papers/lux-decentralized-cloud/sections/08-economic-model.tex

\section{Economic Model}
\label{sec:economics}

\subsection{Provider Economics}

A provider's profit in epoch $t$ is:

\begin{equation}
    \Pi_{\mathcal{P}, t} = \underbrace{\sum_{i} p_i \cdot q_i}_{\text{service revenue}} - \underbrace{c_{\text{infra}} + c_{\text{stake}}}_{\text{costs}} - \underbrace{\sigma_{\text{penalty},t}}_{\text{slash losses}}
\end{equation}

where $p_i$ and $q_i$ are the price and quantity for service $i$,
$c_{\text{infra}}$ is infrastructure cost (hardware, bandwidth, electricity),
$c_{\text{stake}}$ is the opportunity cost of locked stake, and
$\sigma_{\text{penalty},t}$ is any slashing penalty incurred.

\subsection{Stake-Weighted Provider Selection}

Users select providers through a stake-weighted lottery modified by reputation:

\begin{equation}\label{eq:selection}
    \Pr[\text{select } \mathcal{P}] = \frac{S_{\mathcal{P}} \cdot \mathsf{Rep}(\mathcal{P})}{\sum_{\mathcal{P}'} S_{\mathcal{P}'} \cdot \mathsf{Rep}(\mathcal{P}')}
\end{equation}

This creates a positive feedback loop: providers with high stake and high
reputation receive more traffic, earn more revenue, and can afford to stake
more. The reputation component prevents pure plutocracy---a high-stake
provider with poor service quality loses reputation and traffic despite
its stake advantage.

\subsection{Slashing Conditions}

Providers are slashed for four categories of violation:

\begin{enumerate}
    \item \textbf{SLA breach.} Failing to meet committed latency, availability,
    or durability targets. Penalty: $1\%$--$5\%$ of stake per violation,
    scaling with severity.

    \item \textbf{Data loss.} Failing a proof-of-spacetime challenge, indicating
    data loss or unavailability. Penalty: $5\%$--$10\%$ of stake.

    \item \textbf{Equivocation.} Producing conflicting receipts for the same
    service interaction (evidence of fraud). Penalty: $100\%$ of stake
    (full slashing).

    \item \textbf{Censorship.} Selectively refusing to serve specific capsules
    (detected via statistical analysis of receipt patterns). Penalty:
    $10\%$--$50\%$ of stake.
\end{enumerate}

\begin{proposition}[Economic Finality of Slashing]
Under the Lux slashing model, a rational provider with stake $S$ and
expected epoch revenue $R$ will not engage in equivocation if:
\begin{equation}
    S > \frac{R \cdot T_{\text{remaining}}}{\Pr[\text{detection}]}
\end{equation}
where $T_{\text{remaining}}$ is the remaining staking epochs. For the
minimum stake requirement and typical revenue, this condition is satisfied
when $\Pr[\text{detection}] > 0.01$.
\end{proposition}

\subsection{Market Equilibrium}

In the long run, the provider market converges to a competitive equilibrium
where provider margins approach zero economic profit (revenue equals cost
including opportunity cost of capital):

\begin{equation}
    \lim_{t \to \infty} \Pi_{\mathcal{P}, t} = 0 \quad \text{for all } \mathcal{P} \text{ in competitive equilibrium}
\end{equation}

This is the standard result for competitive markets. The Lux model achieves
this equilibrium faster than centralized markets because: (i)~provider
switching costs are near zero, removing the friction that sustains
supranormal profits; (ii)~reputation is public and verifiable, reducing
information asymmetry; and (iii)~market clearing is automated and
transparent, eliminating price discrimination.

\subsection{Network Effects Without Lock-In}

The Lux provider market exhibits network effects (more providers attract
more users, which attract more providers) without the lock-in that
typically accompanies network effects in centralized platforms. The
mechanism is the open protocol: all providers implement the same
interface, so a user who joins the network to access one provider
can seamlessly use any other. The network effect accrues to the
protocol, not to any individual provider.