unit_e_economics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<script>\n",
       "code_show=true; \n",
       "function code_toggle() {\n",
       " if (code_show){\n",
       " $('div.input').hide();\n",
       " } else {\n",
       " $('div.input').show();\n",
       " }\n",
       " code_show = !code_show\n",
       "} \n",
       "$( document ).ready(code_toggle);\n",
       "</script>\n",
       "The raw code for this IPython notebook is by default hidden for easier reading.\n",
       "To toggle on/off the raw code, click <a href=\"javascript:code_toggle()\">here</a>."
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('''\n",
    "<script>\n",
    "code_show=true; \n",
    "function code_toggle() {\n",
    " if (code_show){\n",
    " $('div.input').hide();\n",
    " } else {\n",
    " $('div.input').show();\n",
    " }\n",
    " code_show = !code_show\n",
    "} \n",
    "$( document ).ready(code_toggle);\n",
    "</script>\n",
    "The raw code for this IPython notebook is by default hidden for easier reading.\n",
    "To toggle on/off the raw code, click <a href=\"javascript:code_toggle()\">here</a>.''')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import types\n",
    "\n",
    "class Validator:\n",
    "    def __init__(self, deposit, start_dynasty):\n",
    "        # Used to determine the amount of wei the validator holds. To get the actual\n",
    "        # amount of wei, multiply this by the deposit_scale_factor.\n",
    "        self.deposit = deposit\n",
    "        self.start_dynasty = start_dynasty\n",
    "        self.end_dynasty = 100000000\n",
    "        self.is_slashed = False\n",
    "        self.total_deposits_at_logout = 0\n",
    "        # The address which the validator's signatures must verify against\n",
    "        self.addr = None\n",
    "        self.withdrawal_addr = None\n",
    "\n",
    "\n",
    "class Checkpoint:\n",
    "    def __init__(self):\n",
    "        # track size of scaled deposits for use in client fork choice\n",
    "        self.cur_dyn_deposits = 0\n",
    "        self.prev_dyn_deposits = 0\n",
    "        # track total votes for each dynasty\n",
    "        self.cur_dyn_votes = {0: 0}\n",
    "        self.prev_dyn_votes = {0: 0}\n",
    "        # Is a vote referencing the given epoch justified?\n",
    "        self.is_justified = False\n",
    "        # Is a vote referencing the given epoch finalized?\n",
    "        self.is_finalized = False\n",
    "\n",
    "\n",
    "class CasperContract:\n",
    "\n",
    "    def __init__(self):\n",
    "\n",
    "        # Map of validators and validator index\n",
    "        self.validators = dict()\n",
    "\n",
    "        # Next available validator index\n",
    "        self.next_validator_index = 0\n",
    "\n",
    "        # Current dynasty, it measures the number of finalized checkpoints\n",
    "        # in the chain from root to the parent of current block\n",
    "        self.dynasty = 0\n",
    "\n",
    "        # Map of the change to total deposits for specific dynasty\n",
    "        self.dynasty_wei_delta = {0: 0.0}\n",
    "\n",
    "        # Total scaled deposits in the current dynasty\n",
    "        self.total_curdyn_deposits = 0\n",
    "\n",
    "        # Total scaled deposits in the previous dynasty\n",
    "        self.total_prevdyn_deposits = 0\n",
    "\n",
    "        # Mapping of dynasty to start epoch of that dynasty\n",
    "        self.dynasty_start_epoch = {0: 0}\n",
    "\n",
    "        # Mapping of epoch to what dynasty it is\n",
    "        self.dynasty_in_epoch = {0: 0}\n",
    "\n",
    "        self.checkpoints = {0: Checkpoint()}\n",
    "\n",
    "        # Is the current expected hash justified\n",
    "        self.main_hash_justified = False\n",
    "\n",
    "        # Value used to calculate the per-epoch fee that validators should be charged\n",
    "        self.deposit_scale_factor = {0: 1.0}\n",
    "\n",
    "        self.last_nonvoter_rescale = 0.0\n",
    "        self.last_voter_rescale = 0.0\n",
    "\n",
    "        self.current_epoch = 0\n",
    "        self.last_finalized_epoch = 0\n",
    "        self.last_justified_epoch = 0\n",
    "\n",
    "        # Reward for voting as fraction of deposit size\n",
    "        self.reward_factor = 0.0\n",
    "\n",
    "        # Expected source epoch for a vote\n",
    "        self.expected_source_epoch = 0\n",
    "\n",
    "        # Running total of deposits slashed\n",
    "        self.total_slashed = {0: 0.0}\n",
    "\n",
    "        # ***** Parameters *****\n",
    "\n",
    "        # Length of an epoch in blocks\n",
    "        self.EPOCH_LENGTH = 50\n",
    "\n",
    "        # Withdrawal delay in blocks\n",
    "        self.WITHDRAWAL_DELAY = 1.5e4\n",
    "\n",
    "        # Logout delay in dynasties\n",
    "        self.DYNASTY_LOGOUT_DELAY = 700\n",
    "\n",
    "        self.BASE_INTEREST_FACTOR = 7e-3\n",
    "        self.BASE_PENALTY_FACTOR = 2e-7\n",
    "        self.MIN_DEPOSIT_SIZE = 1.5e21\n",
    "        self.ETHER_IN_WEI = 1e18\n",
    "        self.ONE_WEI = 1e-18\n",
    "\n",
    "        self.DEFAULT_END_DYNASTY = 100000000\n",
    "\n",
    "        # ****** Pre-defined Constants ******\n",
    "\n",
    "        self.SLASH_FRACTION_MULTIPLIER = 3\n",
    "\n",
    "    # Returns number of epochs since finalization.\n",
    "    def esf(self):\n",
    "        return self.current_epoch - self.last_finalized_epoch\n",
    "\n",
    "    # Compute square root factor\n",
    "    def sqrt_of_total_deposits(self):\n",
    "        epoch = self.current_epoch\n",
    "        ether_deposited_as_number = 1 + math.floor(\n",
    "            max(self.total_prevdyn_deposits, self.total_curdyn_deposits) *\n",
    "            self.deposit_scale_factor[epoch - 1] /\n",
    "            self.ETHER_IN_WEI\n",
    "        )\n",
    "\n",
    "        sqrt = ether_deposited_as_number / 2.0\n",
    "        for i in range(20):\n",
    "            sqrt = (sqrt + (ether_deposited_as_number / sqrt)) / 2.0\n",
    "        return sqrt\n",
    "\n",
    "    def deposit_exists(self):\n",
    "        return self.total_curdyn_deposits > 0.0 and self.total_prevdyn_deposits > 0.0\n",
    "\n",
    "    def in_dynasty(self, validator_index, _dynasty):\n",
    "        start_dynasty = self.validators[validator_index].start_dynasty\n",
    "        end_dynasty = self.validators[validator_index].end_dynasty\n",
    "        return (start_dynasty <= _dynasty) and (_dynasty < end_dynasty)\n",
    "\n",
    "    # Increment dynasty when checkpoint is finalized.\n",
    "    def increment_dynasty(self):\n",
    "        epoch = self.current_epoch\n",
    "        # Increment the dynasty if finalized\n",
    "\n",
    "        if self.dynasty not in self.dynasty_wei_delta:\n",
    "            self.dynasty_wei_delta[self.dynasty] = 0.0\n",
    "\n",
    "        if epoch < 2 or self.checkpoints[epoch - 2].is_finalized:\n",
    "            self.dynasty += 1\n",
    "            self.total_prevdyn_deposits = self.total_curdyn_deposits\n",
    "\n",
    "            if self.dynasty - 1 in self.dynasty_wei_delta:\n",
    "                self.total_curdyn_deposits += self.dynasty_wei_delta[self.dynasty - 1]\n",
    "\n",
    "            self.dynasty_start_epoch[self.dynasty] = epoch\n",
    "        self.dynasty_in_epoch[epoch] = self.dynasty\n",
    "        if self.main_hash_justified:\n",
