 comes up, Alice gets it.

The benefit of this arrangement is that it is completely fair: Bob pays the amount of ETH exactly equal to the expected value of the lottery ticket he receives. There are no chaotic liquidity dynamics surrounding potential acquisitions, nor concerns about oracle price validity. If Bob buys 10% of the ocelots, then he has a 10% chance of getting it.

However, Alice may still not be too happy with the deal. After all, she loves her ocelot for more than its cash value. Here, she has a 10% chance of losing it instantly.

Furthermore, lottery-style fragmentation does nothing for Alice to find liquidity or a fair price. In this example, let's assume both Alice and Bob agree that her Ocelot is worth 10 ETH. In real life, this is unlikely to be true, and Alice may have to hold an auction or negotiate privately with Bob to set the price.

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Martingale Fractionalization

Martingale fragmentation solves these problems while maintaining the perfect mathematical fairness of lottery fragmentation.

Like lottery splits, Martingale splits rely on randomness to determine ownership: Alice sells 50% of her ocelots in the form of Martingale Shares or Mortys.

Over time, her remaining ownership will shrink and grow randomly in a process called Martingale, which means every step is fair. The process ends when her ownership drops to 0% or returns to 100%. As this settlement occurs over time, these shares can be traded on markets such as Uniswap, facilitating liquidity and price discovery.

At any time, Alice can replace the ocelot she uses as collateral with any other wizard hat ocelot. This means that Mortys does not represent pieces of her specific Ocelot, but pieces of the cheapest delivered or floor priced Ocelot in their category. This feature, along with Alice's ability to buy back Wizard Hat Ocelot Mortys on the open market, allows Alice to reclaim her Ocelot if luck is not in her favor.

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Mechanism Details

open a vault

Alice uses her wizard hat ocelot as collateral to open a new wizard hat ocelot vault. The vault's initial balance is 100 wizard hat ocelot Mortys.

As mentioned earlier, Alice can always replace the wizard hat ocelot she uses as collateral with any other wizard hat ocelot.

MortyCategory

Alice's Vault and Mortys are in the Wizard Hat Ocelot category, which means they can only be created with a Wizard Hat Ocelot. All Mortys of a given class are fungible. This is similar to the case of Maker, where all DAI is fungible even if it was created by different people in different vaults with different collateral.

Alice could have chosen a more restrictive category, such as an ocelot that has both a wizard hat and a scarf. Alternatively, she can choose a class with more relaxed requirements, such as the floor Ocelot class, which can be created with any Ocelot. More complex classes are possible, such as a class of Mortys that can be minted with an ocelot or two armadillos (NFTs from entirely different projects).

In this case, she chose to mint Wizard Hat Ocelot Mortys because they have the best combination of price and existing liquidity on Uniswap.

Mortys for sale

Alice sells her 50 Mortys on Uniswap's Wizard Hat Ocelot Morty / ETH market, reducing her balance in the Vault to 50 Mortys.

buy pool

From the buyer's (in this case Uniswap LP) perspective, these Morty's have no connection to Alice's specific Vault. Instead, each Morty represents a share of ownership in the Wizard Hat Ocelot Purchase Pool, which collectively constitutes a counterparty to Alice and all other Wizard Hat Ocelot Vault owners.

Martingale Settlement

Now that Alice's Vault balance is no longer 100, the process of Martingale Settlement begins.

Every night at midnight, the Morty Protocol flips one coin per Vault. If the coin comes up heads, Alice sends one of her Mortys into the buying pool. If tails, the buy pool hands one of the Mortys to Alice.

So, after the first flip, either Alice has 51 Morty and the buy-in pool has 49, or Alice has 49 Morty and the buy-in pool has 51.

This process repeats daily until Alice has either 0 Mortys or 100 Mortys. If she has 0 Mortys, she will give all ocelots currently in her vault to the buying pool. If she has 100 Morty, she will get her Ocelot back. Either way, the process will end.

Martingale Math

Because every coin toss is fair, this process is called a martingale, which means that Alice's expected balance of Morty never changes.

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View: https://colab.research.google.com/drive/1tMq0Cqa5o3T-da9m0WdBqou2CJ7QMChQ?usp=sharing

Seller NFT Retrieve

If luck is against her, Alice has two different ways to get her ocelot back.

The first way is to replace the ocelot in her Vault with another ocelot that she doesn't value much.

The second way is to mint new Wizard Hat Ocelot Mortys, or buy them on the open market, and use them to increase her Vault balance, possibly all the way up to 100.

