papers/lux-fraud-proofs/sections/08-economic-incentives.tex

\section{Economic Incentives}


The economic design ensures rational actors behave honestly while minimizing capital requirements.

\subsection{Bond Requirements}

Asserters must stake bonds proportional to the value secured:

\begin{equation}
B_{\text{required}} = \max(B_{\text{min}}, \alpha \times \text{TVL}_{\text{rollup}})
\end{equation}

where $\alpha$ is the security parameter (typically 0.1-1\%) and TVL is the total value locked.

\subsection{Bond Slashing}

Invalid assertions result in bond slashing:

\begin{equation}
\text{Slash}_{\text{amount}} = \begin{cases}
B \times \beta_1 & \text{first offense} \\
B \times \beta_2 & \text{second offense} \\
B & \text{third offense}
\end{cases}
\end{equation}

where $\beta_1 < \beta_2 < 1$ implement progressive penalties.

\subsection{Challenger Rewards}

Successful challengers receive rewards from slashed bonds:

\begin{equation}
R_{\text{challenger}} = \text{Slash}_{\text{amount}} \times (1 - \phi)
\end{equation}

where $\phi$ is the protocol fee (typically 1-5\%).

\subsection{Griefing Attack Prevention}

To prevent frivolous challenges:

\begin{enumerate}
    \item Challengers must stake equal to defender's bond
    \item Failed challenges result in challenger slashing
    \item Exponentially increasing stakes for repeat challenges
    \item Reputation system tracking challenge history
\end{enumerate}