    "            self.expected_source_epoch = epoch - 1\n",
    "        self.main_hash_justified = False\n",
    "\n",
    "    def insta_finalize(self):\n",
    "        epoch = self.current_epoch\n",
    "        self.main_hash_justified = True\n",
    "\n",
    "        if epoch > 0:\n",
    "            self.checkpoints[epoch - 1].is_justified = True\n",
    "            self.checkpoints[epoch - 1].is_finalized = True\n",
    "            self.last_justified_epoch = epoch - 1\n",
    "            self.last_finalized_epoch = epoch - 1\n",
    "        else:\n",
    "            self.checkpoints[0].is_finalized = True\n",
    "            self.checkpoints[0].is_justified = True\n",
    "            self.last_justified_epoch = 0\n",
    "            self.last_finalized_epoch = 0\n",
    "\n",
    "    # Returns the current collective reward factor, which rewards the dynasty for high-voting levels.\n",
    "    def collective_reward(self):\n",
    "        epoch = self.current_epoch\n",
    "        live = self.esf() <= 2\n",
    "        if not self.deposit_exists() or not live:\n",
    "            return 0.0\n",
    "        # Fraction that voted\n",
    "        cur_vote_frac = 0\n",
    "        if self.expected_source_epoch in self.checkpoints[epoch - 1].cur_dyn_votes:\n",
    "            cur_vote_frac = self.checkpoints[epoch - 1].cur_dyn_votes[\n",
    "                                self.expected_source_epoch] / self.total_curdyn_deposits\n",
    "        prev_vote_frac = 0\n",
    "        if self.expected_source_epoch in self.checkpoints[epoch - 1].prev_dyn_votes:\n",
    "            prev_vote_frac = self.checkpoints[epoch - 1].prev_dyn_votes[\n",
    "                                 self.expected_source_epoch] / self.total_prevdyn_deposits\n",
    "\n",
    "        vote_frac = min(cur_vote_frac, prev_vote_frac)\n",
    "        return vote_frac * self.reward_factor / 2.0\n",
    "\n",
    "    # Reward the given validator & miner, and reflect this in total deposit figured\n",
    "    def proc_reward(self, validator_index, reward):\n",
    "        # Reward validator\n",
    "        self.validators[validator_index].deposit += reward\n",
    "        start_dynasty = self.validators[validator_index].start_dynasty\n",
    "        end_dynasty = self.validators[validator_index].end_dynasty\n",
    "        current_dynasty = self.dynasty\n",
    "        past_dynasty = current_dynasty - 1\n",
    "        if (start_dynasty <= current_dynasty) and (current_dynasty < end_dynasty):\n",
    "            self.total_curdyn_deposits += reward\n",
    "        if (start_dynasty <= past_dynasty) and (past_dynasty < end_dynasty):\n",
    "            self.total_prevdyn_deposits += reward\n",
    "        if end_dynasty < self.DEFAULT_END_DYNASTY:  # validator has submit `logout`\n",
    "            self.dynasty_wei_delta[end_dynasty] -= reward\n",
    "\n",
    "    # Removes a validator from the validator pool\n",
    "    def delete_validator(self, validator_index):\n",
    "        self.validators[validator_index] = None\n",
    "\n",
    "    def total_curdyn_deposits_in_wei(self):\n",
    "        return self.ONE_WEI * math.floor(self.total_curdyn_deposits * self.deposit_scale_factor[self.current_epoch])\n",
    "\n",
    "    def total_prevdyn_deposits_in_wei(self):\n",
    "        return self.ONE_WEI * math.floor(self.total_prevdyn_deposits * self.deposit_scale_factor[self.current_epoch])\n",
    "\n",
    "    def deposit_size(self, validator_index):\n",
    "        return self.ONE_WEI * math.floor(\n",
    "            self.validators[validator_index].deposit * self.deposit_scale_factor[self.current_epoch])\n",
    "\n",
    "    # Called at the start of any epoch\n",
    "    def initialize_epoch(self, epoch):\n",
    "\n",
    "        # must track the deposits related to the checkpoint _before_ updating current_epoch\n",
    "        self.checkpoints[epoch] = Checkpoint()\n",
    "        self.checkpoints[epoch].cur_dyn_deposits = self.total_curdyn_deposits_in_wei()\n",
    "        self.checkpoints[epoch].prev_dyn_deposits = self.total_prevdyn_deposits_in_wei()\n",
    "\n",
    "        self.current_epoch = epoch\n",
    "\n",
    "        self.last_voter_rescale = 1.0 + self.collective_reward()\n",
    "        self.last_nonvoter_rescale = self.last_voter_rescale / (1.0 + self.reward_factor)\n",
    "\n",
    "        if epoch > 0:\n",
    "            self.deposit_scale_factor[epoch] = self.deposit_scale_factor[epoch - 1] * self.last_nonvoter_rescale\n",
    "            self.total_slashed[epoch] = self.total_slashed[epoch - 1]\n",
    "\n",
    "        if self.deposit_exists():\n",
    "            # Set the reward factor for the next epoch.\n",
    "            adj_interest_base = self.BASE_INTEREST_FACTOR / self.sqrt_of_total_deposits()\n",
    "            # self.reward_factor = adj_interest_base\n",
    "            self.reward_factor = adj_interest_base + self.BASE_PENALTY_FACTOR * (self.esf() - 2)\n",
    "            # ESF is only thing that is changing and reward_factor is being used above.\n",
    "            assert self.reward_factor > 0.0\n",
    "        else:\n",
    "            # Before the first validator deposits, new epochs are finalized instantly.\n",
    "            self.insta_finalize()\n",
    "            self.reward_factor = 0\n",
    "\n",
    "        # Increment the dynasty if finalized\n",
    "        self.increment_dynasty()\n",
    "\n",
    "    def deposit(self, value):\n",
    "        assert value >= self.MIN_DEPOSIT_SIZE\n",
    "        validator_index = self.next_validator_index\n",
    "        start_dynasty = self.dynasty + 2\n",
    "        scaled_deposit = value / self.deposit_scale_factor[self.current_epoch]\n",
    "        self.validators[validator_index] = Validator(scaled_deposit, start_dynasty)\n",
    "        self.next_validator_index += 1\n",
    "\n",
    "        if start_dynasty not in self.dynasty_wei_delta:\n",
    "            self.dynasty_wei_delta[start_dynasty] = 0\n",
    "\n",
    "        self.dynasty_wei_delta[start_dynasty] += scaled_deposit\n",
    "        return validator_index\n",
    "\n",
    "    def logout(self, validator_index):\n",
    "\n",
    "        # Check that we haven't already withdrawn\n",
    "        end_dynasty = self.dynasty + self.DYNASTY_LOGOUT_DELAY\n",
    "        assert self.validators[validator_index].end_dynasty > end_dynasty\n",
    "\n",
    "        self.validators[validator_index].end_dynasty = end_dynasty\n",
    "        self.validators[validator_index].total_deposits_at_logout = self.total_curdyn_deposits_in_wei()\n",
    "        self.dynasty_wei_delta[end_dynasty] -= self.validators[validator_index].deposit\n",
    "\n",
    "    def withdraw(self, validator_index):\n",
    "        # Check that we can withdraw\n",
    "        end_dynasty = self.validators[validator_index].end_dynasty\n",
    "        assert self.dynasty > end_dynasty\n",
    "\n",
    "        end_epoch = self.dynasty_start_epoch[end_dynasty + 1]\n",
    "        withdrawal_epoch = end_epoch + self.WITHDRAWAL_DELAY\n",
    "        assert self.current_epoch >= withdrawal_epoch\n",
    "\n",
    "        # Withdraw\n",
    "        if not self.validators[validator_index].is_slashed:\n",
    "            withdraw_amount = self.ONE_WEI * self.validators[validator_index].deposit * self.deposit_scale_factor[\n",
    "                end_epoch]\n",
