If one said Re'Kha had the confidence of winning a mental battle with the Clan Heads, even she wouldn't believe it. After all, this was her first time participating in the auction. As for the Clan Heads, they had probably been in one too many times.
So, they were well-versed with all the ins and outs of the auction process. Moreover, they would be veterans of the game. Therefore, even if in a situation it appeared as if she was making them suffer a loss, it wouldn't have been the truth.
Rather, it was a fact she was being played by them. So, if she didn't wish to waste all her money on a worthless item, she had to be careful and not play the game of numbers against anyone before judging the worth of the auction item through her own means.
She mentally repeated the same many times, etching the fact in her mind to not get into a fight with anyone in the place.