Ah, I think I can stymy with 2 nonconstant advisors. Namely, let and . We (setting up an adversarial ) precommit to setting if and if ; now we can assume that always chooses , since this is better for .

Now define and . Note that if we also define then is bounded; therefore if we can force or then we win.

Let’s reparametrize by writing and , so that .

Now, similarly to how worked for constant advisors, let’s look at the problem in rounds: let , and for . When determining , we can look at . Let . Let’s set to 1 if ; otherwise we’ll do something more complicated, but maintain the constraint that : this guarantees that is nondecreasing and that .

If then and we win. Otherwise, let , and consider such that .

We have . Let be a set of indices with for all , that is maximal under the constraint that ; thus we will still have . We shall set for all .

By the definition of :

For , we’ll proceed iteratively, greedily minimizing . Then:

Keeping this constraint, we can flip (or not flip) all the s for so that . Then, we have , if , and for , if .

Therefore, , so we win.

Seems also like the “playing dead” behaviour. If you’re under attack and aren’t going to summon/indicate allies (via sadness) or enforce your boundary yourself (via anger) or appease the attacker (via submission), another option is to give up on active response and hope that if you play dead just right, they’ll lose interest for some reason. Many attackers’ goals are better served by a responsive opponent; and attacking someone dead is both potentially unhealthy and no fun.