    "        else:\n",
    "            # prevent a negative lookup in total_slashed\n",
    "            if 2 * self.WITHDRAWAL_DELAY > withdrawal_epoch:\n",
    "                base_epoch = 0\n",
    "            else:\n",
    "                base_epoch = withdrawal_epoch - 2 * self.WITHDRAWAL_DELAY\n",
    "\n",
    "            recently_slashed = self.total_slashed[withdrawal_epoch] - self.total_slashed[base_epoch]\n",
    "            fraction_to_slash = recently_slashed * self.SLASH_FRACTION_MULTIPLIER / self.validators[\n",
    "                validator_index].total_deposits_at_logout\n",
    "\n",
    "            # can't withdraw a negative amount\n",
    "            fraction_to_withdraw = max((1.0 - fraction_to_slash), 0.0)\n",
    "\n",
    "            deposit_size = self.ONE_WEI * math.floor(\n",
    "                self.validators[validator_index].deposit * self.deposit_scale_factor[withdrawal_epoch])\n",
    "\n",
    "            withdraw_amount = self.ONE_WEI * math.floor(deposit_size * fraction_to_withdraw)\n",
    "\n",
    "        self.delete_validator(validator_index)\n",
    "        return withdraw_amount\n",
    "\n",
    "    # Process a vote message\n",
    "    def vote(self, validator_index, source_epoch, target_epoch):\n",
    "\n",
    "        # Record that this vote took place\n",
    "        in_current_dynasty = self.in_dynasty(validator_index, self.dynasty)\n",
    "        in_prev_dynasty = self.in_dynasty(validator_index, self.dynasty - 1)\n",
    "\n",
    "        current_dynasty_votes = 0\n",
    "        if source_epoch in self.checkpoints[target_epoch].cur_dyn_votes:\n",
    "            current_dynasty_votes = self.checkpoints[target_epoch].cur_dyn_votes[source_epoch]\n",
    "\n",
    "        previous_dynasty_votes = 0\n",
    "        if source_epoch in self.checkpoints[target_epoch].prev_dyn_votes:\n",
    "            previous_dynasty_votes = self.checkpoints[target_epoch].prev_dyn_votes[source_epoch]\n",
    "\n",
    "        if in_current_dynasty:\n",
    "            current_dynasty_votes += self.validators[validator_index].deposit\n",
    "            self.checkpoints[target_epoch].cur_dyn_votes[source_epoch] = current_dynasty_votes\n",
    "        if in_prev_dynasty:\n",
    "            previous_dynasty_votes += self.validators[validator_index].deposit\n",
    "            self.checkpoints[target_epoch].prev_dyn_votes[source_epoch] = previous_dynasty_votes\n",
    "\n",
    "        # Process rewards.\n",
    "        # Pay the reward if the vote was submitted in time and the vote is voting the correct data\n",
    "        reward = 0\n",
    "        if self.expected_source_epoch == source_epoch:\n",
    "            reward = self.validators[validator_index].deposit * self.reward_factor\n",
    "            self.proc_reward(validator_index, reward)\n",
    "\n",
    "        # If enough votes with the same source_epoch and hash are made,\n",
    "        # then the hash value is justified\n",
    "        two_thirds_curdyn = current_dynasty_votes >= self.total_curdyn_deposits * 2.0 / 3.0\n",
    "        two_thirds_prevdyn = previous_dynasty_votes >= self.total_prevdyn_deposits * 2.0 / 3.0\n",
    "        enough_votes = two_thirds_curdyn and two_thirds_prevdyn\n",
    "\n",
    "        if enough_votes and not self.checkpoints[target_epoch].is_justified:\n",
    "            self.checkpoints[target_epoch].is_justified = True\n",
    "            self.last_justified_epoch = target_epoch\n",
    "            self.main_hash_justified = True\n",
    "\n",
    "            # If two epochs are justified consecutively,\n",
    "            # then the source_epoch finalized\n",
    "            if target_epoch == source_epoch + 1:\n",
    "                self.checkpoints[source_epoch].is_finalized = True\n",
    "                self.last_finalized_epoch = source_epoch\n",
    "\n",
    "        return reward\n",
    "\n",
    "    # Cannot sign two votes for same target_epoch; no surround vote.\n",
    "    def slash(self, validator_index):\n",
    "\n",
    "        validator_deposit = self.deposit_size(validator_index)\n",
    "        slashing_bounty = validator_deposit / 25\n",
    "        self.total_slashed[self.current_epoch] += validator_deposit\n",
    "        self.validators[validator_index].is_slashed = True\n",
    "\n",
    "        # if validator not logged out yet, remove total from next dynasty\n",
    "        # and forcibly logout next dynasty\n",
    "        end_dynasty = self.validators[validator_index].end_dynasty\n",
    "        if self.dynasty < end_dynasty:\n",
    "            deposit = self.validators[validator_index].deposit\n",
    "            self.dynasty_wei_delta[self.dynasty + 1] -= deposit\n",
    "            self.validators[validator_index].end_dynasty = self.dynasty + 1\n",
    "\n",
    "            # if validator was already staged for logout at end_dynasty,\n",
    "            # ensure that we don't doubly remove from total\n",
    "            if end_dynasty < self.DEFAULT_END_DYNASTY:\n",
    "                self.dynasty_wei_delta[end_dynasty] += deposit\n",
    "            # if no previously logged out, remember the total deposits at logout\n",
    "            else:\n",
    "                self.validators[validator_index].total_deposits_at_logout = self.total_curdyn_deposits_in_wei()\n",
    "\n",
    "        return slashing_bounty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ethereum and Casper economics\n",
    "\n",
    "### General definitions\n",
    "\n",
    "Let's start giving some generic useful definitions used extensively.\n",
    "\n",
    "\n",
    "#### Epoch\n",
    "An epoch is a set of $\\sigma$ subsequent blocks where $\\sigma \\in \\mathbb{N}$ is called \"epoch size\".\n",
    "\n",
    "Given the epoch size $\\sigma$, and the set of all the existing blocks $\\{b_{genesis}, b_1, ..., b_i\\}$ we define the _n-th_ epoch as $ e_{n,\\sigma}=\\{b_{n\\sigma}, b_{n\\sigma+1}, ..., b_{n\\sigma+\\sigma-1}\\} $.\n",
    "\n",
    "the epoch size $\\sigma$ is a static parameter initialized and never changed after the final definition of the protocol. For simplicity it will not be part of further difinitions.\n",
    "\n",
    "\n",
    "#### Dynasty\n",
    "A dynasty is a set of epochs that have been finalized together. This represents the dynasty of validators that is active for such epochs.  \n",
    "\n",
    "If we define the set of all epochs $E=\\{e_0, ..., e_n\\}$ and the set of all dynasties $D=\\{d_0, ..., d_n\\}$ then we can define the _dynasty function_ $d:E\\rightarrow D$ that maps any _epoch_ to its _dynasty_.\n",
    "\n",
    "In optimal scenarios, where finalization happens every epoch, the function will constatly be in the form of $d(e_n)=d_n$.\n",
    "\n",
    "#### Initial parameters\n",
    "Casper has been defined with a set of initial parameters configured to achieve specific returns under specific conditions[1]:\n",
    "\n",
    "- 200k ETH minimum total deposits for casper to be active\n",
    "- ~4 months withdraw delay\n",
    "- logout delay at 700 dynasties\n",
    "- Base Interest Factor at $7\\cdot10^{-3}$ to achieve a 5% yield with ~$10^{7}$ ETH in total deposits.\n",
    "- Base Penalty Factor at $2\\cdot10^{-7}$ so that if 50% of validator are offline then after ~3 weeks, the remaining pool will form a new majority.\n",
