papers/zoo-tokenomics/sections/10-security-and-game-theory.tex

\section{Security and Game Theory}


\subsection{Validator Incentive Alignment}

Zoo's staking mechanism aligns validator incentives with network health:

\textbf{Reward Structure:}
\begin{itemize}
\item \textbf{Base Rewards}: 60\% of transaction fees (proportional to stake)
\item \textbf{Performance Bonus}: +10\% for 99.9\%+ uptime
\item \textbf{Correctness Bonus}: +5\% for zero invalid state transitions
\end{itemize}

\textbf{Slashing Conditions:}
\begin{itemize}
\item \textbf{Double-signing}: 50\% stake slashed + ejection
\item \textbf{Prolonged downtime} (>24h): 5\% stake slashed
\item \textbf{Invalid state transition}: 100\% stake slashed + ejection
\item \textbf{Censorship} (ignoring valid transactions): 10\% stake slashed
\end{itemize}

\textbf{Game Theory Analysis:}

Expected value of honest vs dishonest behavior:

\begin{align}
EV_{\text{honest}} &= R \times (1 + 0.10 + 0.05) = 1.15R \\
EV_{\text{dishonest}} &= R \times P_{\text{undetected}} - S \times P_{\text{detected}}
\end{align}

where:
\begin{itemize}
\item $R$: Base reward
\item $S$: Slashing penalty (0.5-1.0× stake)
\item $P_{\text{detected}}$: Probability of detection (>99\% for double-signing)
\end{itemize}

For double-signing attack:
\begin{align}
EV_{\text{attack}} &= R \times 0.01 - 0.5 \times \text{Stake} \times 0.99 \\
&\approx -0.495 \times \text{Stake}
\end{align}

Since $EV_{\text{attack}} < 0$ for any reasonable stake amount, rational validators choose honesty.

\subsection{Sybil Resistance}

Zoo implements multi-layered Sybil resistance:

\begin{enumerate}
\item \textbf{Stake Requirements}: Minimum 100M $\KEEPER$ to validate (0.01\% of supply)
\item \textbf{Identity Verification}: Validators must KYC (comply with AML/CFT)
\item \textbf{Reputation System}: Track record visible (uptime, accuracy, community votes)
\item \textbf{DAO Ejection}: Community can vote to remove malicious validators (66\% threshold)
\end{enumerate}

\subsection{Experience Marketplace Attacks}

Potential attack vectors and mitigations:

\subsubsection{Attack: Low-Quality Experience Spam}

\textbf{Vector:} Attacker submits hundreds of useless experiences to pollute marketplace

\textbf{Mitigation:}
\begin{itemize}
\item Minimum effectiveness threshold: +3\% vs baseline
\item Blind testing: DAO validators assess without seeing author identity
\item Deposit requirement: 1M $\KEEPER$ per submission (returned if approved)
\item Reputation penalty: Rejected submissions decrease author's future success rate
\end{itemize}

\subsubsection{Attack: Experience Plagiarism}

\textbf{Vector:} Attacker copies existing experience, submits as their own

\textbf{Mitigation:}
\begin{itemize}
\item Similarity detection: Compare embedding vectors against existing experiences
\item Timestamp priority: First submission wins in disputes
\item Attribution enforcement: Derivative works must credit originals (smart contract enforced)
\item DAO adjudication: Plagiarism claims reviewed by Experience Curation Board
\end{itemize}

\subsubsection{Attack: Wash Trading Experiences}

\textbf{Vector:} Attacker creates experience, uses Sybil accounts to inflate usage statistics

\textbf{Mitigation:}
\begin{itemize}
\item Payment requirement: All inferences cost IC or $\KEEPER$ (Sybil becomes expensive)
\item Usage pattern analysis: Flag accounts with unusual patterns (same experience repeatedly)
\item Effectiveness verification: Independent DAO testing confirms claimed improvements
\end{itemize}

\subsection{DAO Governance Attacks}

\subsubsection{Attack: Whale Voting Domination}

\textbf{Vector:} Large holder acquires >50\% of supply, controls all votes

\textbf{Mitigation:}
\begin{itemize}
\item Quadratic voting: 51\% of supply = only 71\% of votes (not enough for 75\% constitution amendments)
\item Delegation: Small holders can pool votes via delegation
\item Executive Director veto: Can override votes that violate 501(c)(3) mission
\item Market liquidity: Acquiring 51\% requires buying from existing holders (price impact prohibitive)
\end{itemize}

\textbf{Cost Analysis:}

To acquire 51\% (1.02T $\KEEPER$):
\begin{itemize}
\item At \$0.02/token: \$20.4B initial cost
\item Price impact: 51\% acquisition likely drives price to \$0.10+ (10× slippage)
\item Total cost: \$50-100B (exceeds market cap of most crypto projects)
\item Voting power: $\sqrt{1.02T} / (\sqrt{1.02T} + \sqrt{0.98T}) \approx 51.02\%$ (marginally above threshold)
\end{itemize}

This makes governance takeover \textbf{economically infeasible}.