Consensus Mechanism and Economic Model

The original Bitcoin blockchain uses a consensus model referred to as Nakamoto consensus [@nakamoto2008peer]. It uses a sequential model in which a block is built, mined, and verified, and consensus about it is formed by nodes building subsequent blocks on top of it, based on the longest chain rule. While the proof-of-work challenge (mining) that must be solved for every block provides tamper-resistance for the chain, the associated computational effort decides Poisson winning rate. Proof of Work consensus mechanism leads to waste of computational resources and constraints on scalability.

The leading proposals for removing the constraints and resource consumptions of proof-of-work adapt Byzantine Fault Tolerant (BFT) consensus algorithms [@kwon2014tendermint; @moniz2020istanbul]. In general, finalizing blocks through BFT consensus requires a known set of participants, a super-majority of which must be honest and only partial synchrony [@lamport2019byzantine].

BFT consensus has been combined with proof-of-stake (PoS) to create incentive mechanism for a secure and permissionless system. Under PoS, all participating nodes are required to deposit a (financial) stake that can be taken away if they violate the protocol's rules. The amount of influence given to each node is proportional to its fraction of total stake. Then the economic pressure (i.e., the stake at risk) to follow the protocol is correlated with a node's influence. In addition, the deposited stake has the added benefit of preventing Sybil attacks. PoS system, compared to Proof of Work systems, is more efficient in utilizing capital costs while maintaining the security and temper proof nature of the chain. Most of the projects in the current Web3 blockchain world are based on PoS, including Ethereum2.0, Solana, Polkadot, Algorand etc..

The ETM/P consensus mechanism is based on delegated Proof of Stake (DPoS). Like PoS, DPoS allocates token inflation rewards and governing power based on the state distribution and staked value of the nodes. DPoS differs from PoS in two aspects:

• There is a relatively small number of validation nodes during each epoch and they are usually identified in terms of reputation and security, in addition to holding large amount of stake;

• Other nodes may delegate their stake to the large stake holders and share the reward directly via contracting.

Recent events and theoretical analysis may illustrate the advantages of using Delegated Stake of Proof mechanism.

• Efficiency, scalability and operational stability. Many academic works have shown that Byzantine Byzantine Fault Tolerant (BFT) consensus algorithms, without assuming a global synchrony, need a certain degree of centralization to ensure safety and liveness [@harvey2021defi]. Many public blockchains have tried to solve this problem by various means but have not fully resolved this problem. For example, Solana has had multiply times of breakdown due to synchrony issues. Layer 2 solutions, such as optimism, has been exposed to attacks. Restricting the proposition and validations of blocks to a small number of accredited nodes can apparently improve stability.

• Economic stability. The staking reward and transaction fee reward are the engines of growth and there is a natural demand for participation. In Ethereum2.0, there exists a high threshold (32ETH and indefinite lockup time) to become validators. The demand of participation engendered third party DeFi services such as Lido and derivative product like stETH. This has been one of the causes of recent market collapse and has led to the instability of ETH token system. With Delegated Stake of Proof mechanism, small stake holders can easily participate by voting, staking and rewards sharing with known, accredited nodes in the system.

• The Delegated Stake of Proof mechanism does not undermine decentralization. Each node has sufficient autonomy both economically and in terms of expressing its view, since each node can choose to stake or un-stake at any given time, by itself or delegate to any node of its choice. Moreover, the ETM DAO (Decentralized Autonomous Organization) will provide a fertile ground for the exchanges of ideas and information communication.

The ETM token is the native and governance token of the ETM/P blockchain. It is used as the medium of exchange and store of value in the ETM infrastructure. ETM token has several important characteristics that make it the ideal currency for Web3.0 applications and DeFi2.0. It is completely compatible with ERC standards, with regulated inflation and broad distribution. Transactions can be done on ETM/P main net with low fees and deterministic finality. By design of the blockchain, a scalable fully replicated structure that is shared among all participants and guarantees a consistent view of all user transactions by all participants in the ETM system. The on-chain governance of Decentralized Autonomous Organization (DAO) and the distribution of inflated ETM/P token depend on the staking mechanism. Moreover, staking mechanism in ETM/P is essential to the consensus mechanism and economic incentive. As a Delegated Proof of Stake blockchain, the ETM/P requires potential validators nodes to lock up a security deposit denominated in ETM/P tokens in a smart contract, in order to participate in the random selections of validators for each round. Staking prevents low cost "sybil" attacks (where one actor masquerades as many individuals to gain undue influence over the network) and acts as a deposit that can be slashed if the validator attempts to commit malicious behaviors. The probability of a node becoming an actual validator is determined by the proportion of its stake vis a vis the total stake escrowed in this smart contract. 21 validators are re-elected in each round. Within each round, these validators process the transaction on the main net according to the Istanbul Byzantine fault tolerant consensus mechanism. The ordering of these 21 nodes is subjected to persistent permutations. Validators receive rewards in 3 ways:

• Validators receive staking reward, distributed via the dynamic equilibrium mechanism from the token inflation.

