The break-even price b (obtained through an optimally biased
bent coin) tells us that when we offer a challenge
MAXCSP classic ( belief (R,ar) , confidence)
[offerer claims there is a problem where ar CANNOT be satisfied]
with approximation ratio ar, we know that ar > b.
We have a lower bound for ar for offering.

Can we also get an upper bound? Yes: ???? if we have a problem PT where
all solutions satisfy less than T. In this case, T > ar > b.
If an agent accept our challenge, we give it PT to solve and
we know that

strange: no longer reason about profit but about whether supporting
or discounting will happen.

If ar >> b: offerer has possibility of supporting
(if ar < b: acceptor would discount, if acceptor is rational)

How much bigger than b should ar be? Depends on the problem size.
If we have a problem PT of allowed problem size where
all solutions satisfy less than T. 
If ar = T, we will have support: offerer gives PT as problem and offerer wins support.