Solovay rank-comparison game

In the Solovay rank-comparison game, Players I and II produce $x,y\in {\omega }^{\omega }$; ill-founded codes lose before ranks are compared, and among well-order codes the prescribed inequality between $\Vert x\Vert$ and $\Vert y\Vert$ decides the winner. No strategy for Player I can uniformly produce a well-order code at least as long as every code produced by Player II.