papers/hanzo-checkout/sections/04-payment-orchestration.tex

\section{Payment Orchestration}


\subsection{Multi-Processor Architecture}

Hanzo Checkout integrates with multiple payment processors to optimize for cost, success rate, and availability:

\begin{equation}
\mathcal{G} = \{g_1, g_2, \ldots, g_n\}
\end{equation}

where each gateway $g_i$ has characteristics:
\begin{itemize}
    \item $fee_i(a)$: transaction fee function
    \item $success_i$: historical success rate
    \item $latency_i$: average response time
    \item $cards_i \subseteq \mathcal{CARD\_TYPES}$: supported card types
\end{itemize}

\subsection{Routing Algorithm}

\begin{definition}[Routing Score]
For transaction $T$ and gateway $g$, the routing score is:
\begin{equation}
score(T, g) = w_s \cdot success_g - w_f \cdot fee_g(T.a) - w_l \cdot latency_g
\end{equation}
where $w_s, w_f, w_l$ are merchant-configurable weights.
\end{definition}

\begin{algorithm}
\caption{Intelligent Payment Routing}
\begin{algorithmic}[1]
\Function{RoutePayment}{$T$, $\mathcal{G}$}
    \State $eligible \gets \{g \in \mathcal{G} : supports(g, T)\}$
    \If{$eligible = \emptyset$}
        \State \Return \textsc{NoEligibleGateway}
    \EndIf
    \State $scores \gets \{(g, score(T, g)) : g \in eligible\}$
    \State $primary \gets \arg\max_{(g,s) \in scores} s$
    \State $result \gets$ \Call{ProcessPayment}{$T$, $primary$}
    \If{$result.success$}
        \State \Return $result$
    \EndIf
    \State \Comment{Automatic failover}
    \For{$g \in eligible \setminus \{primary\}$ \textbf{by} $score$}
        \State $result \gets$ \Call{ProcessPayment}{$T$, $g$}
        \If{$result.success$}
            \State \Return $result$
        \EndIf
    \EndFor
    \State \Return \textsc{AllGatewaysFailed}
\EndFunction
\end{algorithmic}
\end{algorithm}

\subsection{Dynamic Fee Optimization}

Transaction fees vary by card type, transaction amount, and geographic region. We model the fee structure as:

\begin{equation}
fee(T, g) = base_g + rate_g \cdot T.a + surcharge(T.card\_type, g)
\end{equation}

\begin{theorem}[Cost Minimization]
For a set of transactions $\mathcal{T}$ over time period $t$, our routing algorithm achieves cost within $(1 + \epsilon)$ of optimal:
\begin{equation}
\sum_{T \in \mathcal{T}} fee(T, route(T)) \leq (1 + \epsilon) \sum_{T \in \mathcal{T}} \min_{g \in \mathcal{G}} fee(T, g)
\end{equation}
where $\epsilon \rightarrow 0$ as $|\mathcal{T}| \rightarrow \infty$.
\end{theorem}