Proof of Stake Simulator

In this repository we present a Proof-of-Stake Simulator written in Julia. We used this simulator in order to study the trend of Gini coefficient under different consensus algorithms.

Parameters

• n_epochs: The number of epochs to be simulated, that corresponds to the number of blocks (virtually) validated.
• proof_of_stake: The type of PoS to be used. It takes values in the set Weighted, OppositeWeighted, GiniStabilized.
• initial_stake_volume: The initial number of coins, distributed among the peers according to the next parameter.
• initial_distribution: The initial distribution of coins among the validators. It takes values in the set Uniform, Gini, Random.
• n_peers: The number of participants (the same as $N$ in the formulas above) in the blockchain that aim to be selected as validators.
• n_corrupted: The number of validators in the blockchain that could exhibit corrupted behavior according to a probability p_fail.
• p_fail: The probability that a corrupted validator tries not to validate correctly the block.
• penalty_percentage: The percentage of coins removed (slashed) from the amount of coins staked by the corrupted validators, in case they show corrupted behavior.
• p_join: The probability, at each epoch, of a new user to join the validators. The new user can be labeled as corrupted with a probability equal to the initial ratio of corrupted peers over the total number of peers.
• p_leave: The probability, at each epoch, of any validator to quit the pool.
• join_amount: The amount of coins owned by a peer that just joined the set of validators. It takes values in the set Average, Random, Max, Min.

How to use

First import the required simulator:

include ("src/Simulator.jl")

be sure to point the correct src folder.

Next, create a Parameter object containing all the parameters. A basic set of parameters can be created as follows:

parameters = Parameters()

Then, each parameter can be changed individually. In order to execute a simulator, we require two other elements: an initial stake and a set of corrupted peers. The first one can be created as follows:

stakes = generate_peers(parameters.n_peers, 
                            parameters.initial_stake_volume, 
                            parameters.initial_distribution, 
                            parameters.starting_gini);

Then the subset of corrupted peers, is simply created as follows

corrupted = rand(1:parameters.n_peers, parameters.n_corrupted)

We can finally run an experiment as follows:

history, peers = simulate(stakes, corrupted, parameters);

The variable history will contain the Gini coefficient computed at the end of each epoch, and peers will contain the number of peers at the end of each epoch. Examples can be found in the examples folder, and are described below.

Experiment 1 and 2

Online notebook available:

We use Weighted PoS in order to show the trend for $g$ to go to 1, and OppositeWeighted PoS in order to show the trend for $g$ to go to 0

Experiment 3

Online notebook available:

We use GiniStabilized PoS to show that it is possible to control the Gini coefficient $g$. We set a target value $\theta = 0.3$ and plot the trend of $g$. In particular, we chose a Constant update for GiniStabilized

Experiment 4

Online notebook available:

We use GiniStabilized PoS and Linear updates, showing that it is possible to obtain a smooth trend for the Gini coefficient around the target value $\theta$.

Experiment 5

In this experiment we want to run different simulations on different types of ${\tt g_funct}$ All the simulations share a lot of parameters (such as the number of epochs, the number of peers, the PoS type and so on), but they differ on the function applied to $s$ at each epoch. We remark that:

• Constant $$s = k$$
• Linear $$s = |s - \theta| / k$$
• Quadratic
• $$s = |s - \theta|^2 / k$$ We run the following five simulations:

1. Constant, $k=1 / 1000$
2. Linear, $k = 10$
3. Linear, $k = 100$
4. Quadratic, $k = 10$
5. Quadratic, $k = 100$

Test it online here:

Authors

• Alberto Leporati (alberto.leporati@unimib.it)
• Lorenzo Rovida (lorenzo.rovida@unimib.it)

Made with <3 at Bicocca Security Lab, at University of Milan-Bicocca.