If you have checked our *infoblock* about the **history of rewards**, you already know how the pot is composed and what are the sources of rewards distributed to operators

*infoblock* about the **history of rewards**, you already know how the pot is composed and what are the sources of rewards distributed to operators

the incentive mechanism is the main engine of the public blockchains

the incentive mechanism is the main engine of the public blockchains

10%

2%

5%

It is through it that operators are rewarded for the service and encouraged to act in favor of the protocol

10%

2%

5%

6.25 BTC

2 ETH

32 TRX

16 XTZ

+ 2 XTZ per *endorsement*

Bitcoin

Ethereum

Tron

Tezos

6.25 BTC

2 ETH

32 TRX

16 XTZ

+ 2 XTZ per *endorsement*

Bitcoin

Ethereum

Tron

Tezos

pay a fixed rewards per block produced

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In the Cardano blockchain, the reward mechanism is one of the most important security components of the Ouroboros protocol

developed through extensive scientific research to ensure that the mechanism leads to a decentralization of the network in the long term

**Different** from other blockchains,** the distribution of rewards** **is not fixed** per block

**Different** from other blockchains,** the distribution of rewards** **is not fixed** per block

Instead, the rewards distributed to stake pools and their delegators involve

$$f$$

$$(s, \sigma)$$

$$= \frac{R}{1 + a_0} \cdot \left( \sigma' + s' \cdot a_0 \cdot \frac{\sigma' - s' \frac{z_0 - \sigma'}{z_0}}{z_0} \right)$$

To understand the mechanism, we can look in detail at the components that are used in the calculation and how each one influences the rewards

$$f$$

$$(s, \sigma)$$

We will first consider how the reward of the stake pool is calculated as a function of **stake**

$$f$$

$$(s, \sigma)$$

is a **function** that calculates the rewards of each entity in the network based on two factors of the stake pool ...

$$f$$

$$(s, \sigma)$$

$$f$$

the stake pool's pledge

the total **stake** of the stake pool

$$(s, \sigma)$$

$$f$$

Both values are relative to the total ADAs in circulation, meaning they represent a fraction of the amount the stake pool controls of existing coins

$${s}$$

$$f$$

The fraction referring to the pledge represents the stake delegated by the pool operators themselves

$$(s, \sigma)$$

$$f$$

represents the **total delegated stake**, including the pledge and the stake of the delegators

$$ \sigma$$

$$(s, \sigma)$$

$${s}$$

$$f$$

$$(s, \sigma)$$

If there was only one stake pool, we could distribute the entire **pot of rewards** to this one regardless of other factors

$$= {R} $$

Let's assume that this pot contains a total of **200 thousand ADAs**

**200 thousand ADAs**

$$f$$

$$(s, \sigma)$$

$$= {R} $$

Let's assume that this pot contains a total of

**200 thousand ADAs**

To divide the pot proportionally to the relative stake of each entity, we need to consider the parameter **σ** multiplying the total rewards in the pot

$$= {R} \cdot$$

$$ \sigma$$

$$f$$

$$(s, \sigma)$$

$$= {R} $$

Vamos supor que esse pote contém um total de

$$= {R} \cdot$$

$$ \sigma$$

Ignoring pledge for now, if a stake pool holds 1% of all circulating ADA

$$ \sigma = 0.01 $$

**200 thousand ADAs**

$$f$$

$$(s, \sigma)$$

$$= {R} $$

Vamos supor que esse pote contém um total de

$$= {R} \cdot$$

$$ \sigma$$

$$ \sigma = 0.01 $$

it would receive 1 % of the pot

$$(s, \sigma)$$

$$f$$

$$= {200000} \cdot {0.01}={2000}$$

**200 thousand ADAs**

The problem that emerges from associating the rewards in a directly proportional way is that *stake pools* with higher stakes always receive most of the rewards

becoming larger and possibly centralizing the network through huge entities

To control the growth of the rewards of a single stake pool, there is the concept of a **saturation point** that limits the reward gain

$${z_0}$$

$${z_0}$$

= saturation point

Currently, it corresponds to approximately

equivalent to about 212 million ADAs

Through this parameter, we limit the amount of stake considered in the calculation of rewards up to a maximum of 0.667% of total ADA

σ

σ'

to denote that participation will be capped by the saturation point

Let's put a line

σ

σ'

$${z_0}$$

$$ \sigma = 0.01 $$

$$(s, \sigma)$$

$$f$$

$$= {200000} \cdot {0.0667}={1334}$$

$$f$$

$$(s, \sigma)$$

$$= {R} \cdot$$

$$ \sigma'$$

= saturation point

**200 thousand ADAs**

In our previous example, a stake pool would be limited to receive a maximum of

$${z_0}$$

$$ \sigma = 0.01 $$

$$f$$

$$(s, \sigma)$$

$$= {R} \cdot$$

$$ \sigma'$$

$$(s, \sigma)$$

$$f$$

$$= {200000} \cdot {0.00667}={1334}$$

= saturation point

**200 thousand ADAs**

The purpose of the pledge is *to protect the network* from a Sybil attack

However, we are not yet considering how the * pledge* influences the calculation of rewards

providing greater rewards for operators who commit and delegate their own funds to the stake pool and discouraging the creation of several pools with low stake

$${a_0}$$

as the **pledge influenc**e factor, currently set to

$${a_0}$$

The Ouroboros protocol implements the parameter

$${a_0} = {0.3}$$

Writing the reward calculation function including the **pledge influence** factor and the** stake pool pledge**

*Let's skip the saturation point, for now, to try to keep it simple*

$$f$$

$$(s, \sigma)$$

$$= \frac{R}{1 + a_0} \cdot \left( \sigma + s \cdot a_0 \right)$$

$${a_0}$$

The last changes we need to make to the formula are related to *the saturation point*, which also needs to be included in the calculation

$${z_0}$$

$${s}$$

$${s'}$$

multiplying one more term to finally get to the final form of the reward function

We limit the **pledge** to *the saturation point* in the same way as we did with the total stake

$${s}$$

$${s'}$$

$$f$$

$$(s, \sigma)$$

Note that **if** the pledge influence factor is null

$$f$$

$$(s, \sigma)$$

$${a_0}=0$$

*we have again the reduced form*

$$f$$

$$(s, \sigma)$$

$$= {R} \cdot$$

$$ \sigma'$$

Since the rewards of a stake pool are calculated with the function described, the value obtained is adjusted by a **performance factor** that weights the rewards in relation to the number of blocks produced

β

σ

**Produced Blocks**

**21600**

*representing a fraction in the form of** *

This factor is calculated by

fraction of **blocks produced by the pool** in a epoch

β

σ

**Produced Blocks**

**21600**

the fraction of **relative stake** controlled by the pool

β

σ

This factor is calculated by

They are fractions that must obtain the same value over time

β

σ

so that the fraction of blocks generated is proportional to the controlled stake

β

σ

Since the drawing of *slots* to define the entities that will produce blocks works like a lottery, sometimes a pool can produce more or less blocks than expected

but on average the performance factor should be equal to 1 for pools with ideal performance

but on average the performance factor should be equal to 1 for pools with ideal performance

*slots* to define the entities that will produce blocks works like a lottery, sometimes a pool can produce more or less blocks than expected

There is a difference in the reward for generating more or less blocks, but **there is no fixed value of rewards** as in other networks

In the long run, the reward is proportional to the stake controlled by the *stake pool*

**there is no fixed value of rewards** as in other networks

In the long run, the reward is proportional to the stake controlled by the *stake poo*l

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