    "- the minimum deposit is 1500 ETH creating ~900 validators considering ~$10^{7}$ ETH in total deposits."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Deposit scale factor\n",
    "This function is used to scale the deposited amount of the validator when it enters the validator set, and then to scale any dimension related to deposits up till the total deposited amount at the moment of attempting a withdraw.\n",
    "\n",
    "We introduce here the _deposit scale factor function_ defined in the following way:\n",
    "\n",
    "$$\n",
    "\\begin{equation*}\n",
    "    d_{sf}(t) =\n",
    "        \\begin{cases}\n",
    "          1                                      & t = 0 \\\\\n",
    "          d_{sf}(t-1) \\frac{1+c_r(t)}{1+r_f(t)}  & \\text{otherwise} \\\\\n",
    "        \\end{cases}\n",
    "\\end{equation*}\n",
    "$$\n",
    "\n",
    "where $r_f(t)$ is the _reward factor_ and $c_r(t)$ is the _collective reward_.\n",
    "\n",
    "At the epoch $t$, given $d_v(d)$ the dynasty _votes_ for the dynasty d $d$ and $d_{td}(d)$ the dynasty _total deposits_ then we can define $c_r(t)$ the _collective reward function_ as:\n",
    "\n",
    "$$ c_r(t)=min\\Big(\\frac{d_v(d(t-1))}{d_{td}(d(t))}, \\frac{d_v(d(t-1)-1)}{d_{td}(d(t)-1)}\\Big) \\frac{r_f(t)}{2}$$\n",
    "\n",
    "given the _reward factor_ $r_f(t)$ defined as:\n",
    "\n",
    "$$\n",
    "r_f(t)=\\frac{7\\cdot10^{-3}}{\\sqrt{{\\frac{1 + max\\big(d_{td}(d(t)),d_{td}(d(t-1))\\big) d_{sf}(t-1)}{10^{18}}}}}+2\\cdot10^{-7}e_{sf}(t)=\\frac{7\\cdot10^{-12}}{\\sqrt{1 + max\\big(d_{td}(d(t)),d_{td}(d(t-1))\\big) d_{sf}(t-1)}}+2\\cdot10^{-7}e_{sf}(t)\n",
    "$$\n",
    "\n",
    "\n",
    "Specifically $7\\cdot10^{-3}$ is the _base interest factor_ and $2\\cdot10^{-7}$ is the _base penalty factor_, those are a protocol initial parameters. $10^{18}$ represents a scaling factor equivalent to the amount of _wei_s per _ether_. The function $e_{sf}(t)$ measures the distance in epocs between the epoch $t$ and the last finalized epoch."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now assume that finalization will be accomplished every epoch and the deposits will not vary in time. In this scenario if we set the total constant deposits in the system to $10^{7}$ ETH (casper's ideal scenario) we can observe the bahvior of $d_{sf}(t)$ as it linearly decreases with a yield of ~5%/yr:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "BASE_INTEREST_FACTOR = 7e-3\n",
    "time_span = int(1 * (365 * 24 * 3600 / (15 * 50)))  # 1 year of epochs\n",
    "deposits = 10e24\n",
    "dsf = [1.0]\n",
    "\n",
    "def reward_factor(dyn):\n",
    "    global deposits\n",
    "    sqrt_dep = math.sqrt(1 + (deposits * dsf[dyn] / 1e18))\n",
    "    return BASE_INTEREST_FACTOR / sqrt_dep\n",
    "\n",
    "def collective_reward(dyn):\n",
    "    return reward_factor(dyn) / 2.0\n",
    "\n",
    "for dyn in range(0, time_span):\n",
    "    new_dsf = dsf[dyn] * (1 + collective_reward(dyn)) / (1 + reward_factor(dyn))\n",
    "    dsf.append(new_dsf)\n",
    "\n",
    "plt.plot(range(len(dsf)), dsf)\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('deposit scale factor')\n",
    "plt.axis([0, len(dsf), 0.94, 1.0])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vote reward\n",
    "\n",
    "In the previous paragraph we've shown that a validator would actually lose ETH over time just for being part of the system even in perfect conditions; to counterbalance this casper introduces a reward for succesful votes.\n",
    "\n",
    "Every time a validator successfully gets a vote included in a block he will receive a reward equal to its current deposit multiplied by $r_f$.\n",
    "This reward will compound with the deposit eventually making up for the loss and actually granting a positive yield.\n",
    "Given the current validator deposit $v_d(t)$ then we define the vote reward $v_r(t)$ as:\n",
    "\n",
    "$$\n",
    "v_r(t)=v_d(t)\\cdot r_f(t)\n",
    "$$\n",
    "\n",
    "We then include this reward in the previous model and observe that the validators' return over time is linearly increasing in optimal finalization scenarios at a rate of ~4.6%/yr respective of their deposit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compound yield per month:\n",
      "1:\t0.39%\n",
      "2:\t0.77%\n",
      "3:\t1.16%\n",
      "4:\t1.55%\n",
      "5:\t1.93%\n",
      "6:\t2.31%\n",
      "7:\t2.70%\n",
      "8:\t3.08%\n",
      "9:\t3.46%\n",
      "10:\t3.84%\n",
      "11:\t4.22%\n",
      "12:\t4.60%\n",
      "\n"
     ]
    }
   ],
   "source": [
    "tot_deposits = [10e24]\n",
    "deposits = tot_deposits[0]\n",
    "yield_ = []\n",
    " \n",
    "s = \"Compound yield per month:\\n\"\n",
    "for epoch in range(0, time_span):\n",
    "    deposits *= (1 + reward_factor(epoch))\n",
    "    tot_deposits.append(deposits*dsf[epoch])\n",
    "    yield_.append(tot_deposits[epoch]/tot_deposits[0])\n",
    "    if epoch%3504 == 3503:\n",
    "        s += f'{(int)(epoch/3503)}:\\t{\"{:.2%}\".format(yield_[epoch]-1)}\\n'\n",
    "    \n",
    "plt.plot(range(len(yield_)), yield_)\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('deposit scale factor')\n",
    "plt.axis([0, len(yield_), 1.0, 1.05])\n",
    "\n",
    "plt.show()\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In optimal finalization scenarios the expected yield is function of the total amount of deposits in the system. If we consider deposits to remain constant after a certain time $T$ we can describe the expected _deposit scale factor_ as:\n",
    "\n",
    "$$\n",
    "v_d(t)= v_d(t-1)\\cdot\\big(d_{sf}(t) + r_f(t)\\big)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_roi(time_span, deposit):\n",
    "    c = CasperContract()\n",
    "\n",
    "    c.initialize_epoch(0)\n",
    "    c.deposit(deposit)\n",
    "    roi = []\n",
    "\n",
    "    for i in range(1, time_span):\n",
    "        c.initialize_epoch(i)\n",
    "        c.vote(0, i - 1, i)\n",
    "        roi.append(c.deposit_size(0) / deposit * 1e18)\n",
    "\n",
    "    return roi\n",
    "\n",
    "time_span = int(1 * (365 * 24 * 3600 / (15 * 50)))  # 1 year of epochs\n",
    "\n",
    "d = list()\n",
    "for deposit in range(1, 50, 1):\n",
    "    roi = generate_roi(time_span, deposit * 0.5e24)\n",
    "    d.append(roi[len(roi)-1])\n",
    "\n",
    "plt.plot([x * 0.5 for x in range(1, len(d)+1)], d)\n",
    "plt.xticks(np.arange(0, len(d)*0.5, 5))\n",
    "plt.xlabel('total deposits in ETH * $10^6$')\n",
    "plt.ylabel('deposit scale factor')\n",
    "plt.axis([0, 24, 1.025, 1.225])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Suboptimal finalization\n",
    "\n",
    "In case more than a third of the validators will go offline (and stay so) the _base penalty factor_ will kick in causing the rapid shrinking of non-voting validators (how fast depends on how much stake is not voting) and eventually this will lead to a new super-majority of voters being formed so that finalization can continue.\n",
    "\n",
    "For example if we consider the scenario where 50% of the total deposits is own by non-voting validators we will obtain the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "voters yearly yield: 3.49%\n",
      "non-voters yearly yield: -53.31%\n"
     ]
    }
   ],
   "source": [
    "c = CasperContract()\n",
    "\n",
    "c.initialize_epoch(0)\n",
    "c.deposit(5e24)\n",
    "c.deposit(5e24)\n",
    "\n",
    "roi_online = []\n",
