The three-action zero-sum discrepancy-free region

Let $S=\{s_3,s_2,s_1\}$ with $s_3<s_2<s_1$. Let $o_{\mathrm{zs}}$ denote the zero-sum scoring-play outcome and let the antagonistic self-interest game use AvA tie-breaking. Three-action discrepancy-free-region conjecture. There is no discrepancy between these games if

$$s_2\leq 2s_3\quad\text{or}\quad s_1\geq s_2+s_3.$$

The claim is inferred from computational plots of the three-action parameter space and is explicitly presented as a conjecture; no proof or resolution is given.