Reading the primer. I will do dive in the proof part later ;-)
Do you view vote buying as a one time thing compared to vote incentivizing which is more recurrent?
Aren't you assuming that the only interest in voting will be monetary as soon as there are dividends? This is rather a pessimistic view that no one will vote for other reasons like security. I have to admit I totally think the same, unfortunately.
This scenario would happen if there is no cooperation between witnesses (to agree on prices) and no cooperation between users( let's make Pool A number 1 to earn more) . But we all know consensus is hard to achieve and the incentive to be selfish would be greater.
I am thinking of another equilibrium: the witness offers dividends until she reaches a certain position, say TOP 20 or 10. At this position, it is much harder for to get kicked out, so the witness can stop or lower the dividends and not look at the dividend market. What do you think?
By the way, I view those witness pools as a way for small witnesses to compete with the big players and companies we (will) have around here. EOS is a perfect example of what I expect to happen from a DPOS chain.