I strongly believe that Static is better (and it would make much more strategic the protection of the earlier planets, with low Influence upkeep) but obviously it would make the curve less steep.
It's not necessarily a problem though, and I like the idea of solving Influence deficit by abandoning only a few planets (the most expansive ones).
It would also make conquering enemy planets even when you know that you won't be able to hold them a very valid strategic option, as they would lose their old Influence low upkeep and gain a quite high Influence upkeep when reconquered.
Mathematically, Static influence cost progression would change the calculations made by Oberlus a lot, making the unaffordable cost come later, and only preventing from creating a new colony, not endangering the already-existing Empire.
I wonder also whether Influence focus should cancel Influence cost on a planet ? It would certainly make easier (maybe too easy, I have trouble estimating it) managing Influence deficit, and if we don't implement it that way, it would mean that with exponential Influence cost, the Influence cost of a planet could get higher than its Influence production when on Influence focus, making getting out of deficit impossible (except by abandoning planets).
Note too that imho Influence should not be a constraint for Empires at early game; this would add nothing and make the game only more tedious. It should begin to be something to care for at mid-game, and be a real problem only at end-game.
The "colonize everywhere" only becomes tedious rather than fun at end-game (and is less fun at mid-game, I reckon) and the exponential progression of production and research only becomes a problem rather than a boon at late mid-game.
I think one thing that is omitted in your plans is the exponential curve of Influence production : of course if Influence production is as much exponential than Influence cost, we're back to the initial problem and Influence wouldn't bring anything to the game.
We need an exponential curve for Influence cost, I think there is consensus about that. But also a different, slower (and more dependant on the player's choices and strategic success) exponential curve for Influence production (number of planets put to Influence focus * some IP-boosting techs or buildings or policies) can help diversifying the available strategies and make for a more interesting game.
Oberlus may be right to want to centralize the discussion here, so I'll answer Vezzra here.
Vezzra wrote: ↑Sun Nov 08, 2020 2:22 pmThe fact that there is no policy that's optimal for all kind of "empire shapes", and that switching policies comes with a cost. Meaning, you have to decide how you want to expand, and how you want to "shape" your empire, then choose which policy you want to go for that's best for your intended strategy.
Of course you can try to switch back and forth between different policies, but as I said, that will come with a cost, and frequent switching of course needs to be made not viable, so you have to stick to a certain choosen strategy. Only switching if there is a really good reason.
OK, definitely people playing a strategic game like FreeOrion are bound to consider planification fun (or at least challenging intellectually), so I accept your argument that trying to predict which Empire shape one should use and then choosing the right Policy accordingly could be interesting (as well as trying to cope with the discrepancies between what was planned and what actually occurred later).
I wonder if it's enough though ? Especially, having too clear-cut Empire shapes and corresponding Policies (I mean, when choosing a particular Policy becomes a no-brainer) would be quite uninteresting and unchallenging.
I like this idea much better that the one of having Influence deficit lower Stability/Happiness as it was proposed earlier; if Stability just doesn't grow anymore but doesn't go down either, it's a real problem for the Empire that is in Influence deficit, but he still can limp on for a while (with the Production and Research of planets already at a high enough Stability) and that makes going in Influence deficit for some time a valid strategy in some situations, which (as I emphasized before) enriches the game.