    "roi_offline = []\n",
    "\n",
    "for i in range(1, time_span):\n",
    "    c.initialize_epoch(i)\n",
    "    if i < 4:\n",
    "        c.vote(0, i-1, i)\n",
    "    elif i < 2630:\n",
    "        c.vote(0, 3, i)\n",
    "    else:\n",
    "        c.vote(0, i-1, i)\n",
    "    \n",
    "    roi_online.append(c.deposit_size(0) / 5e24 * 1e18)\n",
    "    roi_offline.append(c.deposit_size(1) / 5e24 * 1e18)\n",
    "    \n",
    "plt.plot(range(len(roi_online)), roi_online, label=\"online\")\n",
    "plt.plot(range(len(roi_offline)), roi_offline, label=\"offline\")\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('deposit scale factor')\n",
    "plt.legend(loc='center right')\n",
    "plt.axis([0, len(roi_online), 0.4, 1.1])\n",
    "plt.show()\n",
    "\n",
    "print(f'voters yearly yield: {\"{:.2%}\".format(roi_online[len(roi_online)-1]-1)}')\n",
    "print(f'non-voters yearly yield: {\"{:.2%}\".format(roi_offline[len(roi_offline)-1]-1)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case instead that validators are not relyable in voting on time or correctly we are going to witness a slight lower reward rate for the whole network and a decrease in their reward whenever they are unable to vote more than ~%60 of the time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the case where a super-majority of the validators votes, but 30% of them is constantly offline, we can see how the yearly yield shrinks for voting and non-voting nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "voters yearly yield: 3.35%\n",
      "non-voters yearly yield: -5.82%\n"
     ]
    }
   ],
   "source": [
    "c = CasperContract()\n",
    "\n",
    "c.initialize_epoch(0)\n",
    "c.deposit(7e24)\n",
    "c.deposit(3e24)\n",
    "\n",
    "roi_online = []\n",
    "roi_offline = []\n",
    "\n",
    "for i in range(1, time_span):\n",
    "    c.initialize_epoch(i)\n",
    "    c.vote(0, i - 1, i)\n",
    "    roi_online.append(c.deposit_size(0) / 7e24 * 1e18)\n",
    "    roi_offline.append(c.deposit_size(1) / 3e24 * 1e18)\n",
    "    \n",
    "plt.plot(range(len(roi_online)), roi_online, label=\"online\")\n",
    "plt.plot(range(len(roi_offline)), roi_offline, label=\"offline\")\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('deposit multiplier')\n",
    "plt.legend(loc='upper left')\n",
    "plt.axis([0, len(roi_online), 0.93, 1.04])\n",
    "plt.show()\n",
    "\n",
    "print(f'voters yearly yield: {\"{:.2%}\".format(roi_online[len(roi_online)-1]-1)}')\n",
    "print(f'non-voters yearly yield: {\"{:.2%}\".format(roi_offline[len(roi_offline)-1]-1)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit-e token inflation\n",
    "\n",
    "In this section we ananlyze the model given for the Unit-e token inflation a we try to put in prospective with the economic model given from the casper model.\n",
    "\n",
    "The target total supply of Unit-e is $e$ billion units, where $e$ is the matematical constant that can be characterized by the infinite series:\n",
    "\n",
    "$$\n",
    "e = \\frac{1}{2}\\sum_{k=0}^{\\infty}\\frac{k+1}{k!}\n",
    "$$\n",
    "\n",
    "We want to complete the token issuance in 50 years and to do so we plan to adjust the block reward exaclty every 1,971,000 blocks, this interval is called _period_ and corresponds to 1 year if we account for block time to be of 16 seconds. We define then the _block reward function_ $B_r(p)$ for the _period_ $p$ as:\n",
    "\n",
    "$$\n",
    "    B_r(p) = \\frac{1}{2}\\frac{p+1}{p!}\n",
    "$$\n",
    "\n",
    "As per [3] we decided to have a high initial token supply in order to prevent strong inequitabilty especially caused by coumpounding effects in early joiners. To achieve so the genesis block will contain $1.5\\cdot10^9$ units, that comes from the formula above summing the results for $p=0$ and $p=1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In practice we slightly adjust those values to bring the total supply after 50 year very close to 271828182845904523 satoshis.\n",
    "\n",
    "$$ B_r(2) = 37.5 \\quad \\text(units) $$\n",
    "$$ B_r(3) = 17 \\quad \\text(units) $$\n",
    "$$ B_r(4) = 5.5 \\quad \\text(units) $$\n",
    "$$ B_r(5) = 1.5 \\quad \\text(units) $$\n",
    "$$ B_r(6) = 0.31 \\quad \\text(units) $$\n",
    "\n",
    "For the sake of this work we will also refer as _inflation_ the depreciation of the token caused solely by the dilution effect of the growing supply.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 2700x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The perfect reward schedule is [3750000000.0, 1666666666.6666665, 520833333.3333334, 125000000.0, 24305555.555555556]\n",
      "The adjusted reward schedule is [3750000000, 1700000000, 550000000, 150000000, 31000000]\n",
      "The perfect total supply is: 2.718281828459045e+17 satoshis\n",
      "The adjusted total supply is: 2.7182751e+17 satoshis\n",
      "The difference is: 7e+03 units\n"
     ]
    }
   ],
   "source": [
    "UNIT = 100_000_000\n",
    "init_blk_rw = 50 * UNIT\n",
    "initial_supply = 1_500_000_000 * UNIT\n",
    "block_yr = 60*60*24*365/16\n",
    "blk_rw_yr = [3750000000, 1700000000, 550000000, 150000000, 31000000]\n",
    "\n",
    "def perf_blk_rw(yr):\n",
    "    return 0.5 * ((yr+2)/math.factorial(yr+1)) * init_blk_rw\n",
    "\n",
    "def adj_blk_rw(yr):\n",
    "    return blk_rw_yr[yr-1]\n",
    "\n",
    "def tot_supply(yr):\n",
    "    supply = initial_supply\n",
    "    for i in range(0, yr):\n",
    "        supply += adj_blk_rw(((int)(i/10))+1) * block_yr\n",
    "    return supply\n",
    "\n",
    "def inflation(yr):\n",
    "    return (tot_supply(yr)/tot_supply(yr-1)) - 1\n",
    "\n",
    "inf = []\n",
    "for i in range(1, 51):\n",
    "    yr = i*block_yr\n",
    "    inf.append(inflation(i))\n",
    "\n",
    "plt.figure(figsize=(18, 4), dpi=150, facecolor='w', edgecolor='k')\n",
    "\n",
    "plt.subplot(1,3,1)\n",
    "plt.plot(range(len(inf)), inf, label=\"inflation\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('inflation rate')\n",
    "plt.legend(loc='upper right')\n",
    "plt.axis([0, len(inf)-1, 0, 0.05])\n",
    "\n",
    "plt.subplot(1,3,2)\n",
    "plt.plot(range(10), inf[0:10], label=\"inflation\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('inflation rate')\n",
    "plt.legend(loc='upper right')\n",
    "plt.axis([1, 9, 0.0325, 0.05])\n",
    "plt.xticks(np.arange(10), (range(1,11)))\n",
    "\n",
    "supply = []\n",
    "for i in range(1, 51):\n",
    "    supply.append(tot_supply(i))\n",
    "    \n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(range(len(supply)), supply, label=\"total supply\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('total supply')\n",
    "plt.legend(loc='lower right')\n",
    "plt.axis([0, len(supply)-1, 1.5e17, 2.75e17])\n",
    "\n",
    "plt.show()\n",
    "\n",
    "expected_supply = 2.71828182845904523e17\n",
    "actual_supply = tot_supply(50)\n",
    "perfect_rewards = [perf_blk_rw(1),perf_blk_rw(2),perf_blk_rw(3),perf_blk_rw(4),perf_blk_rw(5)]\n",
    "print(f'The perfect reward schedule is {perfect_rewards}')\n",
    "print(f'The adjusted reward schedule is {blk_rw_yr}')\n",
    "print(f'The perfect total supply is: {expected_supply} satoshis')\n",
    "print(f'The adjusted total supply is: {actual_supply} satoshis')\n",
    "print(f'The difference is: {\"{:.0e}\".format((expected_supply - actual_supply)/1e8)} units')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit-e validators economic model\n",
