TL;DR

• USUALx is USUAL's staked token version that provides governance power, economic rights, and automatically compounds rewards from native USUAL distributions.

• USUALx holders receive 10% of all USUAL distributions, 33,33% of system fees, and future rights to the DAO treasury.

• As fewer users stake their tokens, USUALx holders receive increased rewards, resulting in higher yields for those who participate long-term.

• The system is designed to prioritize sustainable, long-term growth by aligning incentives for committed users. This system rewards long-term believers over those who might be tempted to simply farm tokens and sell them.

  
  

Introduction

A quite usual man once said:

Like the tortoise, steady and humble in stride,
While the hare takes a rest with his fleeting pride,
Each step you take, rewards will grow,
Compounding in ways the impatient won’t know.

At the heart of Usual, two key players take center stage: the tortoise and the hare. The tortoise, a cautious and methodical veteran, embodies patience and discipline, playing the long game with a clear focus on sustainable and long-term value. The hare, by contrast, is a swift and daring risk-taker, eager to seize immediate opportunities and maximize short-term yield. While these two players are not in direct competition, their decisions inevitably influence each other’s outcomes.

This dynamic creates a delicate balance—a game of strategy and trade-offs played within the game of money which is Usual. The rewards and penalties within the system shape this game, creating a matrix of choices and outcomes. Each participant, whether tortoise or hare, navigates this matrix based on their unique goals and risk tolerance.

However, this is no static game… The dynamic has changed and continues to evolve.

With the Token Generation Event (TGE) and the airdrop around the corner, so will be the USUAL token alongside its staked counterpart, USUAL; a new product that vastly changes the dynamic of USUAL. As such, this article explores the game theory given the new introduction of USUALx; revealing how it shapes the decision-making landscape for both the value-driven tortoise and the risk-demanding hare.

Understanding USUALx

While USUAL is the native token, it does not directly have governance or economic rights and is fully liquid. USUALx, on the other hand, is the staked & liquid (LST) version of USUAL which claims both governance power and economic rights. These economic rights fall into three main categories:

1. Distribution:
   10% of all USUAL distributed is allocated as rewards to USUALx holders. Rewards are auto-compounded, making USUALx a self-compounding financial instrument. This mechanism applies to any future USUAL distributed to USUALx as rewards.

2. Allocation of USUAL-denominated fees:

   One-third (approximately 33.33%) of all USUAL used to pay system fees is allocated as rewards for USUALx holders. These fees include, but are not limited to, unstaking fees for USUALx and early redemption fees for USD0++. As the use of USUAL for system fees grows with new features, this allocation will remain constant.

3. Revenue Switch Mechanism:

   The DAO accrues treasury from interest earned on USD0 collateral. While currently undistributed, a revenue switch mechanism will redirect this treasury as dividends to USUALx holders. This ensures that users must stake USUAL to claim economic value when the revenue switch is activated.

Using this information, we can estimate the APY for USUALx. Specifically, the APY can be calculated based on the proportion of USUAL staked in the system and the 10% distribution right.

Disclaimer:
The calculations are based on conservative assumptions, including a 25% staking rate. The airdrop and Binance Launchpool were assumed to be fully liquid to ensure a prudent estimation. Our goal was to avoid inflating the numbers excessively and provide a realistic outlook.

For reference, 41% of veCRV is staked, which is close to the 50% staked estimate used above. Even at higher staking percentages, USUALx still provides a relatively high yield. A few examples of other protocols and the percentage of their tokens staked are as follows:

*Data taken as of December 10th, 2024.

Regardless, the rewards estimated do not account for the built-in decision matrix, which can further amplify these rewards. As noted in the second economic right above, 33% of all USUAL-denominated fees are allocated as rewards to USUALx holders. This can result in higher yield for USUALx holders as other stakers leave (directing more USUAL to them).

Overall, USUALx is structured to be a high-yielding financial instrument, with rewards amplified as short-term users exit, strengthening the alignment of long-term users with the protocol.

Diving into this further, we can see how the game theory for the system works around USUALx.

Game theory behind the system

The system incentivizes long-term participation through steady rewards and redistributes fees from departing short-term users. This approach strengthens loyal users' positions while ensuring their interests align with the protocol's goals. The resulting equilibrium creates dynamic rewards for long-term stakers, driven by two factors: the proportion of users staking (with fewer stakers receiving higher rewards) and the redistribution of rewards from departing users to those who remain.

