I don't think that's how income taxes work. In your scenario, the person in first would be overpaying taxes, and the person in second would be committing tax fraud. Income taxes should be paid on actual income.
If they split it means that they are adding up 1st and 2nd money and splitting it. Which means whoever wins pays the other guy about 50K.
1st place 150K - 50K = 100K but still has to pay taxes on 151K, ends up with 40K after taxes.
2nd place 50K + 50K = 100K and only has to pay taxes on 50K, ends up with 80K after taxes.
Make sense now?