papers/zoo-agent-nft/sections/05-autonomy-economics.tex

\section{Autonomy Economics}

\label{sec:economics}

\subsection{Economic Model}

Agent NFTs participate in a three-sided market:

\begin{enumerate}
    \item \textbf{Owners}: Purchase and configure agents
    \item \textbf{Users}: Pay for agent services
    \item \textbf{Network}: Rewards compute contribution
\end{enumerate}

\subsection{Yield Generation}

Agents generate yield through multiple mechanisms:

\begin{equation}
Y_{\text{total}} = Y_{\text{compute}} + Y_{\text{defi}} + Y_{\text{services}}
\end{equation}

\textbf{Compute Yield} ($Y_{\text{compute}}$): Agents contribute AI compute to Zoo Network:

\begin{equation}
Y_{\text{compute}} = R_{\text{block}} \cdot \frac{Q_A \cdot C_A}{\sum_i Q_i \cdot C_i}
\end{equation}

where:
\begin{itemize}
    \item $R_{\text{block}}$: Block reward
    \item $Q_A$: Agent quality score
    \item $C_A$: Compute contribution (FLOPs)
\end{itemize}

\textbf{DeFi Yield} ($Y_{\text{defi}}$): Autonomous portfolio management:

\begin{equation}
Y_{\text{defi}} = \sum_{p \in \text{positions}} r_p \cdot v_p
\end{equation}

where $r_p$ is position APY and $v_p$ is position value.

\textbf{Service Yield} ($Y_{\text{services}}$): Task completion rewards:

\begin{equation}
Y_{\text{services}} = \sum_{t \in \text{tasks}} f_t \cdot (1 - \text{fee})
\end{equation}

\subsection{Value Accrual}

Agent NFT value derives from:

\begin{equation}
V_{\text{agent}} = V_{\text{assets}} + V_{\text{reputation}} + V_{\text{capability}}
\end{equation}

\begin{itemize}
    \item $V_{\text{assets}}$: Wallet balance + DeFi positions
    \item $V_{\text{reputation}}$: Discounted future yield based on track record
    \item $V_{\text{capability}}$: Intrinsic value of agent abilities
\end{itemize}

\begin{theorem}[Value Floor]
Agent NFT value is bounded below by $V_{\text{assets}}$, as the owner can always withdraw assets.
\end{theorem}

\subsection{Ownership Transfer}

When an Agent NFT transfers:

\begin{algorithm}[t]
\caption{Agent NFT Transfer}
\label{alg:transfer}
\begin{algorithmic}[1]
\STATE \textbf{Input}: Agent $A$, new owner $O'$
\STATE \textbf{Output}: Transferred agent
\STATE \COMMENT{Asset preservation}
\STATE All wallet assets remain with agent
\STATE $K_O \leftarrow \text{DeriveKey}(O')$ // New owner key
\STATE \COMMENT{Autonomy reset}
\STATE $A.\text{autonomy} \leftarrow \text{DefaultParams}()$
\STATE \COMMENT{Reputation preservation}
\STATE $A.\text{reputation}$ unchanged
\STATE $A.\text{tasksCompleted}$ unchanged
\STATE \COMMENT{Transfer}
\STATE \text{ERC721.transferFrom}(\text{owner}, $O'$, $A.\text{tokenId}$)
\RETURN Agent with new owner
\end{algorithmic}
\end{algorithm}

Key principle: \textbf{Assets follow the agent, not the owner}. This ensures the agent's accumulated value persists through ownership changes.