*4.5. Incentives and Punishment Strategies*

Although the contributions of this manuscript include performance improvement and security guarantees by EconLedger, this section briefly discusses incentive design while leaving detailed analysis for future investigation. EconLedger uses an incentive mechanism to reward validators who behave honestly and make contributions in the PoENF block generation and chain finality process. At the end of a block generation cycle, transactions fees included in the confirmed block construct a rewarding fees pool that can be distributed to all validators in the current round. The incentive mechanism uses ENF score to evaluate a validator's contribution, and reward fees that are distributed to *vi* ∈ *D* are proportional

to its ENF score *si*. Let *S* = {*<sup>s</sup>*1,*s*2, ...,*sn*} denote ENF scores, the reward rule is defined as follows:

$$\gamma\_i = \frac{\frac{1}{s\_i}}{\sum\_{i}^{u} \frac{1}{s\_i}} \mathcal{R}\_\prime \tag{3}$$

where *γi* is the reward fee that *vi* obtains from the total reward fees R during current block generation round. The smaller the ENF score of a validator, the higher the reward fees it can gain. As the variations of ENF proofs from all honest nodes are trivial during ENF collection time, collected rewarding fees in R are almost evenly distributed to honest contributors. As ENF fluctuations are randomly generated from power grids and vary at different times, Byzantine nodes can only gain marginal benefits by using duplicated or arbitrary ENF proofs that have large ENF scores.

In addition to rewarding fees, the credit stake *ci* of a honest validator *vi* will also increase by one as a reputation reward. The higher the credit stake *c*, the higher the probability that a validator is selected as a PoENF committee member. Unlike PoS, credits in EconLedger are not directly associated with any type of currency, and they are not transferable in any format of transactions. Therefore, all users are encouraged to behave honestly to gain more benefits by increasing their reputation credits. Moreover, credit stake *c* of a node cannot excel an upper-bounded limitation *Cmax*, for instance, no more than 10. Therefore, an adversary cannot simply accumulate its credit stake to achieve mining centralization and then control the majority power of the network.

A punishment strategy is also designed to discourage dishonest behaviors, such as withholding its ENF proof, proposing multiple blocks in current round, or violating chain extension rules. After PoENF committee selection, each *vi* ∈ *D* must deposit a fixed amount of fees to its *security stake sci*. If any misbehaving actions in consensus process *vi* are detected, the balance of *sci* will be slashed as punishment. In addition, its credit stake *ci* also decreases by one. Given the assumption that an adversary can only compromise no more than *f* nodes on the network, the slashing security deposit rule can increase financial cost if attackers use these compromised nodes to disturb consensus protocol, while reducing credit stake results in the lower probability that Byzantine nodes can be selected as committee members.
