📐Mathematical Modeling

Mathematical Modeling

The P2P exchange utilizes mathematical models to ensure efficient, secure, and fair trading:

Escrow and Dispute Resolution

Escrow Security: The smart contract escrow system is mathematically modeled to ensure that assets are only released when both parties meet the trade conditions.

The escrow condition can be expressed as:

$$\text{Escrow}(A, B) = \begin{cases} A \to B & \text{if trade conditions are met} \\ A \to A & \text{if trade conditions are not met} \end{cases}$$

Where 𝐴 and 𝐵 represent the trading parties.

Incentive Compatibility

A penalty model is implemented to discourage bad behavior. If a party attempts to back out after agreeing to a trade, they may forfeit a portion of their assets, ensuring both parties are incentivized to complete the transaction.

Atomic Swaps are mathematically defined to ensure that cross-chain trades are atomic, meaning they either fully complete or do not occur at all:

$$\text{Atomic Swap}(A, B) = \begin{cases} \text{Success}(A \to B) & \text{if HTLC conditions are met} \\ \text{Reversal}(B \to A) & \text{if conditions are not met} \end{cases}$$