You can add gold to petty cash to buy inducements. For the team that has the higher team value (so the team that wouldn't get inducements) it works pretty straight forward.
Example: If that team wants an Apo (100k), it adds 100k gold to petty cash and buys an Apo.
For the team with the lower team value (which already gets inducements) things are slightly more complicated if they want to add petty cash.
Example: The difference in team value is 100k. The team with the lower TV wants a wizard (150k). This team would now have to add 150k (=the complete amount!) to petty cash to be able to get that wizard. Adding 50k would not do the trick.
The reason for that is that the sequence goes like this:
(1) withdraw money from your bank account to petty cash. This money is added to your TV
(2) calculate the TV difference.
(3) Get inducement money based on the TV difference after you've withdrawn money from your account.
So in the example above we have team A with TV 1000 and team B with TV 1100.
Team A gets 100k inducements but wants a wizard. Team A adds 50k to petty cash thinking that 100k + 50k = 150k = wizard.
But the game adds the 50k to team A's team value making it TV 1050.
Then it calculates the TV difference to team B which now is 50k.
And gives team A 50k of inducements.
That plus the 50k in petty cash make 100k inducements and team A still cannot hire a wizard.
A complete list of inducements:
Just keep in mind that not all Star Players are available in the computer game. Here is the list of the ones you can get: