Here’s one way to do it in Pandas-way
You could groupby on Auction_ID and take rank() on Bid_Price with ascending=False
In [68]: df['Auction_Rank'] = df.groupby('Auction_ID')['Bid_Price'].rank(ascending=False)
In [69]: df
Out[69]:
Auction_ID Bid_Price Auction_Rank
0 123 9 1
1 123 7 2
2 123 6 3
3 123 2 4
4 124 3 1
5 124 2 2
6 124 1 3
7 125 1 1