Central Bank

🧮 RTIM Module

The Real-Time Inflation Module (RTIM) is an advanced economic adaptor that is designed to maintain and govern a healthy in-game economy. As players navigate through the world of Pett.ai, they witness the bank's agility firsthand. But how does it work?

🤖 This entity will operate autonomously, continuously analysing in-game market trends, player behaviours and on-chain $PAI price action with the role of implementing responsive and adaptive monetary policies to ensure a balanced economic environment!

Picture a scenario where Pett.ai's token, the in-game currency, surges in value by a whopping 15% versus the dollar, in a 1-hour period. Like a vigilant guardian of the economy, the Pett.ai Central Bank steps in to promptly respond, adjusting the prices of in-game items and rewards by a variable factor along a inflation/deflation pricing curve according to the RTIM Module.

💰 On-Chain Pricing

At the core of this system is a methodical data fetching process. The module gathers trading price information every hour. However, to avoid potential exploitation and sudden market manipulation, the module employs a unique smoothing mechanism.

Once the data is collected, the module computes the Real-Time Inflation Metric (RTIM) off-chain. This metric is pivotal in understanding the real-time value of the in-game currency, reflecting the latest market conditions. Based on the RTIM and the overall economic needs of the game, the Central Bank makes calculated decisions to either inflate or deflate the in-game currency's value.

The function that governs the RTIM Module goes as follows,

RTIM(i)=∑k=110[1+[∑n=13pi−n+1n∑j=13pjj−1]−1]−1×1k  , where pi is the price p at time i\text{RTIM}(i)= \sum^{10}_{k=1} \left[ 1 + \left[ \frac{\sum^3_{n=1} \frac{p_{i-n+1}}{n}}{\sum^3_{j=1} \frac{p_j}{j}} -1\right]^{-1} \right]^{-1}\times\frac{1}{k} \ \ , \ \text{where } p_i \text{ is the price } p\text{ at time }i

To have a better understanding of how it would work in the wild, we’ve simulated a random walk for a token price as described below.

DateToken PriceΔRTIM Index🍔 Price2024−06−01  00:00$0.5650.00%1.0005.002024−06−01  01:00$0.5853.54%0.9914.962024−06−01  02:00$0.6287.35%0.9784.892024−06−01  03:00$0.73216.56%0.9524.762024−06−01  04:00$0.83213.66%0.9174.592024−06−01  05:00$0.788−5.29%0.8844.422024−06−01  06:00$0.8457.23%0.8564.282024−06−01  07:00$0.844−0.12%0.8354.182024−06−01  08:00$0.8450.12%0.8364.182024−06−01  09:00$0.8753.55%0.8304.152024−06−01  10:00$0.8911.83%0.8304.152024−06−01  11:00$0.98710.78%0.8124.062024−06−01  12:00$1.0455.88%0.7933.972024−06−01  13:00$1.0621.63%0.7743.872024−06−01  14:00$1.1023.77%0.7523.762024−06−01  15:00$1.1352.99%0.7333.672024−06−01  16:00$1.26111.10%0.7063.532024−06−01  17:00$1.255−0.48%0.6833.422024−06−01  18:00$1.2912.87%0.6613.312024−06−01  19:00$1.232−4.57%0.6443.222024−06−01  20:00$1.053−14.53%0.6263.132024−06−01  21:00$1.1085.23%0.6103.052024−06−01  22:00$1.1816.59%0.5993.002024−06−01  23:00$1.136−3.81%0.5902.95\begin{array}{|c|c|c|c|c|} \hline \text{Date} & \text{Token Price} & \text{$\Delta$} & \text{RTIM Index} & \text{🍔 Price} \\ \hline 2024-06-01\ \ 00:00 & \$0.565 & 0.00\% & 1.000 & 5.00 \\ 2024-06-01\ \ 01:00 & \$0.585 & 3.54\% & 0.991 & 4.96 \\ 2024-06-01\ \ 02:00 & \$0.628 & 7.35\% & 0.978 & 4.89 \\ 2024-06-01\ \ 03:00 & \$0.732 & 16.56\% & 0.952 & 4.76 \\ 2024-06-01\ \ 04:00 & \$0.832 & 13.66\% & 0.917 & 4.59 \\ 2024-06-01\ \ 05:00 & \$0.788 & -5.29\% & 0.884 & 4.42 \\ 2024-06-01\ \ 06:00 & \$0.845 & 7.23\% & 0.856 & 4.28 \\ 2024-06-01\ \ 07:00 & \$0.844 & -0.12\% & 0.835 & 4.18 \\ 2024-06-01\ \ 08:00 & \$0.845 & 0.12\% & 0.836 & 4.18 \\ 2024-06-01\ \ 09:00 & \$0.875 & 3.55\% & 0.830 & 4.15 \\ 2024-06-01\ \ 10:00 & \$0.891 & 1.83\% & 0.830 & 4.15 \\ 2024-06-01\ \ 11:00 & \$0.987 & 10.78\% & 0.812 & 4.06 \\ 2024-06-01\ \ 12:00 & \$1.045 & 5.88\% & 0.793 & 3.97 \\ 2024-06-01\ \ 13:00 & \$1.062 & 1.63\% & 0.774 & 3.87 \\ 2024-06-01\ \ 14:00 & \$1.102 & 3.77\% & 0.752 & 3.76 \\ 2024-06-01\ \ 15:00 & \$1.135 & 2.99\% & 0.733 & 3.67 \\ 2024-06-01\ \ 16:00 & \$1.261 & 11.10\% & 0.706 & 3.53 \\ 2024-06-01\ \ 17:00 & \$1.255 & -0.48\% & 0.683 & 3.42 \\ 2024-06-01\ \ 18:00 & \$1.291 & 2.87\% & 0.661 & 3.31 \\ 2024-06-01\ \ 19:00 & \$1.232 & -4.57\% & 0.644 & 3.22 \\ 2024-06-01\ \ 20:00 & \$1.053 & -14.53\% & 0.626 & 3.13 \\ 2024-06-01\ \ 21:00 & \$1.108 & 5.23\% & 0.610 & 3.05 \\ 2024-06-01\ \ 22:00 & \$1.181 & 6.59\% & 0.599 & 3.00 \\ 2024-06-01\ \ 23:00 & \$1.136 & -3.81\% & 0.590 & 2.95 \\ \hline \end{array}

