Blow-up conjecture for maximally imbalanced strongly playable RPS games

An $m$-player $(2n+1)$-$RPS$ game is a game with $2n+1$ objects and $m$ players interacting through the paper's $RPS$ payoff structure. A blow-up of a game $G_1$ at an object replaces that object by a copy of another game $G_2$, with strategies and payoffs induced by the corresponding projection. Let $m<n$, and let $G_1$ be the most imbalanced yet strongly playable $(2m+1)$-$RPS$ game. Let $G_2$ be the most imbalanced yet strongly playable $(2(n-m)+1)$-$RPS$ game. Blow-up conjecture. The most imbalanced yet strongly playable $m$-player $(2n+1)$-$RPS$ game is equivalent to the blow up of $G_1$ with $G_2$ at the most balanced object of $G_1$. The preceding construction describes blow-ups and gives the relevant equilibrium correspondence, but the stated equivalence is left as a conjecture in the source.