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Mathematical functions are changing our lives as we know them. They are solving our problems in a structural, efficient and fast way, leaving behind our illogicality. The human brain has amazing capabilities, but coherent thoughts and actions are sometimes buffered via our emotions, leading to a less desired outcome. This is especially the case in our financial world, where our decisions can easily be obfuscated leading to irrationality. By using a mathematical function that creates a relationship between the supply of an asset and its price, we can reduce volatility and create a more forwarded guided valuation.

# Human Irrationality = Errors + Volatility

Humans are governed by their emotions, not their minds, we are irrational entities. As a result, we can make decisions that are not in our self-interest, leading to errors and cognitive bias. This affects us every day, whether it be as simple as our breakfast choice or more importantly, our financial decisions. Emotions including gluttony, fear, lust, and desire have an impact on our centralized monetary system. These financial choices of an individual can have large impacts on the economy, resulting in economic instability and volatility. Economist Karl Marx first introduced the theory that explains why capitalism is inevitably vulnerable to the ‘boom and bust’ cycle. According to him, these alternating phases of economic expansion and contraction are as much directed by investor and consumer psychology than the principles of the current market and economy.

# Decentralized Automated Market Maker

To moderate the effects of behavioral economics, thus moderating human error we can use a systematic mathematical function to create a relationship between the supply of an asset and the price. A token bonding curve does exactly this. It is essentially a decentralized automated market maker, built using a smart contract on a blockchain network. To simplify this, let’s break it down, a token bonding curve contains three key aspects.

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1. The token standard- the issuance and supply of an asset.
2. The bond(s)- the reserved collateral.
3. The curve- the mathematical function.

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Each of these parameters can be altered to fulfill a desired incentive or model. This means bonding curves can be designed to match the behavior you want from investors or the public to the type of function that incentives that particular action.

# Use Cases

There are many application scenarios for which a token bonding curve can be used, including raising funds, making bets, dynamically pricing a good and even as a currency. A great example is the token bonding curve used on the [SORA](https://sora.org) network. SORA is a substrate network built for the DeFi future, it uses a token bonding curve as its primary market maker. The token supply of XOR (the native token of SORA) is elastic, meaning the token price is a function of the token supply, with a greater increase in supply will result in a greater value. This function benefits SORA as their economic system is built around Richard Werner’s ‘A Quantity Theorem of Disaggregated Credit’; creation and allocation of purchasing power for new goods and services or technology implementations results in the growth of an economy without inflation.

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SORAs bonding curve uses a simple model where there are two linear functions: a Buy-Price Function and a Sell-Price Function. The buy function is a simple linear function with the equation Y=MX+C. With m being the gradient of the function and c being a constant value.

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 ![](https://cdn.hackernoon.com/images/flyOvusxnrSGGNZa43Ox47MrS4t1-t993ny5.png)

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In simple words, SORA’s token bonding curve is essentially an infinitely liquid, decentralized central bank. At any time, you can buy newly minted XOR tokens from the token bonding curve using some specific reserve assets, or sell your XOR tokens (which are instantly burned) for one of those assets. This allows for more forward-guided price predictability, making XOR tick all three attributes of money.

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 ![](https://cdn.hackernoon.com/images/flyOvusxnrSGGNZa43Ox47MrS4t1-tua3nos.png)

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Another instance of a bonding curve is [NOIR](https://noir.digital). NOIR is a phygital (physical + digital) wine token on the SORA network. Each NFT token is tied to a bottle of luxury wine, so buying NOIR tokens is the same as buying bottles of the wine. NOIR is dynamically priced, using a continuously priced XYK function. The way NOIR token operates is that there is a contract that holds quantity X of NOIR and quantity Y of XOR, and always maintains the invariant that XY=K for some constant K. Redeeming the bottle of wine burns the NOIR token, increasing the XOR value of the NFT.

 

 ![](https://cdn.hackernoon.com/images/flyOvusxnrSGGNZa43Ox47MrS4t1-8hc3nbj.png)

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Rational Valuation Using Price Functions Token bonding curves are the solution to reducing volatility and human error. A bonding curve manages the supply of an asset in a rational way, where the price of an asset is determined by the supply. This occurs without the involvement of humans or a central government, to create a system that avoids the boom-bust problems of traditional economies and the deflationary economics of many digital currencies, such as Bitcoin. A bonding curve creates a predictable flow between assets, creating a safety barrier for irrationality. In the use-case of SORA, it uses a multi-collateralized bonding function to limit the volatility and generate instant liquidity via continuous burn and minting. In terms of NOIR, the bonding curve creates a dynamically priced market based on the scarcity of NOIR tokens in relation to XOR. Via using a decentralized automated market maker, we can securely create a structural, efficient and fast way to limit irrational variability.

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