Below you can find a visual representation of the current RTIM module under ideation.

🎁 UBI Module

More than just a regulator, the central bank also emerges as a benefactor, transcending its traditional role as a mere regulator and evolving into a pivotal benefactor within the gaming ecosystem. This transformation is primarily manifested through its innovative approach to Universal Basic Income (UBI), a concept where all players could receive an unconditional sum of money, ensuring a foundational economic stability within the game.

This redistribution, ingeniously tied to a leaderboard system, adds a competitive edge to the game. Players strive not just for victory, but also for economic dominance, knowing that their in-game financial prowess can yield tangible rewards. But how does it all tie together?

The Central Bank will be tracking all in-game players’ activities and deem them eligible to specific financial aid. Sometimes, the worst gamblers are just a win away… 🎰

🦢 Black Swan Events

The RTIM doesn’t stop there. It weaves in a tapestry of simulated economic events, from black swan occurrences like natural disasters to market crashes and commodity shortages. These events are more than mere obstacles; they are catalysts that compel players to adapt, strategise, and survive, mirroring the unpredictability of real-world economies.

Do you remember the wheat shortage of Summer 2021 due to COVID? Let’s pray it doesn’t repeat and affect the consumable prices…! 🍔

For modelling the probability distribution of the black swan events we will be using the Normal-Inverse Gaussian (NIG) probability density function due to its heavy-tailed nature. Its heavy tails capture the higher probability of extreme changes in market conditions, making it a more appropriate tool for representing the risk of black swan events in financial data.

f(x∣α,β,μ,δ)=αeδα2−β2+β(x−μ)πK1(αδ2+(x−μ)2)δ2+(x−μ)2f(x|\alpha, \beta, \mu, \delta) = \frac{\alpha e^{\delta\sqrt{\alpha^2 - \beta^2} + \beta (x - \mu)}}{\pi} \frac{K_1\left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}{\sqrt{\delta^2 + (x - \mu)^2}}

(parameters are not disclosed to avoid manipulation)

These buffers serve as both safety nets and opportunities, challenging players to think long-term and explore new avenues for revenue generation. It’s a dance of risk and reward, where each decision can tip the scales of fortune.

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