Replacing values for large amounts of data - Python

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Hello everybody,
I am having this dataset of data:

product    Marketplace    product_type
1                  200               X
2                  300               A
2                  400               A
2                  200               A
3                  500               A
3                  400               A
3                  300               B

The output is looking like this:

product    Marketplace    product_type
1                  200               X
2                  300               A
2                  400               A
2                  200               A
3                  500               B
3                  400               B
3                  300               B

Basically, I'm changing the product type values if they differ for the same product. I tried the following code, but it works extremely hard for large amounts of data. Is there anything I could do about this or some suggestions?

What I have tried:

mp_correspondence = {200:1, 
                     300:2,
                     400:3,
                     500:4,
                    }
df['ranking'] = df['Marketplace'].map(mp_correspondence)
df
product_list = set(df['product'])
for i in product_list:
    df_product_frame = df[df['product'] == i].copy()
    nr_rows = df_product_frame['product'].count()
    if nr_rows > 1:
        df['product_type'] = (df.assign(ranking=df['Marketplace'].map(mp_correspondence)) \
                         .sort_values('ranking').groupby('product')['product_type'].transform('first'))