Making Markets for Rewards in a Global Economy

@po_oamen|October 18, 2024 (3m ago)124 views

This article provides a high-level overview of market-making for loyalty rewards and highlights key technical considerations for doing so effectively. It also introduces the Dual Value Market Maker (DVMM) algorithm as a suitable approach for enabling efficient reward markets within a decentralized, trustless system.

Introduction

Rewards, broadly defined as incentives provided by businesses to their customers, are among the most enduring and effective strategies for fostering customer loyalty. Their origins date back to ancient times, with some evidence of their use in Egyptian marketplaces [1]. However, it wasn’t until the 18th century that rewards began to take on a more recognizable form, where businesses issued copper tokens that could be exchanged for future purchases to their customers [1]. Today, rewards programs have evolved into a complex, multi-dimensional strategy, with more than 80% of businesses worldwide incorporating some form of loyalty initiative—ranging from points and discounts to coupons, cashback, free products, free shipping, and more [2]. The global loyalty market, currently valued at over $100 billion, is expected to surpass $200 billion by 2027 [4] and this growth trajectory shows no sign of slowing down, particularly as technological innovation and customer-centric solutions continue to advance.  Blockchain technology, in particular, is poised to revolutionize the loyalty space by creating decentralized, trustless systems that can fuel unparalleled customer engagement.

In this exposition, I will explore the concept of market-making for rewards in the global economy, particularly leveraging a decentralized and trustless system. The emphasis on decentralization and trustlessness is crucial, as these characteristics provide the optimal framework for serving a universal economy that comprises millions of businesses worldwide, each with its strategy, goals, and vision. A decentralized and trustless perpetual running machine ensures that no central authority holds disproportionate influence, while simultaneously offering a zero downtime, frictionless, secure, and transparent environment that works anywhere, and that eliminates the need for trust among parties.  Most importantly, this approach aligns seamlessly with the global scale and complexity of modern rewards ecosystems.

Market Making

At its core market-making, refers to the provision of liquidity to facilitate the "tradability" of an asset. In the case of rewards, it would mean the provision of liquidity to facilitate the exchange of rewards between businesses. In essence, making markets for rewards would allow a business customer to exchange the rewards earned from that business for those of another. This concept is in the words of  Bryan Pearson  "a loyalty leap," as it fundamentally reshapes the loyalty landscape, unlocking new possibilities for customer engagement and business growth. While there are many compelling reasons for businesses to open up their rewards programs (make them interoperable)—ranging from increased customer retention to expanded market reach—this paper does not delve into those motivations. Readers interested in exploring the rationale behind exchangeable rewards are encouraged to review existing literature, such as the insightful works published by the Me Protocol Team and similar projects leading innovation in this area. Instead, this work focuses on the technical and operational aspects of "making markets for rewards," specifically within the context of a decentralized, trustless infrastructure

To make a market for any asset, a Market Maker is needed. Think about the times when you wanted to buy stocks, shares, or cryptocurrencies—you simply went online and made the purchase. You were able to buy because someone else (an institution or another entity) was willing to sell. Similarly, when you decided to sell that asset, you could do so because someone else was willing to buy. The entity buying or selling from you is a market maker, providing the liquidity you need to enter or exit the market; making the market for you! It is important to note that this is different from peer-to-peer trades, where you need to find someone willing to buy or sell at a specific price. A market maker, on the other hand, is always ready to buy or sell at nearly every price level, regardless of the market dynamics of the asset.

From a technical perspective, market makers can be broadly classified into three main types: traditional, electronic, and automated. Traditional market makers rely on human traders to manually place bids (buy orders) and asks (sell orders) to create a market. These traders ensure liquidity by actively managing buy and sell orders, responding to changes in demand and supply in real time. With the advancement of technology, electronic market makers emerged, automating this process. Electronic systems now handle the task of placing and managing orders, significantly increasing efficiency and reducing human error. The most groundbreaking type of market maker, especially within decentralized systems, is the Automated Market Maker (AMM).