Purchase Pool Settlement

If the Vault's balance reaches 0, ownership of any ocelots in it reverts back to the purchase pool, at which point a number of different design options are possible.

excitation

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excitation

Vault Owner Incentives

When Alice chose to use her ocelot to cast and sell Mortys, she risked losing it. Why is she doing this?

First, she has quick access to liquidity at a fair price, assuming an active market exists.

Second, there is likely to be high demand for long-term exposure to NFT categories like the Wizarding Hat Ocelot, especially from those who cannot purchase the entire Wizarding Hat Ocelot themselves. Because Alice is fulfilling this need, and taking the risk of doing so, she will likely receive compensation in the form of a higher price than she would have gotten by selling her ocelots outright.

Third, although Alice now faces Martingale risk, she has eliminated a large portion of the wizard hat ocelot bottom price risk. Depending on the volatility of the ocelot's price, her overall risk could be significantly lower.

Vault incentive

The existence of a liquid Morty marketplace could be very useful to the ecosystem of its parent NFT. For example, Morty Price can be used as an index for the people on the floor.

Given the important role of Vault owners, it might make sense to incentivize them directly. For example, a floor perp protocol might use some of its profits to compensate Morty Vault owners who put their stake to LPs on Uniswap's Morty Market.

Malicious retrieval

The purpose of Martingale Settlement (Martingale settlement) is to ensure that Morty buyers have a probability to request to receive NFT. However, there is a potential attack vector that prevents this from happening.

If Alice opens 50 different Vaults, on average she will lose 25 Morty and gain 25 Morty per flip. By moving these Mortys between her vaults, she can stabilize their balance for long periods of time.

If this behavior becomes widespread and negatively affects the perceived value or utility of Mortys, the Morty Protocol can charge Vault owners a fee when they add Mortys to their Vault and forward the revenue to the buying pool.

A simpler solution is to turn off the ability to add Mortys back to the Vault, since the ability to swap collateral still allows Vault owners to save NFTs they don't want to lose.

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Buying Pool Risk

Alice's risk in this system is relatively easy to understand: if her Vault balance is 50 Morty and she does nothing, she has a 50/50 chance of losing her ocelot.

basic situation

basic situation

First, assume that the only Vault owner in the system is Alice, who has sold 10 Mortys, 5 of them to Bob and 5 to Charlie. If Alice wins her first coin toss and wins 1 Morty, then Bob and Charlie will lose 1 Morty together, or 0.5 Morty each—a full 10% of the position.

More Vaults

However, as the vault grows, Bob and Charlie's relative risk begins to shrink. Suppose there are n Vaults, each with an average short of 50 shares, so this buying pool includes 50n Mortys.

The number of flips won by the airdrop forms a binomial distribution with variance n/4.

Bob and Charlie still only own 10 shares each, or 1/(5n) of the total, and their variance will be 1/(20n) per flip, shrinking rapidly as n grows.

Automatically unflip

We can completely eliminate long variance if there are at least two vaults.

Imagine there is an even number of Vaults, say 4. In this case, we can pair them randomly and flip the coin only once per pair, so that the "heads" flip of the first member of the pair automatically becomes the "tails" flip of the second member. Note that while we are reducing the number of bits of randomness in the system, each individual Vault will still experience Martingale.

That way, even though individual Vault balances will change with rollovers, the amount of outstanding long Morty never changes. Even with an odd number of short vaults, we can use this method by simply selecting a vault at random to exclude it from this round of flipping.

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Alternative Martingales

We can also change the random process used for settlement as long as it remains a Matingale.

For example, the coin tossing process described above may take a long time to complete. What if we designed a process that was guaranteed to end in a fixed amount of time?

Suppose Alice's vault is short n Mortys at a given time (meaning its balance is 100-n)

Our alternative Martingale system randomly decides whether to refund all n Morty's or let her walk away with her NFT, or add a Morty to her short position. In order to be a Martingale, she must have a probability of 1/(n+1) to get back n Mortys and a probability of n/(n+1) to short an additional Morty.

For example, if Alice has just minted and sold 2 Mortys, so her balance is 98 Mortys, she will have a 1/3 chance of gaining 2 Mortys for a total balance of 100, and a 2/3 chance of losing a Morty , making the balance 97. Her expected payoff is 1/3*2-2/3*1=0

This is the process necessary to become a Martingale.

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in conclusion

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in conclusion

Mortys are a strange but mathematically pure way to create partial exposure to the NFT category.

It's unclear how much demand there is for them, but they're certainly interesting to think about.

This article is from The Way of Defi, reproduced with authorization.

This article is from The Way of Defi, reproduced with authorization.