# The Mathematics of Token Inflation.

eSkillz Games

The future of sports gaming

Web 3.0 P&E NFT Metaverse

Overview

This article looks at the mathematics of token inflation (not token price inflation), how to measure it and how to use that information.

Background

Recently there have been a number of high-profile crypto casualties of hyper-inflation or hyper-deflation, where the token’s price goes up or down so violently it breaks the ecosystem. Play To Earn (P2E) projects are at risk of both because they are constantly paying out every day, and huge price swings can be very problematic. Not too long ago Axie Infinity had to throttle the flow of SLP from P2E because the price of SLP had plummeted.

Crypto and P2E are still relatively new, so there is almost no public information as to how to manage inflation and deflation. Though over time as the platforms mature, they will improve. Here at eSkillz Games, as we plan our tokenomics, it’s something we’ve been worried about and we are looking for ways to reduce these risks. To assist us, we hired a mathematician to help us understand the theories better and ultimately, to help us write algorithms to measure and control the rate of inflation.

The following article looks at The Theory of Money, how it can be used to measure inflation, and how we intend to use it to try to control it. Before we move on, it is worth noting that it is very difficult to control inflation when things change suddenly, just look at how governments and national banks across the world are struggling to do just that as inflation spikes.

The Quantity Theory of Money

The fundamental theory for the quantity theory of money is: –

MV = PT

Where;

M is the total supply of money. In our case the total number of circulating tokens,

V is the velocity of circulation. This is defined as the number of times a unit of currency is used in a transaction per year,

P is the price level. It isn’t measured directly, rather we calculate the change in P to give us the inflation rate,

is the number of transactions. And it refers to the total number of transactions that take place for items of value in the game economy.

Using the Model to Predict Inflation

MV = PT

Apply a change in the price (inflation) caused by a change in the money supply: –

(M + ∆M) V = (P + ∆P) T

From here we can rearrange to match up to inflation rates with our variables. First, forecast an inflation rate based on a change in the money supply: –

((M + ∆M) V − PT) / (PT = ∆P) / P

Note that the expression on the left is the inflation rate as a percentage.

Suppose you wanted to target a specific inflation rate r: –

∆M = (TP (1 + r) — MV) / V

This expression will give you the total number of new tokens that would need to be minted into circulation.

Managing Your Token’s Inflation

Most central banks are tasked with maintaining an annual inflation rate of 2%, and they essentially do this by minting and burning money both directly and indirectly by trying to dissuade people from spending. We’ve decided to target a 10% inflation rate for our payment token. By using the above formula, we can run an algorithm to monitor our token supply to target a 10% annual inflation through the minting and burning of our token.

We are also working on a more advanced algorithm to control the daily spend on Play To Earn payments by looking at the token’s price, daily spend, rate of inflation, number of transactions, and amount of tokens coming back to us through marketplace purchases, etc, and recent trends. By limiting the maximum amount of tokens that can be distributed per day, we hope to better control our token flow.

Conclusions

Projects have failed because they weren’t able to control hyper deflation, which led to a death spiral.

By using algorithms, we can monitor our eco-systems in real-time.

It’s important to maintain a treasury that allows you to burn tokens.

It’s important to have tokens available to mint but it must be done in a controlled manner i.e. 10% p.a.

You should consider capping daily token mint from P2E payments.

Projects that are unaware of the risks of hyperinflation or deflation and don’t track the flow of their own tokens are prone to collapse, if and when the token price moves dramatically.

As the Play to Earn genre matures, we’ll get better at developing tools to control token flow and inflation.

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