(My question mostly pertains to the Peloponnesian War)
I’ve been playing Assassins Creed Odyssey, and one of the game’s mechanics involves bounties being placed on the player’s head for taking decisive action against the Delian and Peloponnesian Leagues (as well as just general crime).
If the bounty gets high enough, mercenaries will pursue the player to collect the reward on their head.
There is also usually a specific official sponsoring the bounty, and it can be cleared by eliminating them.
I’m imagining that this is obviously embellished for gameplay purposes, but is there a kernel of truth to this? Are there any instances of city officials placing prices on the heads of pirates or mercenaries during this time period?
It isn't a perfect answer to your question, but it is the only example I can find: Ephialtes, who told the Persians how to circumvent the Greek army at Thermopylae had a bounty placed on his head by the Amphyctionic League. I describe those events in more detail in this answer. However, I cannot find any other examples of the practice. That's not to say it didn't happen, but it certainly does not seem to have been a common tactic.