I don't think it is fair t award money for being in the cup but not playing either. every game a team has the chance to get eliminated, so it wouldn't be fair to have others teams sit at home getting the same money and no chance of elimination that week...
I'm not sure what you mean with the bots, but if you mean that if you have to play bots often you have lower income, then I don't think that is bad either, since you have more chance to advance an other round...
I don't think it is possible to come up with a system that is fair to all and distributes money fairly to all in the same time.
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