It has been reported that the value for successfully completing a given encounter at a given age (fighting or negotiating) is a constant, and if so that would mean that there is a base value (dependent on age of the player) for completing all of GE (you can score more by failing a few times, but they might be ignoring that). This means that it is possible to compute the base total points available for totally completing GE that week, and the first goal may well be some percentage of that. Each round after that seems to go up by about 20% (but not exactly), so perhaps that percentage goes up by 20% and gets rounded each round.
There is then the conversion of GE Points to crowns, and there is likely a fairly simple formula for converting GE Points to Crowns, at least for the first round, and either that same formula is used each round, or perhaps there is a scale factor by round so they go up slower (or faster) than the number of points needed. It might also be possible that the crowns for round 1 is computed based on the sum of a value based on the age of the players (which might not scale exactly with the GE points available).
To confirm these, we would need to collect the number of points needed per round for a number of guild/competitions, the crowns rewarded, the number of players of each age that was in that group, the number of GE Points a player of each age earns from each encounter (or at least the base maximum sum). We probably also want to know if there was any loses that earned some GE points, as this might adjust the number of points needed for the next round.
A lot of data to collect and process.