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 Alternative transitive games are flows proof with pseudoflows \begin{sepproof}[Transitive Games Are Flows Lemma (\ref{gameflow})] \ \\ Let $\mathcal{H}$ be an execution of the Transitive Game on graph $\mathcal{G}$ and $j$ the convergence turn. We will show that a flow from $A$ to $B$ can be constructed such that $\sum\limits_{v \in N^{+}\left(A\right)}x_{Av} = Loss_{A, j}$. First, we construct a pseudoflow $X$ on $G$ as follows: \begin{equation*} \begin{gathered} \forall v, w \in \mathcal{V}, x_{vw} = \sum\limits_{\overset{i = 0}{Player\left(i\right) = w}}^jy_i \enspace, \mbox{ where}\\ Steal(y_i, v) \in Turn_i \end{gathered} \end{equation*} The configuration described above is a pseudoflow \cite{amo} because \begin{equation*} \forall v,w \in \mathcal{V}, \sum\limits_{\overset{i = 0}{Player\left(i\right) = w}}^jy_i \leq DTr_{v \rightarrow w, 0} = c_{vw} \enspace. \end{equation*} By the definition of $X$, it holds that \begin{equation} \label{desiredoutgoingflow} \sum\limits_{v \in N^{+}\left(A\right)}x_{Av} = Loss_A \enspace. \end{equation} Suppose that $X$ contains a excess node $v$. In this node it is \begin{equation*} \sum\limits_{w \in N^{-}\left(v\right)}x_{wv} > \sum\limits_{w \in N^{+}\left(v\right)}x_{vw} \enspace. \end{equation*} By the definition of $X$ however, $v$ stole more than she was stolen, thus does not follow the conservative strategy. We have reached a contradiction, thus there exist no excess nodes in $X$.