There is a demand for Luxuries from each faction among the Empire's elite, so the Empire regularly posts procurement announcements to officially import Luxuries from each faction.

Every day at 12:00 UTC, the Empire's procurement announcements are posted, and the quantities and prices for imported items vary daily. Since this is a very important factor in controlling the inflation of the black market, we developed our own Automated Token Distributor (ATD) and integrated it into the procurement system. The ATD automatically adjusts the quantity and price of the daily POs and stabilizes the inflation of $VALOR.

Overview

The Automated Token Distributor (ATD) is a core component of VALOR's token distribution strategy. This document explains the ATD’s budget distribution mechanisms.

The below models can be updated due to the balance update

1. Budget Distribution

ATD’s budget distribution framework employs a probabilistic approach based on a standard normal distribution to allocate resources effectively across various tokens and market segments.

Key Definitions and Variables

**Normal Distribution (PDF)**: A probability distribution function used to allocate budgets fairly, with a mean of 0 and a standard deviation of 1.**Budget Allocation Ratios**: Ratios are derived from the PDF to determine the portion of the total budget allocated to each token.**Total Budget**: It is set at 110% of the inflow over 24 hours. It is rounded down to 9 decimal places, and the remainder is discarded.

Process Explanation

**Total Budget Calculation**:Case 1 (Accumulated Inflow < Accumulated Outflow):

The total budget is set at 110% of the inflow over the past 24 hours plus any carried-over budget

Case 2 (Accumulated Inflow > Accumulated Outflow):

The total budget is set at sum of each sSPL supply and ideal price.

Maximum budget = (Accumulated Inflow - Accumulated Outflow) * 1.1

**Random Factor Generation**:Generate a random number within the range of [-0.5, 0.5] from a normal distribution with a mean of 0 and a standard deviation of 1. This controls the variability in budget allocation.

**Budget Allocation**:Convert these densities into budget allocation ratios:

Allocate the total budget to various tokens using these ratios:

2. Price Setting

The ATD's price-setting mechanism dynamically adjusts token prices around an ideal price to reflect market values.

Key Definitions and Variables

Standard Deviation Calculation

Price Determination Model

Random Price Determination Model

**Detailed Process**

**Define Price Range**:Establish the effective price range for the next pricing cycle:

**Generate PDF**:**Calculate Area Under Curve**:Determine the total probability area under the PDF within the defined range:

**Generate Random Factor and Set Next Price**:Select a random value within the range [0, A], and determine the corresponding price using the inverse cumulative distribution function (CDF):

**Final Quantity Adjustment**:Calculate the maximum quantity that can be purchased with the allocated budget:

Adjust the final price using the actual quantity purchased:

Data

Examples

PDF and simulation when the ideal price is 2.28

PDF and simulation when the ideal price is 50.4

$B_{total} = \left\lfloor (1.1 \times Inflow) \times 10^9 \right\rfloor / 10^9$

Here, $Inflow$ is the inflow over the past 24 hours.

$B_{total} = \sum S \times P_{idl}$

Calculate the probability density $p(x_i)$ for each random factor $x_i$. This density influences how the budget is divided. The probability density function is:

$p(x_i) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x_i^2}{2}}$

$R_i = \frac{p(x_i)}{\sum_{j=1}^{9} p(x_j)}$

$B_i = \left\lfloor R_i \times B_{total} \times 10^9 \right\rfloor / 10^9$

**Ideal Price (**$P_{idl}$**)**: The target price for the tokens.

**Previous Price (**$P_{prv}$**)**: The market price of the token before adjustment.

**Next Price (**$P_{nxt}$**)**: The price of the token after adjustment.

**Standard Deviation (**$\sigma$**)**: Controls the spread of price values around $P_{idl}$

The standard deviation $\sigma$ is calculated as:

$\sigma = \sqrt{\frac{P_{idl}^2}{2 \ln(10)}}$

This calculation determines the range of price fluctuations around the ideal price $P_{idl}$, adjusting for market volatility.

This model dynamically calculates the next token price using a probability distribution function centered on $P_{idl}$.

$\text{Effective Price Range} = [P_{prv} \times 0.7, P_{prv} \times 1.3]$

Create a normal distribution centered on $P_{idl}$ with the calculated $\sigma$.

$A = \int_{P_{prv} \times 0.7}^{P_{prv} \times 1.3} f(x) \, dx$

$P_{nxt} = f^{-1}(r)$

Here, $f^{-1}$ is the inverse function of the CDF, accurately determining the price corresponding to the random value $r$.

$Q_i = \left\lfloor \frac{B_i}{P_{nxt}} \right\rfloor$

Round down to ensure accurate quantity calculation. (If $Q_i < 1$, set $Q_i$ to 1)

$P_{final} = \left\lfloor \frac{B_i}{Q_i} \times 10^3 \right\rfloor / 10^3$

The final price $P_{final}$ is rounded down to 3 decimal places.

$B_i^\text{new} = B_i - (Q_i \times P_{final})$

Token | Ideal Price ($VALOR) |
---|---|

Voodoo Doll ($VD)

1.5300

Gold Teeth ($GT)

2.5800

JB Whiskey ($JBW)

3.0000

Canteen ($CT)

4.5250

G Badge ($GB)

4.8750

Holy Water ($HW)

9.0500

Used Engine ($UE)

13.6083

Enhanced Bullet ($EB)

20.6000

Oil Lighter Case ($OLC)

27.4250