papers/hanzo-dso/sections/09-incentive-mechanisms-and-poai-integratio.tex

\section{Incentive Mechanisms and PoAI Integration}

\label{sec:incentives}

\subsection{Proof-of-AI (PoAI) Attestations}

Each prior submission includes a PoAI attestation containing:
\begin{itemize}[leftmargin=1.5em]
    \item \textbf{TEE report:} Trusted execution environment attestation proving
          the prior was generated by legitimate ASO execution.
    \item \textbf{Task metrics:} Information gain $\Delta I$, utility improvement
          $\Delta U$, and compute cost.
    \item \textbf{Holdout results:} Performance on a reserved validation set.
\end{itemize}

\subsection{Emission Formula}

The reward for submitting prior $i$ is:
\begin{equation}
    R_i = \gamma \Delta I_i + \beta \Delta U_i - \lambda_c \cdot \text{cost}_i,
    \label{eq:emission}
\end{equation}
where:
\begin{itemize}[leftmargin=1.5em]
    \item $\gamma = 1.0$: Weight for information gain (measured as KL divergence
          between prior and posterior task distributions).
    \item $\beta = 0.5$: Weight for utility improvement (measured as
          pass-rate improvement on holdout tasks).
    \item $\lambda_c = 0.1$: Cost penalty (discouraging wasteful compute).
\end{itemize}

\subsection{Quality Score Evolution}

Quality scores evolve via exponential moving average:
\begin{equation}
    q_i^{(t+1)} = (1 - \rho) \cdot q_i^{(t)} + \rho \cdot q_i^{\text{new}},
\end{equation}
where $\rho = 0.1$ is the update rate and $q_i^{\text{new}}$ is the latest
validation score. This smooths out noise while allowing quality to track genuine
changes.

\subsection{Game-Theoretic Analysis}

\begin{proposition}[Honest Submission is Nash Equilibrium]
Under the DSO incentive structure, honest prior submission is a Nash equilibrium
when the expected reward for honest submission exceeds the expected reward for
any deviating strategy:
\begin{equation}
    \mathbb{E}[R_{\text{honest}}] - D_{\min} > \mathbb{E}[R_{\text{deviate}}] - \sigma D_{\min}.
\end{equation}
This holds when $\gamma \Delta I_{\text{honest}} + \beta \Delta U_{\text{honest}} > (1 - \sigma) D_{\min}$,
i.e., when honest priors generate meaningful information gain and utility
improvement relative to the bond.
\end{proposition}

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