Dual-ve model


Any adoption of ve(3,3) has an extremely high likelihood of Solidly's outcome over a given time horizon. Further, an AMM does not have a treasury backing or a bonding mechanism. There's no 3, 3. No such assumption can be made.

The whole point of the Olympus DAO 3,3 equilibrium is to allow the protocol to accumulate tokens for the treasury. Even if the equilibrium changes to (-3, -3), the protocol has an undepletable treasury which incentivizes the players to coordinate a return to (3, 3). There is no comparable mechanism with an AMM. Simply put, as long as the value of emissions outweighs the value of incentives (fess and bribes), the design temporarily works - you're paying less than a dollar to get a dollar. As soon as that balance flips, the design is prone to a quick collapse without remedy. Real-world examples from forks of Solidly all share Solidly's "end state" due to a flawed game theory.

To fix the shortfalls of Solidly-tape AMMs, and avoid the inherent trap of a negative price feedback loop of a project's governance token, we suggest the following framework.

1) A balanced circulating token supply to mitigate downward price pressure

2) No hyper-inflationary token emissions and rebalancing mechanisms

3) No NFTS

4) Offer adversarial control mechanisms.

Comments: While the solution to 3) is a technicality (transferability deeply contradicts alignment of interests, however re-hypothecation may be an option), 1) is built into the USDFI design already. 2) aggressive token inflation can serve a specific purpose; it dilutes whales who come in early for "too cheap". Rebalancing them with more tokens even when locked is counterintuitive and adds more inflation on top of inflation. Additionally, aggressive token inflation is an incredibly delicate balancing act: A protocol with a massively inflating supply with not enough demand to offset goes to zero (what we call Pandora's Box effect). So what's the solution? Here, USDFI has an distinct advantage: being a Universal DeFi Banking protocol, it operates the only ecosystem with veTokenomics, AMM and a native stablecoin with a bonding-like treasury. Leveraging the composability within the same protocol, the solution 2) and 4) is: create vote-escrowed USDFI, veUSDFI.

The Game Theory of dual-ve

The assumption in the game theory of veUSDFI is as follows:

Users form beliefs about the fundamental value of the veTokenomics of the USDFI ecosystem. These are based on the value and utility around the ecosystem as a whole. However, users (specifically whales) also form beliefs about the beliefs of users and whales, a Nuhmann like contra-factually stabilized belief-expectation-equilibrium.

Players are most likely to stake STABLE when they anticipate an expansion in utility and/or price. Players are most likely to sell when they anticipate a contraction in utility and/or price. Players are most likely to stake USDFI when they do not have a strong directional bias but don’t anticipate significant downside. Selling has the negative effect of pushing the price down, but only when selling STABLE. In contrast to Olympus' design, the selling of USDFI has no price effect because it's a stable asset.

Further, in this coordination game whales can always get diluted with capital, the equilibrium of the whale is not to speculate so the perfect equilibrium for the veSTABLE holder is to stake and the veUSDFI holders is to stake. By having two price processes, we can now engage in a non zero sum game and achieve cooperation. We establish two adversarial control mechanisms.

The non-zero-sum game

In a zero-sum game, one user's gain is exactly balanced by the other user's loss. This is the case with all single-ve bribing games, where users are competing for a fixed pool of rewards.

To transform this into a non-zero-sum game, we need to change the structure of the game so that the users' interests are not entirely opposed, and there is potential for mutual benefit. It's important to understand that if players can bribe with either token, the game remains zero-sum because the total amount of rewards remains fixed. Users just have more options in terms of how they can try to maximize their share of the rewards, especially because STABLE and USDFI both have a stochastic price processes of their own. The users do not compete to modify a single price process only.

Here are the high-level aspects of the non-zero-sum game design:

  1. Shared Rewards: Instead of having a fixed pool of rewards that users compete over, we introduce a mechanism with veUSDFI where users can cooperate to increase the total pool of rewards. For example, users are rewarded for actions that benefit the overall health of the protocol, such as providing protocol-owned-liquidity or participating in governance when acquiring and vote escrowing USDFI. This way, users increase their individual rewards by working together, strengthening the design and creating a situation where the total gains with a stablecoin asset are more than zero.

  2. Cooperative Strategies: We introduce strategies that allow users to cooperate or form alliances. For example, users can agree to vote together or pool their resources to increase their collective influence with the introduction of more capital to the protocol. This creates situations where users can both benefit from their cooperation, making the game non-zero-sum.

  3. Multi-objective Games: Instead of having a single objective (maximizing individual rewards), we introduce multiple objectives that players can strive for. For example, users are rewarded for contributing to the stability of the protocol, promoting fair distribution of rewards, and other benefit from USDFI 1 always economically having the value of USD $1 in the protocol. This creates a more complex game where users can achieve different combinations of objectives, and the success of one user does not necessarily mean a loss for the other.

  4. Alternative Bribing Mechanism: If users bribe with either a governance tokens or a stablecoin, and the protocol rewards players differently based on the type of bribe, the game becomes non-zero-sum. Users can earn additional rewards by bringing in the stablecoin. These rewards are not subtracted from the existing pool of tokens, thus making the total gains possible more than zero. The game changing dynamics are:

    • Different Rewards: The protocol rewards users differently based on the type of bribe. For example, bribes made with USDFI could earn different types of rewards or benefits compared to bribes made with STABLE tokens. This could introduce additional strategies and decisions for the users, making the game more complex.

    • Increasing the Total Pool of Rewards: Because the introduction of USDFI as an alternative bribe increases the total pool of rewards, the game becomes non-zero-sum. For example, if the protocol uses the USDFI to buy more STABLE tokens and add them to the reward pool, then the total gains are more than zero. User not only compete for the existing pool of CRV tokens but also for the additional rewards.

    • Influence on Governance Decisions: If average dollar cost of two different bribe tokens has different weightings in governance decisions, it creates a more complex game where users can achieve different outcomes depending on their choice of bribe. For example, if USDFI has a stronger influence on certain votings and STABLE tokens have a stronger influence on others, users would need to decide which type of bribe to use based on their goals.

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