The Nash Equilibrium and Ve Model in a Sybil Free Environment: Part 1

The lead-up to a be-all-end-all experiment

In game theory, the Nash Equilibrium determines the optimal solution in a non-cooperative game in which each player lacks the incentive to change his/her initial strategy.

With the beginning of DeFi Summer in 2020 and the advent of succulent, yet imaginary yields coming out of the juiciest fruit coin around, liquidity mining programs became the de-facto standard for DeFi protocols to bootstrap their liquidity. At first, this method seemed to be very efficient. However, its weaknesses started to show up over time, as more and more protocols imitated the model.

One farm after the other, native token issuance started to be perceived by investors as a cost-efficient manner to incentivize liquidity providers. Rushed by FOMO, retail participants also chased their piece of the pie and started to engage more actively in protocol governance and operations. Subsequently, so many protocols blindly followed the narrative without giving any further thought to the secondary effects that would later show up.

Among the unintended consequences, which started to become more and more obvious, the emission of inflationary assets from a protocol treasury is the one that stood out the most, up to the point that some external actors referred to this activity as “magic internet money printing”. However, even with this magic, most protocols could not avoid the inherent selling pressure that comes from high token emission rates.

And that’s how a new design that quickly gained traction emerged, the ve model, whose goal was to achieve the perfect game theoretical equilibrium with respect to the incentive alignment of both long-term committed token holders and short-term speculators. This system consisted in giving different weights to different people in a Sybil-free environment.

Looking at it from a DAO perspective, where everything is on-chain, it is easy to support the argument that there must be different reward weights assigned to each participant based on their incentives. For example, short-term traders should have less power to influence the protocol’s trajectory and skew it in their favor. For example, if you are a token holder with a long-term commitment to the protocol, you wouldn’t want things like flash loans manipulating gauges, draining community funds…

The basis for understanding this mechanism design in a Sybil-free environment is that there is no credibility behind an Ethereum address. And even if there was, this credibility would be easily traded on a secondary market. Here is where the ve model intervenes by vesting tokens in a 4-year decaying ratio to the people who want long-term success for the protocol.

• If you lock up for the maximum amount of 4 years, then you get 1 veCRV for every CRV
• If you lock up for 1 year, you get 0.5 veCRV for every CRV

Since veCRV decides what pools get whitelisted, what protocols can participate in the flywheel, and who gets CRV rewards… this created a whole ecosystem where bribes became the prevalent law. As a consequence, protocols saw an opportunity to create their own environment within the Curve ecosystem. In doing so, they launched their own stablecoin and attempted to direct liquidity to their own pool in order to benefit from the pegging mechanism that the Curve AMM provides.

Over time, Curve factories became a thing, which democratized access to the flywheel. However, that is not enough to attract enough liquidity. The reason why some Curve pools earn a lot of incentives is because they have a lot of liquidity. In other words, if you are an LP to one of these pools you will get the CRV token, which you could then lock up for more veCRV, which boosts your rewards even more… and now you are a player in a meta-game which you thought would leave the most sophisticated game theorists in disbelief. Going back to the protocol, it is now willing to provide its own incentives on top of the CRV rewards in order to attract liquidity. The problem is that now the protocol needs to convince veCRV holders to vote for its pool. At the beginning, it was not an easy task. You had to find out who those whales were, how to talk to them…But all of a sudden bribes come into play and the Curve wars began, aka “I will give you a percentage of my native token supply so that you vote for my pool”.

As you can see, a new meta game started. From the LPs point of view, if you are a LP and you don’t hold any veCRV, the protocol will act as if you had provided only 40% of your liquidity (you provide 100 units of liquidity and the protocol only takes 40 into account for its calculations). On the contrary, if you hold the maximum amount of veCRV, your contribution gets boosted by a 2.5x multiplier which turns those 40 units of liquidity into 100 units. There are more calculations involved, but this is the basic idea you need to understand.

Essentially, if you want to maximize your CRV rewards, then you must optimize for the amount of veCRV, which means that you have to lock up your tokens for at most 4 years, and who knows what the price of CRV will be in 4 years. Did Curve even exist 4 years ago? This is a big sacrifice considering the huge opportunity cost of being invested in a protocol for such a long period of time.

But that’s not the end of the Curve Wars, since Convex Finance entered the DeFi scene by building a governance layer on top of Curve and its ve design. This was the beginning of a new flywheel that allowed for 3 possible activities with different reward mechanisms respectively.

• Staking LP tokens: Providing liquidity on the Curve and staking those LP tokens into Convex. This lets a user earn boosted $CRV rewards without holding veCRV.
• Staking CRV in exchange for yield-bearing cvxCRV. Rewards for cvxCRV are similar to those of holding veCRV, except for the upside of holding a liquid token plus a 10% CRV distribution from protocol fees.
• Staking and locking CRV for around 1% additional rewards

All these 3 action accrue value for CVX tokens while also increasing the voting power of Convex over Curve. Convex currently holds more than 50% of veCRV

Because of this new unexpected dynamic introduced by Convex, now Convex made it possible for any individual to boost their position, since Convex would lock up CRV in your behalf. On top of, Convex also introduced off-chain voting for emissions. Now there are two options: vote with veCRV, or use CVX tokens.

Remember how at the beginning we mentioned how beneficial Curve’s pegging mechanism was for protocols that issue their own stablecoin like MIM, FRAX…? Well, now this protocols have the alternative of using CVX, which has a lower locking period of 16 weeks.

In part II, we will not cover Votium, Redacted Butterfly accumulating CVX…but rather a more game theoretical approach that will involve well known actors like Andre Cronje and Daniele Sesta. Part II will serve as an introduction to the ve(3,3) model, which combines the ve model with the prisioner’s dilemma implemented by Olympus Dao and its most famous fork Wonderland.

Hope this piece was helpful to understand the origin of the Curve Wars. This series of articles aims to be a primer on the token design mechanism experiments that rode the entire impulse to the top of the 2021 bull market. If you would like to share feedback or disagree with some of the statements made in this article, do not hesitate to reach out on Twitter. If you enjoyed Part I, feel free to share and stay tuned for what’s coming next :)