Automated Market Making

Automated Market Makers (AMMs) operate fundamentally differently from traditional and electronic market makers, as they do not use order books to match buyers and sellers. Instead, AMMs rely on algorithms to manage asset pricing. These algorithms adjust prices based on the ratio of assets in liquidity pools, effectively balancing supply and demand without the need for an intermediary. Since Bancor in 2017 and the groundbreaking success of Uniswap in 2018, AMMs have gained widespread recognition, particularly in decentralized and trustless systems like blockchains. The appeal of AMMs lies in their ability to function autonomously, free from the risks associated with centralized control, such as manipulation, downtime, or censorship. By providing continuous liquidity and operating without the need for a central authority, AMMs have proven to be highly effective in decentralized ecosystems. As a result, they have become the preferred mechanism for enabling decentralized liquidity markets.

Various types of AMMs exist, each defined by the specific algorithm that governs their operations. Some of the most widely used include Constant Function Market Makers (CFMMs), such as Constant Sum Market Makers (CSMMs), Constant Product Market Makers (CPMMs), and Constant Mean Market Makers (CMMM). Other notable types include the Stable Swap Invariant, used in protocols like Curve Finance, and various hybrid models that combine features from multiple AMM types. Additionally, newer models such as Dynamic Automated Market Makers (DAMMs), which adjust liquidity provisioning based on market conditions, and Weighted Automated Market Makers (WAMMs), which use different asset weightings in liquidity pools, have emerged, each offering unique characteristics and behaviors tailored to specific use cases.

Suppose we want to allow for the exchange between a Reward A and another Reward B, using an AMM. We will need to provide some quantity of Reward A, say a , and some quantity of Reward A, say b , in a pool, and then leave the AMM to do its magic. Anyone who wants some B rewards will simply need to deposit some A rewards into the pool, and the AMM will determine the amount of B rewards to give, based on its algorithm, and actually give it.

The constant product algorithm, for example, is in its simplest form expressed as Its main objective is to keep f(a,b) invariant, i.e., the same, throughout the entire lifecycle of its price action, such that:

This means that the product of a (the quantity of Reward A) and b (the quantity of Reward B) in the pool remains constant. We can compute the price of obtaining a unit of Reward B with respect to Reward A, by taking a total differential of f(a,b).

given:

we can differentiate both sides with respect to a and b to obtain:

Rearranging this equation we get:

which is the rate of change of Reward B with respect to Reward A.Thus, the price is a function of the ration of the assets in the pool.

Specifically, when you trade some reward A, say Δa for some reward B say Δb, the exchange token reserves are updated to a new states a' and b':

where and . Also, we have:

Of course the above computation does not take into considerations the exchange fees. When a fee is applied, the amount of Reward B obtained is reduced by a factor of ( 1 - λ), where λ is the fee rate. The new differential becomes:

Solving for the price with the fee we arrive at:

The updated reward reserves are:

where , and . Also, we have:

Making Markets For Rewards

Like many other AMM algorithms, the constant product algorithm is functional but not ideal for market-making reward assets.

Rewards represent a unique asset class, distinct from conventional cryptocurrencies because their intrinsic value is tied to the issuing business and not solely determined by the market forces of supply and demand. For example, a coffee shop might issue 4 coffee points, intending for customers to redeem them for a 10% discount on a $100 coffee purchase. By simple arithmetic, we can infer that each coffee point is worth about 2.5 dollars. Now irrespective of the dynamics in the market this customer should be able to get the discount with those points. If we decide to market-make this coffee point with a pizza point from a nearby store using CPMM, we will soon run into a situation where the coffee points are no longer intrinsically worth $2.5; it could have gone higher or lower based on market forces and this is not the focus of many businesses looking to open up their rewards program.

It seems necessary to find a way to respect the intrinsic value assigned to a reward by the issuing business while still allowing for the influence of market forces. This challenge led to the development of a concept I first proposed in the Me Protocol white paper: the dual-valued AMM algorithms.

Dual Value Market Makers

Dual-valued AMMs (DVMMs) are specifically designed for nuanced asset classes like rewards. They operate by allowing an asset to maintain two values at any given time: an intrinsic value and a relative value. The algorithm determines which value to apply based on specific conditions.

