Do acts decide 'ah we will tour and they pick destinations'
Is it record labels/band management who put on a tour and send notices too all concert promoters and they bid for it
Do acts have much say really in it all
Every which way you can imagine. Just one example of many would be:
An act makes it known their intention to tour. MCD/Aiken/Promoters tender for them to play their city/venue. Group agrees. Set fees, promoter gets the excess. Which is pretty much what you said above.
Another is where a group will hire a company (or may possess that staff themselves) and essentially hire the venues themselves, and just pay the promoters a fee. Group gets the excess.
Honestly though these are just two of a bazillion ways it is done.
Bands will have a booking agent only in some cases will this be a member of the actual band so often the bands themselves will be oblivious to why they haven't played whichever country (e.g. Ireland).
If venues can't meet the needs of what the act requires or subsequently they are booked by another act(s) over the timeframe of tour that city will be overlooked.
There is somewhat of a stumbling block with Livenation being in bed with MCD and overseeing the majority of venues say Dublin (3,Olympia, etc. etc.) that for the most part are unlikely to host events other promoters could wish to put on.
Bookers for event promoters (like MCD) will source acts that are touring / open to touring and commit a date / venue / fee etc. The promoter is then responsible for putting on the show.
Acts will have a booking agent and tour manager to liase with the above
The act turns up, plays, moves onto the next show.
In some cases there are event buyers, who buy the show from the promoter.
Generally the larger the band, the less touring control they actually have as it’s all contract / logistically bassed.