At the beginning of Rise of Rome and Napoleonic, at least - I haven't checked others yet, you can basically get the non-locked players to agree to anything in exchange for a diplomatic agreement on the first turn. Example: as Britain, ask Russia to ally with you and demand all but one of their cities in exchange. They will agree. Next turn, they demand the usual type of payoff.
You can not make any agreements during the first turn but then the computer will beat you to the punch "unfairly."
You can not make any agreements during the first turn but then the computer will beat you to the punch "unfairly."