Monotonicity conjecture for coexistence probabilities in the two-type Richardson model

Consider the two-type Richardson model on $\mathbb{Z}^d$ with $d\geq 2$, normalized so that type 1 has intensity $1$ and type 2 has intensity $\lambda$. Let $G$ be the event of infinite coexistence, and let $P^{1,\lambda}$ denote the law of the process.

Monotonicity conjecture. For $\lambda<\lambda'\in(0,1]$,

$$P^{1,\lambda}(G)\leq P^{1,\lambda'}(G).$$

This conjecture formalizes the expectation that coexistence becomes more likely as the weaker type's intensity increases toward that of the stronger type. It is proposed as a possible route to proving the only-if direction of the coexistence conjecture; no resolution is supplied in the given text.