In the Me Protocol, for instance, the dual-valued algorithm (DVMM) is used to give businesses some control over their reward pools. Every reward is paired against a primary asset (the Me token) to prevent direct pool combinations between different businesses and eliminate the need for multiple combinations. Businesses are able to set the intrinsic value of their rewards, while the relative value is determined by market demand and supply, just like in other AMMs. The Me Protocol's DVMM applies the intrinsic value for every bid and the relative value for every ask. This is intriguing because it allows rewards to be bid at their optimal value, while the ask reflects market dynamics, such that if many users of a business are exchanging their rewards for those of other businesses it becomes more expensive to do so and hence encourages the customers to use their rewards on their brand and it would only go back to become favorable to exchange out if customers from other businesses also exchange their rewards for the those of the concerned business or new liquidity is added. This is in itself very valuable to businesses because it not only helps them satisfy existing customers and acquire new ones but also accounts for the stability of their rewards program.

In DVMMs, the intrinsic and relative values can be computed using different logics. In the Me Protocol, the intrinsic value is a single value R_i , which is the slope of a straight-line equation with zero intercept such that:

Where a is the number of brand rewards A in the pool and m is the number of Me tokens. Usually, this value is taken just when the pool is being activated (time, t = 0), and it is called the optimal value R_opt, such that:

hence businesses are incentivized to setup their rewards pools such that the ratio of rewards to Me tokens in the pool is at the intrinsic value.

A brand can also update the intrinsic value R_i at any time t provided that:

The relative value of the DVMM is determined using another algorithm, which is further detailed in the Me Protocol white paper. However, there are key factors to consider when setting the relative value:

1. Scale Invariance

In the context of AMMs, scale invariance refers to the property where the relative price and behavior of the AMM remain consistent, even when the total liquidity (reserves) in the pool is proportionally scaled up or down. In simpler terms, if you increase or decrease the reserves of both tokens by the same percentage, the price determined by the AMM stays the same. This is crucial because businesses come in different sizes, and the system should function smoothly for both large enterprises and small to medium-sized businesses, regardless of the liquidity they can provide—whether it’s $100 or $100,000. The constant product formula for example is scale invariant, being an homogeneous function:

To prove this, let's scale both a and b by a common factor λ. The new scaled values will be λa and λb. We substitute these into the original equation:

Simplifying the left-hand side:

Now, using the fact that the original product a . b = k, we substitute k into the equation:

For the equation to remain consistent, we must have:

computing the marginal price, we differentiate both sides of the equation λa * λb = λ^2 * K with respect to a:

Using the chain rule for differentiation:

Rearranging the terms to solve for the marginal price, or how much b is received for an additional unit of a:

The marginal price remains:

Even with the scaling factor λ, the marginal price is unchanged, showing that the constant product formula remains scale invariant. This means that scaling the reserves proportionally does not change the relative price behavior of the AMM.

2. Price Sensitivity and Impact

Each time an exchange occurs within an AMM, the price of assets in the pool adjusts. Price sensitivity refers to the degree of this adjustment—it measures how responsive the AMM is to changes in the asset quantities within its liquidity pool. In contrast, price impact is the specific change in price caused by executing a trade. It reflects the difference between the market price before the trade and the new price afterward, as a result of shifts in the asset ratio in the pool.

Price sensitivity is typically influenced by the size of the liquidity pool and the specific AMM algorithm used. For rewards, it's crucial to maintain relatively low price sensitivity to minimize price slippage (the change in price after each trade). Therefore, selecting the right AMM is essential.

We can compute the price sensitivity of any AMM by differentiating the price function P. For the CPMM

The price of asset A in terms of asset B is given by:

To compute the price sensitivity, we need to differentiate the price P _A with respect to a.

Using the quotient rule, this becomes:

The derivative tells us that the price of asset A in terms of B becomes more sensitive as a decreases. This is also applicable to asset B.

