All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Paying cash by the parties participating in the game is impermissible if the whole reward intended to be given only to the winning team, because it is sort of gambling and one of the games of chance as Allah The Exalted prohibited it, where He Said (What means): "O ye who believe! Strong drink and games of chance and idols and divining arrows are only an infamy of Satan’s handiwork. Leave it aside in order that ye may succeed." [Al-Maidah/90].
In this regard, Ibn Hajar Al-Haythami (May Allah have mercy on his soul) stated:"
The stipulation while racing in case of loss in which the loser is obliged to pay sum of money to the winner is impermissible and considered prohibited gambling." [Tohfat Al-Muhtaj vol.9/pp.402].
Lawful competitions are the ones which help a Muslim in Jihad (Fighting for the cause of Allah) and their rewards should be in a form of a sum or amount taken from one team and given to the winner one, whereas other teams aren't paying any cash in this regard. In addition, there is harm if the reward was given from a third party so long as it is not part of the game. And Allah Knows Best.