    "\n",
    "In this section we define the Unit-e initial parameters concerning validators, describe the expected yield and make a simple cost analysis for running such nodes for different market caps."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Target deposits\n",
    "In order to keep the network secure we need a minimum amount of deposits from validators. Risking to be slashed for the amount of $1/3$ of this should be enough of a deterrent to prevent double finalization attempts.\n",
    "The target total deposit $T_d$ we try to estimate is a value tighly coupled to the market evaluation of the coin, hence we can only speculate and try to set it to a reasonable amount.\n",
    "\n",
    "Let's assume a range of evaluation for a single unit from 0.02 \\\\$ to 1 \\\\$ and $T_d = 270\\cdot10^6$ units then the following table emerges:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "market value \t cost of 33% attack\n",
      "0.02$ \t\t 1,800,000.0$\n",
      "0.05$ \t\t 4,500,000.0$\n",
      "0.1$ \t\t 9,000,000.0$\n",
      "0.5$ \t\t 45,000,000.0$\n",
      "1.0$ \t\t 90,000,000.0$\n",
      "\n",
      "This will account for the 18.00% of the inital supply or the 9.93% of the final total supply\n"
     ]
    }
   ],
   "source": [
    "target_total_deposit = 270_000_000 * UNIT\n",
    "print(f'market value \\t cost of 33% attack')\n",
    "print(f'0.02$ \\t\\t {\"{:,}\".format(target_total_deposit * 0.02 / 3 / UNIT)}$')\n",
    "print(f'0.05$ \\t\\t {\"{:,}\".format(target_total_deposit * 0.05 / 3 / UNIT)}$')\n",
    "print(f'0.1$ \\t\\t {\"{:,}\".format(target_total_deposit * 0.1 / 3 / UNIT)}$')\n",
    "print(f'0.5$ \\t\\t {\"{:,}\".format(target_total_deposit * 0.5 / 3 / UNIT)}$')\n",
    "print(f'1.0$ \\t\\t {\"{:,}\".format(target_total_deposit * 1.0 / 3 / UNIT)}$')\n",
    "print()\n",
    "print(f'This will account for the {\"{:.2%}\".format(target_total_deposit/initial_supply)} of the inital supply or the {\"{:.2%}\".format(target_total_deposit/actual_supply)} of the final total supply')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Yield function\n",
    "As we will see again later in the section dedicated to the proposers' economics, we decide to split evenly the block reward between proposers and validators. Furthermore not all the block reward is meant to be credited immediately for either role, more specifically for validators, it will accumulate in a fund at a faster peace than it could be withdrawn, so that we can guarantee some constant yearly yield that is not tightly coupled to the inflation. This helps preventing the case where after the first decade or so, the fast shrinking of the block reward will make the validator role extremely unfavorable due to the exercise costs unless there is a very consistent appreciation of the coin in value that at the moment we cannot forsee.\n",
    "\n",
    "One way to guarantee a fair yield with an aggressive and fast decreasing inflation is to provide a fixed percentage of returns adjusted to the current inflation. We can calculate the value that let us pay out the complete validator fund in 50 years. After this period no more tokens will be issued and we will fallback to the fees to pay both validators and proposers.\n",
    "\n",
    "Given $I_{nf}(i)$ the inflation for year $i$ we define $Y_{yr}$ the yearly inflation-adjusted yield as the one that satisfies the following equation:\n",
    "$$\n",
    "    \\sum_{i=0}^{49} \\frac{B_r(\\lfloor \\frac{i}{10} \\rfloor + 2)}{2}\\cdot1971000 - T_d(I_{nf}(i)+Y_{yr}) = 0\n",
    "$$\n",
    "\n",
    "If we replace the variables with the parameters already defined we find that $Y_{yr}$ is about 3.3%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The leftover in the validator fund after 50 years is about 7e-01 units\n"
     ]
    }
   ],
   "source": [
    "yr_yield_over_infl = 0.0330443687\n",
    "def yield_yr(yr):\n",
    "    return inflation(yr) + yr_yield_over_infl\n",
    "\n",
    "validators_fund = [0]\n",
    "val_rew_payed = [0]\n",
    "prop_rew_payed = [0]\n",
    "for i in range(1, 51):\n",
    "    yr_add_fund = adj_blk_rw(((int)((i-1)/10))+1)*0.5*block_yr\n",
    "    validators_fund.append(validators_fund[i-1] + yr_add_fund - (target_total_deposit*yield_yr(i)))\n",
    "    val_rew_payed.append(val_rew_payed[i-1] + target_total_deposit*yield_yr(i))\n",
    "    prop_rew_payed.append(prop_rew_payed[i-1] + (tot_supply(i)-tot_supply(i-1))*0.5)\n",
    "    \n",
    "plt.plot(range(len(validators_fund)), validators_fund, label=\"validator's fund size\")\n",
    "plt.plot(range(len(val_rew_payed)), val_rew_payed, label=\"payed reward to validators\")\n",
    "plt.plot(range(len(prop_rew_payed)), prop_rew_payed, label=\"payed reward to proposers\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('units')\n",
    "plt.legend(loc='upper left')\n",
    "plt.axis([0, 50, 0, 9e16])\n",
    "plt.show()\n",
    "\n",
    "print(f'The leftover in the validator fund after 50 years is about {\"{:.0e}\".format(validators_fund[len(validators_fund)-1]/1e8)} units')\n",
    "                                                                                              "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any leftover due to non-optimal finalization and voting will cause the exceeding tokens to be burned immediately, so that after the total supply has been issued there are no more tokens in the validator fund.\n",
    "\n",
    "From the figure above is evident that in the first 20 years we accumulate tokens in the validator fund at a faster peace than what we can pay out and in the last 30 viceversa. This behavior causes a change in the real inflation that changes as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 50, 0, 0.05]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Effective inflation considering validator's fund\n",
    "actual_inf = []\n",
    "for i in range(1, 51):\n",
    "    actual_inf.append(inflation(i) - ((validators_fund[i]-validators_fund[i-1])/tot_supply(i-1)))\n",
    "    \n",
    "plt.plot(range(1,51), inf, label=\"inflation\")\n",
    "plt.plot(range(1,51), actual_inf, label=\"real inflation\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('inflation')\n",
    "plt.legend(loc='upper right')\n",
    "plt.axis([1, 50, 0, 0.05])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we then compare the total yield, the inflation and the inflation-adjusted yield we want to achieve, we obtain the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "total_yield_yr = []\n",
    "yield_over_infl = []\n",
    "compound_yield = [1]\n",
    "\n",
    "for i in range(1, 51):\n",
    "    total_yield_yr.append(yield_yr(i))\n",
    "    yield_over_infl.append(yield_yr(i)-inf[i-1])\n",
    "    compound_yield.append(compound_yield[i-1]*(1+yield_yr(i)))\n",
    "    \n",
    "plt.plot(range(len(total_yield_yr)), total_yield_yr, label=\"validator's total yield\")\n",
    "plt.plot(range(len(inf)), inf, label=\"inflation\")\n",
    "plt.plot(range(len(yield_over_infl)), yield_over_infl, label=\"inflation-adjusted yield\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('yield')\n",
    "plt.legend(loc='upper right')\n",
    "plt.axis([0, 49, 0, 0.085])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considering the above set yield, if we want to project the _deposit scale factor_ similarly to what we did for casper, in case of optimal finalization we would obtain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "year \t yield\n",