To find the total price impact for a trade of size Δa (when the reserve changes from a to a + Δa), we integrate the price sensitivity from a to a + Δa:

Evaluating the definite integral gives:

Simplifying:

Thus, the price impact for a trade of size Δa is:

This shows that the impact depends on the trade size Δa and the current reserves a and b in the liquidity pool. Larger trades relative to the pool size cause more significant price shifts.

3. Slippage

Slippage is the difference between the expected price of a trade and the actual price at which the trade is executed, caused by the trade's price impact. Managing slippage in an open rewards economy is crucial, as many business customers may not be familiar with this concept and could become frustrated if they are charged a price different from the one quoted, or if their transaction fails due to a phenomenon (slippage) they don't fully understand.

Conclusion:

In this paper, I have introduced the concept of market-making for rewards in a global economy and explained why it makes sense to create such markets on a decentralized, trustless system. I have highlighted the benefits of using Automated Market Makers (AMMs) as the ideal market-making mechanism due to their autonomous and decentralized nature, while also exploring algorithms suited for managing rewards. To build efficient automated markets for rewards, it is important to recognize that rewards are a distinct asset class with intrinsic value, independent of market fluctuations. Traditional AMMs are not optimal for handling this, which is why I introduced the dual-valued algorithm in the Me Protocol white paper. This approach properly addresses the unique challenges of rewards and has strong potential for creating and managing reward markets on a global scale. Additionally, when choosing an AMM algorithm, it's essential that it is scale-invariant, optimally price-sensitive, and minimizes slippage to provide businesses and their customers with a seamless experience for managing their reward systems.

Thank you for reading, Anon! Keep building.

References

[1] B. J. Kemp, Ancient Egypt: Anatomy of a Civilization, 2nd ed. London, UK: Routledge, 2005.

[2] J. Nagle, “Trading Stamps: A Long History,” The New York Times, Dec. 26, 1971. [Online]. Available: https://www.nytimes.com/1971/12/26/archives/trading-stamps-a-long-history-premiums-said-to-date-back-in-us-to.html. [Accessed: Apr. 22, 2020].

[3] Queue-it, “Loyalty program statistics,” Queue-it Blog, 2023. [Online]. Available: https://queue-it.com/blog/loyalty-program-statistics/#:~:text=More%20than%2090%25%20of%20companies,you'll%20get%20a%20hit. [Accessed: Oct. 17, 2024].

[4] GlobeNewswire, “Global loyalty programs intelligence report 2024: Market to grow by 11.1% to surpass 150 billion this year,” GlobeNewswire, Apr. 4, 2024. [Online]. Available: https://www.globenewswire.com/en/news-release/2024/04/04/2857513/28124/en/Global-Loyalty-Programs-Intelligence-Report-2024-Market-to-Grow-by-11-1-to-Surpass-150-Billion-this-Year-Forecasts-to-2028.html. [Accessed: Oct. 17, 2024].

[5] B. Pearson, The Loyalty Leap: Turning Customer Information into Customer Intimacy. New York, NY: Portfolio, 2012.

[6] Y. Zhang, X. Chen, and D. Park, "Formal Specification of Constant Product (a × b = k) Market Maker Model and Implementation," Runtime Verification, Inc., Oct. 24, 2018.

[7] Hayden Adams, Uniswap contract, [Online]. Available: https://github.com/Uniswap/contracts-vyper.

[8] Vitalik Buterin, "The a*b=k market maker model," [Online]. Available: https://ethresear.ch/t/improving-front-running-resistance-of-x-y-k-market-makers.

[9] M. Egorov, "Automated Market Maker: Curve Finance," Curve Finance, Nov. 2020. [Online]. Available: https://curve.fi/files/stableswap-paper.pdf. [Accessed: Oct. 17, 2024].

[10] Hayden Adams, "Uniswap V2 Core," Uniswap, Mar. 2020. [Online]. Available: https://uniswap.org/whitepaper.pdf. [Accessed: Oct. 17, 2024].

[11] Hayden Adams, Noah Zinsmeister, and Dan Robinson, "Uniswap V3 Core," Uniswap, Mar. 23, 2021. [Online]. Available: https://uniswap.org/whitepaper-v3.pdf. [Accessed: Oct. 17, 2024].