Automated Market Maker (AMM)

Overview

Panana Predictions utilizes an Automated Market Maker (AMM) system tailored for binary outcome markets, ensuring continuous liquidity and dynamic price discovery without the need for traditional order books.

Key Components

1. Liquidity Pool: A shared pool of funds that facilitates trading between outcome shares.
2. Outcome Shares: Tokens representing possible outcomes of a prediction market.
3. Constant Product Formula: Ensures the product of the quantities of outcome shares remains constant, guiding price adjustments.

How It Works

1. Constant Product Formula

In binary outcome markets, the AMM maintains the equation:

$x \times y = k$

Where:

• ( x ) = Quantity of Outcome A shares
• ( y ) = Quantity of Outcome B shares
• ( k ) = Constant product

This formula ensures that any trade affecting the quantity of one outcome share inversely affects the price of the other, maintaining balance in the liquidity pool.

2. Outcome Price Calculation

The price of an outcome is determined by:

$$\text{Price of Outcome A} = \frac{y}{x + y}$$ $$\text{Price of Outcome B} = \frac{x}{x + y}$$

As traders buy shares of an outcome, its price increases due to the reduced availability in the pool, while the opposing outcome's price decreases.

3. Trading Mechanism

Traders interact with the AMM by buying or selling outcome shares:

• Buying Outcome A Shares:
  • Increases the quantity of Outcome A shares in the pool.
  • Decreases the price of Outcome A shares.
  • Increases the price of Outcome B shares.
• Selling Outcome A Shares:
  • Decreases the quantity of Outcome A shares in the pool.
  • Increases the price of Outcome A shares.
  • Decreases the price of Outcome B shares.

When a trade happens, shares of a particular outcome are bought or sold. This affects the outcome pool, redistributing shares and changing their price based on supply and demand. Since Panana Predictions uses an automated market maker (AMM), prices adjust dynamically to reflect market sentiment.

Example: Buying Outcome A Shares

Step 1: Trade Initiation

Bob decides to buy 100 USDC worth of shares for Outcome A in a binary outcome market.

• He adds USDC to the market and receives shares in return.

Step 2: Trading Fee Deduction

info

Fees are not yet defined and may change at any time during the market's beta phase.

A 1.5% trading fee applies:

• Bob contributes: 100 USDC - 1.5% = 98.5 USDC.
• 98 (rounded) shares are added to each outcome pool.

Step 3: Temporary Pool State

After Bob’s trade, the new share distribution is:

Pool	Shares
Outcome A	1098 (rounded)
Outcome B	1098 (rounded)
Liquidity	1000

At this stage, the constant product formula is temporarily broken.

Step 4: Adjusting Outcome A Pool Size

To maintain equilibrium, we calculate the correct number of Outcome A shares using the formula:

$$\text{SharesOutcomeA} = \frac{\text{SharesLiquidityPool}^2}{\text{SharesOutcomeB}}$$

Applying the formula:

Pool	Shares
Outcome B	1098
Liquidity	1000
Outcome A	910 (rounded)

Bob effectively purchased the difference:

$$1098 - 910 = 188$$

Bob received 188 shares of Outcome A for his 100 USDC trade.

Step 5: Impact on Outcome Prices

The trade influences the prices of both outcomes. The new price calculation uses:

$$\text{PriceOutcomeA} = \frac{\text{SharesOutcomeB}}{\sum \text{AllOutcomeShares}}$$ $$\text{PriceOutcomeB} = \frac{\text{SharesOutcomeA}}{\sum \text{AllOutcomeShares}}$$

Applying the values:

$$\text{PriceOutcomeA} = \frac{1098}{1098 + 188} = 0.55$$ $$\text{PriceOutcomeB} = \frac{910}{1098 + 910} = 0.45$$

Bob’s purchase increased the price of Outcome A, reflecting higher market confidence in this result. The AMM ensures continuous liquidity, adjusting prices dynamically as users trade.

Benefits

• Continuous Liquidity: Traders can always buy or sell outcome shares without waiting for a counterparty.
• Dynamic Pricing: Prices adjust automatically based on supply and demand, reflecting the collective market sentiment.
• Decentralization: The AMM operates without intermediaries, ensuring a trustless and transparent trading environment.

Considerations

• Price Slippage: Large trades can significantly impact outcome prices, leading to less favorable rates for traders.

By leveraging the AMM model, Panana Predictions offers a robust and efficient platform for decentralized prediction markets, ensuring fair pricing and ample liquidity for participants.