      "1 \t 8.23%\n",
      "11 \t 4.80%\n",
      "21 \t 3.73%\n",
      "31 \t 3.41%\n",
      "41 \t 3.33%\n"
     ]
    }
   ],
   "source": [
    "plt.plot(range(len(compound_yield)), compound_yield, label=\"validator's compound yield\")\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('deposit scale factor')\n",
    "plt.legend(loc='upper left')\n",
    "plt.axis([0, 49, 1, 9])\n",
    "plt.show()\n",
    "\n",
    "print(f'year \\t yield')\n",
    "for i in range(5):\n",
    "    print(f'{i*10+1} \\t {\"{:.2%}\".format(total_yield_yr[i*10])}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We just defined $Y_{yr}$ in the case where the validators total deposits are $d_{td} = T_d$. Since Unit-e supply is finite we have to adjust this value in case that $d_{td}$ deviates from the target. The easiest and most straightforward way to do it is to define $Y_{yr}(d_{td})$ as a function of the total deposit so that the yield increases or decreses proportionally as $d_{td}$ changes.\n",
    "$$\n",
    "    Y_{yr}(epoch) = \\frac{T_d (I_{nf}(epoch) + Y_{yr})}{d_{td}(epoch)} - I_{nf}(epoch)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the following table emerges for the inflation-adjusted yield in the first year\n",
      "fraction of TD \t yield\n",
      "0.1 \t\t 77.39%\n",
      "0.3 \t\t 22.51%\n",
      "0.5 \t\t 11.54%\n",
      "1 \t\t 3.30%\n",
      "1.2 \t\t 1.93%\n",
      "1.5 \t\t 0.56%\n",
      "2 \t\t -0.81%\n",
      "5 \t\t -3.28%\n"
     ]
    }
   ],
   "source": [
    "y = [[0],[0],[0],[0],[0]]\n",
    "\n",
    "def yield_yr_dep(yr, tot_deposit):\n",
    "    return yield_yr(yr) * (target_total_deposit/tot_deposit) - inflation(yr)\n",
    "\n",
    "for i in np.arange(100_000_000 * UNIT, actual_supply, 100_000_000 * UNIT):\n",
    "    for j in range(0,5):\n",
    "        y[j].append(yield_yr_dep(j*10+1, i))\n",
    "    \n",
    "for j in range(0,5):\n",
    "    plt.plot(range(len(y[j])), y[j], label=f'yield decade {j+1}')\n",
    "    \n",
    "plt.xlabel('deposits 10^8')\n",
    "plt.ylabel('yield')\n",
    "plt.legend(loc='upper right')\n",
    "plt.axis([1, len(y[0])-1, -0.06, 0.2])\n",
    "plt.show()\n",
    "\n",
    "print(\"the following table emerges for the inflation-adjusted yield in the first year\")\n",
    "print(f'fraction of TD \\t yield')\n",
    "for i in [0.1, 0.3, 0.5, 1, 1.2, 1.5, 2, 5]:\n",
    "    print(f'{i} \\t\\t {\"{:.2%}\".format(yield_yr_dep(1, i * target_total_deposit))}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We set now the inital parameters of the Unit-e equivalent of the casper contract."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "class UnitEContract(CasperContract):\n",
    "    \n",
    "    def __init__(self):\n",
    "        CasperContract.__init__(self)\n",
    "        self.BASE_INTEREST_FACTOR = 1.67665e-6\n",
    "        self.BASE_PENALTY_FACTOR = 2e-7\n",
    "        self.MIN_DEPOSIT_SIZE = 0\n",
    "        self.ETHER_IN_WEI = 1e8\n",
    "        self.ONE_WEI = 1e-8\n",
    "\n",
    "    def sqrt_of_total_deposits(self):\n",
    "        epoch = self.current_epoch\n",
    "        units_deposited_as_number = 1 + math.floor(\n",
    "            max(self.total_prevdyn_deposits, self.total_curdyn_deposits) *\n",
    "            self.deposit_scale_factor[epoch - 1] /\n",
    "            self.ETHER_IN_WEI\n",
    "        )\n",
    "        return units_deposited_as_number / (target_total_deposit / 1e8)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case of suboptimal finalization, Unit-e behaves similarly to casper harshly punishing offline nodes, and mildly punishing all the others.\n",
    "\n",
    "In case of constant optimal finalization we obtain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal finalization yearly yield: 3.304417%\n"
     ]
    }
   ],
   "source": [
    "c = UnitEContract()\n",
    "\n",
    "c.initialize_epoch(0)\n",
    "c.deposit(target_total_deposit)\n",
    "\n",
    "optimal_yield = []\n",
    "\n",
    "for i in range(0, (int)(block_yr/50)):\n",
    "    c.initialize_epoch(i)\n",
    "    c.vote(0, i-1, i)\n",
    "    optimal_yield.append(c.deposit_size(0) / target_total_deposit * 1e8)\n",
    "    \n",
    "plt.plot(range(len(optimal_yield)), optimal_yield, label=\"optimal validation\")\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('deposit multiplier')\n",
    "plt.legend(loc='center right')\n",
    "plt.axis([0, len(optimal_yield), 1, 1.034])\n",
    "plt.show()\n",
    "\n",
    "print(f'optimal finalization yearly yield: {\"{:.6%}\".format(optimal_yield[len(optimal_yield)-1]-1)}') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case instread the 50% of the deposits are owned by non-voting validators, again similarly to what we've shown above for casper, we obitain a quick harsh shrinkage of the non-voting validators funds that leads to a new super-majority made with the remaining active validators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.025746219328747655\n",
      "voters yearly yield: 2.57%\n",
      "non-voters yearly yield: -52.89%\n"
     ]
    }
   ],
   "source": [
    "c = UnitEContract()\n",
    "c.BASE_PENALTY_FACTOR = 2.0121e-7\n",
    "c.initialize_epoch(0)\n",
    "deposit = target_total_deposit/2\n",
    "c.deposit(deposit)\n",
    "c.deposit(deposit)\n",
    "\n",
    "roi_online = []\n",
    "roi_offline = []\n",
    "\n",
    "for i in range(1, int(block_yr/50)):\n",
    "    c.initialize_epoch(i)\n",
    "    if i < 4:\n",
    "        c.vote(0, i-1, i)\n",
    "    elif i < 2630:\n",
    "        c.vote(0, 3, i)\n",
    "    else:\n",
    "        c.vote(0, i-1, i)\n",
    "    \n",
    "    roi_online.append(c.deposit_size(0) / deposit * 1e8)\n",
    "    roi_offline.append(c.deposit_size(1) / deposit * 1e8)\n",
    "    \n",
    "plt.plot(range(len(roi_online)), roi_online, label=\"online\")\n",
    "plt.plot(range(len(roi_offline)), roi_offline, label=\"offline\")\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('final deposit multiplier')\n",
    "plt.legend(loc='center right')\n",
    "plt.axis([0, len(roi_online), 0.4, 1.1])\n",
    "plt.show()\n",
    "print(roi_online[len(roi_online)-1]-1)\n",
    "print(f'voters yearly yield: {\"{:.2%}\".format(roi_online[len(roi_online)-1]-1)}')\n",
    "print(f'non-voters yearly yield: {\"{:.2%}\".format(roi_offline[len(roi_offline)-1]-1)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In a less extreme scenario if only 30% of the stake is owned by non-voting validators, then finalization can be achieved and both parties (voters and non-voters) face milder consequences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "voters yearly yield: 2.52%\n",
      "non-voters yearly yield: -4.45%\n"
     ]
    }
   ],
   "source": [
    "c = UnitEContract()\n",
    "\n",
    "c.initialize_epoch(0)\n",
    "c.deposit(target_total_deposit * 0.7)\n",
    "c.deposit(target_total_deposit * 0.3)\n",
    "\n",
    "roi_online = []\n",
    "roi_offline = []\n",
    "\n",
    "for i in range(1, time_span):\n",
    "    c.initialize_epoch(i)\n",
    "    c.vote(0, i - 1, i)\n",
    "    roi_online.append(c.deposit_size(0) / (target_total_deposit * 0.7) * 1e8)\n",
    "    roi_offline.append(c.deposit_size(1) / (target_total_deposit * 0.3) * 1e8)\n",
    "    \n",
