Bid above ask

I had to bid above ask 3 times earlier this year and each time was the same:

1) bid below ask - seller's broker responds to our broker that they already have bids above ask

2) bid slightly above ask - seller's broker responds to our broker that our bid matched very closely with the other buyers and we're in contention (buyer is deciding who would be a better fit - who had waived financing contingency, etc).

3) seller's broker responds and asks for final bids from all parties that have been selected. We bid what we feel that we would be willing to pay and no more. It has to be above previous bid but decide how much the apartment is worth.

4) Win or lose...

Is this how everyone else had bid when over asking?

if the co-op board is quite finincially conservative, how much bidding power would you have if strongly 'believe' you are extremely strong financially when compared to other bidders. E.g
A unit priced at 800k asks for 20% down, long employment history, liquid after closing of 3 years mortgage/maintainance

I don't think the bidding war has much to do with the board assuming all those 'invited' to bid are qualified, even if their finances and bids are not the same. This is most likely just a broker manipulation--they do work for the seller and themselves, and want to attract the highest bids they can. I'd expect the same if I were the seller.

a bidding war for a difficult coop is not just about the money--the bidders show they are financially "desirable" as well so any bidders taken seriously would be qualified.

From experience, could a 'exceptionally' qualified co-op buyer offer less than a 'barely' financially qualified buyer? Can a really uber rich person get a better price?

well, sure if those are the only 2 options a perfectly qualified buyer offering less is still more desirable than an iffy buyer offering more. But generally buyers and their brokers are aware of the requirements more or less so generally most bidders tend to be qualified when bidding for a difficult coop.

how do you interrogate the broker if planing to bid?

To avoid getting involved in an auction, we offered the seller 10% above the highest offer for an apartment we knew we wanted. That way, we weren't picking a number out of a hat in the hopes of exceeding the highest offer; we were simply willing to say that whatever the highest offer was, we were willing to pay 10% more.
We also knew that until a contract is signed, there is nothing to lose in making an offer this way.
The main thing we were trying to avoid was to arbitrarily select an amount which risked being too low than the highest offer (in which case we would lose the apartment), or selecting an amount which would have been way more than other offers.

It worked out well.

To avoid getting involved in an auction, we offered the seller 10% above the highest offer for an apartment we knew we wanted. That way, we weren't picking a number out of a hat in the hopes of exceeding the highest offer; we were simply willing to say that whatever the highest offer was, we were willing to pay 10% more.
We also knew that until a contract is signed, there is nothing to lose in making an offer this way.
The main thing we were trying to avoid was to arbitrarily select an amount which risked being too low than the highest offer (in which case we would lose the apartment), or selecting an amount which would have been way more than other offers.

It worked out well.

10% on a 700K apartment is 70 thousand dollars---that's a lot of bread, Fred !

oops. I mean 10K above asking.

I would tell the broker you'll "bid the ask plus one nuggit."