We were in a similar situation very recently. There was apparently another party interested and bidding against us. We mulled it over a lot and concluded that:
There is no point in offering your maximum price to "blow the other parties out of the water". We figured the other party will go as high as they can anyway, doesn't matter how fast you get tho their maximum price. I don't think people would get scared by a high bid going in against them, they will just reach their maximum limit at some point. If you do put in your own maximum bid straight away, you could end up paying more than you would otherwise have got the property for by going up in smaller increments.
Each time we put in a new bid, we played it down as much as we could (i.e. said we had to consider what it was worth to us given that we had to do work on the place / we were very anxious to keep it under a certain level, etc.). Also, we did not counter-bid straight away, but came back maybe the next day, etc. We did not want to convey the impression that we would happily match any bid that came in against us. At one point, we went out to view the house again, given that the price was going up beyond what we had expected it to, we wanted to check if it was still worth it given the amount of work that would have to be put into it - basically, we tried to put as much doubt in the estate agent's mind as possible so that she would feel we could not be taken for any amount (in case the other bidder was a phantom bidder).
We decided against saying "our offer only stands until tomorrow evening", etc. (this tactic is recommended many times elsewhere in this forum). The reason we decided against this approach was that we were not prepared to walk away that easily as the house was unique. Putting a deadline on our offer would have meant our bluff could easily have been called and our credibility in terms of limits etc. would be gone. Instead, we said that: we like this house and want to buy it, so we are not looking at other houses this week; but we will start looking again next week and arrange viewing of other houses.
Phantom bidder bidding against us? It was impossible to tell, but we think the other bidder was real because: the house was very competitively priced / it was new to the market / it was in a good area / we got others to phone in to the estate agent and enquire about the house, to be told there were two parties bidding on it and it looked like it would "go sale agreed this week". It was of course possible that we were being played but, despite the slack market, people are still buying houses! (actually, three people were bidding for the house we sold ourselves)
To conclude, my advice to your brother is:
Do not bid in large increments - you could overpay for the house and the estate agent could think you are nowhere near the end of your limit yet.
Put up with the stress for an extra week! It could save you several thousand euro. How long would it take him to earn that money?
No harm in dragging it out a bit - in selling our house, our experience was that other bidders tend to drop out for reasons other than money, e.g another house came up / the sale of their own house stalled. He could be left as the last man standing at a lower price than if he bid high straight away.
This is a time for a cool head! The vendor will not let the property go without your brother having the opportunity to bid his maximum price at some stage - he will not lose the property by not acting quickly.
Best of luck to your brother.