    "plt.plot(range(len(roi_online)), roi_online, label=\"online\")\n",
    "plt.plot(range(len(roi_offline)), roi_offline, label=\"offline\")\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('deposit multiplier')\n",
    "plt.legend(loc='upper left')\n",
    "plt.axis([0, len(roi_online), 0.93, 1.04])\n",
    "plt.show()\n",
    "\n",
    "print(f'voters yearly yield: {\"{:.2%}\".format(roi_online[len(roi_online)-1]-1)}')\n",
    "print(f'non-voters yearly yield: {\"{:.2%}\".format(roi_offline[len(roi_offline)-1]-1)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Validators costs\n",
    "In orded to make sure that running a validator node is a feasable business we need to estimate the cost of running such nodes with commercial grade equipment. Amazon provides competive prices for renting hardware, using their cost estimator [4] and what we think the minimum set up that has enough security guarantees, we end up with the following list:  \n",
    "\n",
    "- 1 x Linux on a1.2xlarge  \n",
    "- 5 x Linux on t3.2xlarge  \n",
    "- 1 x EBS backup 2TB  \n",
    "- 800 GB in per month  \n",
    "- 800 GB out per month  \n",
    "- Cloud HSM  \n",
    "\n",
    "Reserving those instance for 5 years and splitting the costs over such periods, including the monthly rent for some of those services we arrive to a sum very close to 27,000$.\n",
    "\n",
    "Given the above estimation follows a table with the minimum amount of stake that is required to break even, netting out the inflation, at different coin evaluations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "market value \t $ investment \t fraction of supply \t fraction of TD\n",
      "0.02 \t\t 40,854,162$ \t 75.15%  \t\t 756.56%\n",
      "0.05 \t\t 16,341,664$ \t 12.02%  \t\t 121.05%\n",
      "0.1 \t\t 8,170,832$ \t 3.01%  \t\t 30.26%\n",
      "0.5 \t\t 1,634,166$ \t 0.12%  \t\t 1.21%\n",
      "1 \t\t 817,083$ \t 0.03%  \t\t 0.30%\n"
     ]
    }
   ],
   "source": [
    "validator_cost = 27_000\n",
    "\n",
    "print(f'market value \\t $ investment \\t fraction of supply \\t fraction of TD')\n",
    "for i in [0.02, 0.05, 0.1, 0.5, 1]:\n",
    "    inv = (int)(validator_cost/(yr_yield_over_infl * i))\n",
    "    inv_s = \"{:,}\".format(inv)\n",
    "    frac_supply = \"{:.2%}\".format(inv*UNIT/i/actual_supply)\n",
    "    frac_TD = \"{:.2%}\".format(inv*UNIT/i/target_total_deposit)\n",
    "    print(f'{i} \\t\\t {inv_s}$ \\t {frac_supply}  \\t\\t {frac_TD}')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit-e Proposers economic model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we want to incentivize vote inclusion and prevent censorhip of validators from purely economic opportunities, and to do so we use the sigmoid function $atan(x)$ to weigth the total reward given to proposers from the coinbase.\n",
    "Furthermore only 10% of the total potential block reward is given immediately to the poposer, while the remaining portion will be awarded at the checkpoint of the next epoch that determines a new dynasty.  \n",
    "In this way we basically award only 10% of the possible reward to proposers immediately and we keep the rest as strong incentive to include as many votes as possible and help finalization.  \n",
    "As for the validator fund any inefficiency due to non-optimal finalization will cause the exceeding funds to be burned."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 2700x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "% votes included \t % block reward \t block reward\n",
      "0% \t\t\t 11.08%   \t\t 2.08\n",
      "5% \t\t\t 11.23%   \t\t 2.10\n",
      "10% \t\t\t 11.40%   \t\t 2.14\n",
      "15% \t\t\t 11.61%   \t\t 2.18\n",
      "20% \t\t\t 11.86%   \t\t 2.22\n",
      "25% \t\t\t 12.18%   \t\t 2.28\n",
      "30% \t\t\t 12.58%   \t\t 2.36\n",
      "35% \t\t\t 13.11%   \t\t 2.46\n",
      "40% \t\t\t 13.84%   \t\t 2.60\n",
      "45% \t\t\t 14.91%   \t\t 2.80\n",
      "50% \t\t\t 16.61%   \t\t 3.11\n",
      "55% \t\t\t 19.73%   \t\t 3.70\n",
      "60% \t\t\t 26.90%   \t\t 5.04\n",
      "65% \t\t\t 49.04%   \t\t 9.19\n",
      "66% \t\t\t 56.39%   \t\t 10.57\n",
      "67% \t\t\t 63.74%   \t\t 11.95\n",
      "70% \t\t\t 79.95%   \t\t 14.99\n",
      "75% \t\t\t 90.96%   \t\t 17.06\n",
      "80% \t\t\t 95.16%   \t\t 17.84\n",
      "85% \t\t\t 97.29%   \t\t 18.24\n",
      "90% \t\t\t 98.56%   \t\t 18.48\n",
      "95% \t\t\t 99.40%   \t\t 18.64\n",
      "100% \t\t\t 100.00%   \t\t 18.75\n"
     ]
    }
   ],
   "source": [
    "def proposer_reward_fraction(vote_fraction):\n",
    "    vote_fraction = ((vote_fraction-0.16) * 25) - 12.5\n",
    "    return 0.1 + ((np.arctan(vote_fraction)+1.5462)/3)*0.9\n",
    "\n",
    "reward_fr = []\n",
    "reward = []\n",
    "for i in range(0,101):\n",
    "    reward_fr.append(proposer_reward_fraction(i*0.01))\n",
    "    reward.append(reward_fr[i]*adj_blk_rw(1)*0.5/UNIT)\n",
    "\n",
    "plt.figure(figsize=(18, 4), dpi=150, facecolor='w', edgecolor='k')\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(range(len(reward_fr)), reward_fr, label=\"% reward\")\n",
    "plt.xlabel('votes included')\n",
    "plt.ylabel('block reward %')\n",
    "plt.axis([1, 100, 0, 1])\n",
    "plt.legend(loc='upper left')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(range(len(reward)), reward, label=\"block reward\")\n",
    "plt.xlabel('block')\n",
    "plt.ylabel('yield')\n",
    "plt.legend(loc='upper left')\n",
    "plt.axis([1, 100, 0, 37.5/2])\n",
    "\n",
    "plt.show()\n",
    "\n",
    "print(f'% votes included \\t % block reward \\t block reward')\n",
    "for i in range(0, len(reward_fr)):\n",
    "    if i % 5 == 0 or i in [65,66,67]:\n",
    "        print(f'{i}% \\t\\t\\t {\"{:.2%}  \".format(reward_fr[i])} \\t\\t {\"{:.2f}\".format(reward[i])}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attacking the protocol (TODO)\n",
    "In this section we will analyze different possible strategies to damage the participant in the protocol through the reward structure. In particular if there is any strategy that leads with a small loss from the attacker to disproportionate losses among one or other actors.\n",
    "\n",
    "\n",
    "#### Validator vs. validator griefing\n",
    "A validator could decide not to vote, to cause the overall reward factor to be shrinked, causing an inferior yield to all the other validators.\n",
    "\n",
    "\n",
    "#### Proposer vs. validator griefing\n",
    "A proposer could decide not to include votes from one or multiple validators hence shrinking their yield and in the worse case preventing finalization.\n",
    "\n",
    "#### Validator vs. proposer griefing\n",
    "A validator could decide not to vote for the sole purpose of damaging the return of the proposers, in fact diminishing circulating supply and lowering the inflation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Danny R., Chih-Cheng L., EIP-1011: Hybrid Casper FFG, URL https://github.com/ethereum/EIPs/blob/master/EIPS/eip-1011.md  \n",
    "[2] Buterin V., Griffith V., Casper the Friendly Finality Gadget, URL https://arxiv.org/abs/1710.09437v3  \n",
    "[3] G. Fanti, L. Kogan, S. Oh, K. Ruan, P. Viswanath, G. Wang, Compounding of Wealth in Proof-of-Stake Cryptocurrencies, URL https://arxiv.org/abs/1809.07468  \n",
    "[4] Amazon price estimator, URL http://calculator.s3.amazonaws.com/index.html"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}