We can illustrate this concept using two decision matrices that show abstract payoffs (these don't reflect actual USUAL rewards). After depositing into USD0++ (or LP) and receiving rewards, users face three choices: exit by cashing out, stay by holding USUAL, or stake their USUAL for USUALx. The following matrix shows how these choices play out.

USD0++ Decision Matrix (Post Deposit)

The highest payoff occurs when users stake USUALx while others remain unstaked. This is because USUALx rewards are a fixed percentage of the total USUAL distribution—when fewer users stake, the reward pool stays constant but each staker receives a larger share. This design sets USUALx apart from typical staking programs, which usually distribute rewards proportionally based on each staker's relative position.

Example (hypothetical)

User 1 and User 2 both have 10,000 USD0++ deposited.

1. Leave: When a user sells their USD0++, they forfeit all future USUAL earnings. Their future payout becomes 0 USUAL, represented as 0 in the matrix.

2. Stay: A user who keeps their USD0++ continues earning USUAL. For example, each user might earn 100 USUAL daily. This scenario is represented by 1 in the matrix.

3. Stake: Users who stake their earned USUAL rewards receive additional USUAL. For instance, 100 staked USUAL might earn 10 USUAL daily (assuming full staking participation). This payout varies based on staking participation—if only half of users stake, the rewards increase since they're independent of total staked amount. In this case, 100 USUAL might earn 20 USUAL daily instead of 10. When all users stake (both User 1 and User 2), the payout is represented as 2. When only some users stake, the payout is represented as 3.

Hypothetical payouts in this example may differ from real payouts. Refer to USUAL dApp or Whitepaper for a better understanding of USD0++ and USUALx payout.

Additionally, staking rewards increase when users unstake and pay fees. One-third (33.33%) of these fees goes to remaining stakers, boosting their returns. This second reward dimension is straightforward: rewards grow as more users exit, as shown in the following matrix.

USUALx decision matrix (Post Stake)

Similar to how the tortoise stays steady and humble on his path while the hare pauses to rest, rewards here compound with each step, ensuring that the most USUAL is distributed to those who remain staked.

Example (hypothetical)

User 1 and User 2 both have 100 USUAL staked (USUALx).

1. Leave: A 10% unstaking fee is applied when users unstake their USUAL. This means that if a user unstakes, they pay a 10 USUAL fee and withdraw 90 USUAL. As a result, the payout for leaving is represented as 1.

2. Stay: Users who stake 100 USUAL may earn 10 USUAL per day. However, when other users leave and pay a 10% unstaking fee, 33% of this fee is reallocated to the remaining stakers. For example, if only User 1 and User 2 are staking, and User 1 leaves, User 2 will receive an additional 3.33 USUAL (33% of the 10 USUAL fee paid by User 1). This, in addition to the 20 USUAL per day earned from staking, results in a total of 23.33 USUAL per day for User 2. This payout is represented as 2, accounting for both the reallocated fees and rewards from the user who left.

Hypothetical payouts in this example may differ from real payouts. Refer to USUAL dApp or Whitepaper for a better understanding of USUALx payout.

Therefore, the complete picture looks like this:

So, how can we best interpret this? USUAL is intentionally designed to ensure that long-term holders reap significantly greater rewards compared to short-term, aggressive farmers. Unlike other protocols that often prioritize short-term farming at the expense of long-term users, our system fosters sustainable growth for the entire ecosystem. This makes USUAL particularly appealing to committed users seeking to maximize value and benefit from long-term deposits as it facilitates an equilibrium among long and short term users unlike other protocols.

In the end, the tortoise crosses the finish line first… but does that make him the winner?

Conclusion

Who wins in the game of money we call Usual? Everyone. The tortoise may cross the finish line first but everyone has the chance to play. In other words, the system is designed to promote long-term growth and sustainability, yet it allows any participant to enter and benefit. Thus, anyone can enter and the difference in reward lies in the rules, which are structured to reward the tortoise over the hare, offering better incentives to those with a long-term commitment.

All users contribute value to the system, but to align incentives and penalties effectively, the framework prioritizes long-term holders over short-term participants. This principle, though it may vary slightly in implementation across features, remains consistent across all current and future Usual offerings, especially USUALx.