• Validators receive a portion of transaction fees.

• Validators benefit from the value increase of the ETM token in the long term.

All rewards are denominated in the ETM/P tokens. This incentivize the validators to act dutifully in the validation process and safeguard the ETM system.

Staking is an essential part of the ETM economic system: it helps to stabilize the token circulation and demand. Staking reward, generated from the aggregate token inflation, is not uniquely distributed to validators. Anyone with ETM tokens can stake to earn reward, much like earning interests from a banking system. The ETM staking reward design achieves the following objectives:

• The staking reward is allocated with fixed inflation in the token system.

• Staking reward per token (marginal reward) increases when staking ratio is low, decreases when the ratio is high.

• Staking reward per token (marginal reward) is adjusted dynamically via a feedback mechanism and changes with the creation of each new block, roughly in every 3 seconds. We call this real time dynamic rebalancing.

The fixed inflation schedule serves to preserve scarcity of the ETM/P token and protect the interests of token holders. On the other hand, excessive inflation can create a range of unintended consequences and causes downward pressure on the token prices (denominated by the stablecoins, for example). Therefore, staking reward needs to be carefully tuned to balance between bounded inflation and incentive for staking nodes. This is also important for attracting new users and expanding the ecosystem. Since all rewards are denominated in ETM/P tokens, even though high reward may boost the inflow of new users in the short term, the potential devaluation of the native token caused by high inflation will discourage users in the long term.

The automatic adjustments of the parameters to control the ETM/P economic system is guided by the real time dynamic rebalancing. This is one of the key features and main innovations of ETM/P for optimizing user incentives and achieving a stable dynamic equilibrium. By updating smart contract aggregate variables after each block, triggered by interaction of users with the smart contract itself, the dynamic equilibrium mechanism improves the reward transparency and price continuity in the economic system. Users can engage more actively in transactions with less risk. Moreover, the smart contracts of ETM/P use dynamic, data driven models to manage risk and provide value to the users.

We outline some details of the real time dynamic rebalancing mechanism and how it achieves a state of equilibrium:

The first year inflation rate is $i=0.1$ and will be adjusted year by year. For more details we refer to the section on ETM tokenomics. We can then calculate the inflation per each block. Let $i_n$ denotes the inflation rate per block, since inflation is always compounded we have

$n=20\times 60\times 24\times 365=10512000.$

$(1+i_n)^n=1+i, \,\,\,\ln(1+i_n)=\frac{1}{n}\ln(1+i).$ Since $i_n$ is very small, we can use the formula $\ln(1+i_n)\approx i_n$ and obtain

$i_n=\frac{1}{n}\ln(1+i).$

We can then calculate the reward to be distributed after each block. Each validator can claim its reward according to its proportion in the staking pool. With the action of each node (stake, un-stake), the smart contract recalculates and updates the current distribution of the staking pool.

We can obtain a simple estimate of the APY given the current data. Let $B_n$ denotes the total token in circulation at the time of block $n$ and $S_n$ denotes the number of tokens staked. $r_n$ denotes the reward per token of the each staking node.

$S_n\times r_n=B_n\times i_n \times(1-\delta).$

Let $\delta$ denotes the direct allocation of the inflation to reward the validators for performing their duties, for now let $\delta=0$. When $S_n/B_n$ is small, marginal reward will automatically increase to incentivize staking. On the other hand, marginal reward will decrease when $S_n/B_n$, in order to incentivize the utilization of the token.

Suppose $B/S$ remains constant, it can be used to estimate the APY, such that

$r=(1+r_n)^n=(1+\frac{B}{S}\cdot \frac{1}{n}\ln(1+i))^n \approx (i+1)^{B/S}.$

This will help the validator estimates the potential P&L and makes decisions dynamically. However, it should be noted this estimate may be far from the true APY as one cannot predict the fluctuation of $S_n/B_n$ as $n$ changes.

It is worth noting that, by smart contract structural design, rational agents in the ETM economic system are incentivized to use feedback control strategies. A feedback control strategy means that implementing the optimal control as a simple deterministic function evaluation at the current state of the system. More concretely, a node searching seeking to maximize stake yield will adjust its token asset allocation by observing the aggregate staking ratio. The feedback control allows us to understand the cause of a decision, and explain its dependence on the state dynamics and policy constraints. A feedback control also allows us to justify the fairness of the token distribution mechanism.

The prospect of modeling and numerical simulation for ETM economic system goes far beyond simple APY estimation. By implementing real time dynamic rebalancing mechanism, ETM opens the door to the wide applications of continuous time financial models, forward backward stochastic differential equations and partial differential equations. Systemic risk, liquidation risk and all kinds of factors can be modeled and simulated much more accurately in the ETM economic system than previous PoS systems. This will pave the way to the composition of complicated financial instruments (the DeFi Lego) with data driven, quantitative risk management.