Tractability conjecture for graph Ramsey achievement games

Let $K_n$ be the complete graph on $n$ vertices, let $A$ be the achievement graph, and let $E^r$ and $E^g$ be the precolored red and green edge sets. Achievement-game tractability conjecture. Graph Ramsey achievement games played on $(K_n,A,E^r,E^g)$ are tractable. This conjecture is motivated by evidence of tractable subcases, although the paper does not establish tractability in the full stated setting.