This post may be a bit of mathematical overkill applied to a simple idea. I'll start with the basic concept, and then run off into mathland to eventually arrive at some possible game system.
Does rep decay over time? I couldn't find it in the rules but it would make a lot of sense in real world terms. Also, otherwise old people would have much more rep than young people simply by having accumulated it. So it would make sense to have rep drop if a character was not interacting with a network.
Conversely, how much rep can you get by doing ordinary work? A character in my game with 0 @-rep who arrived at Phelan's Recourse immediately logged onto the local equivalent to the Mechanical Turk and started doing trivial favors, earning some rep. What rep would he end up with if he kept this up indefinitely?
A simple model is to assume that rep decays with a constant rate 1/T (where T is the time constant, the time it takes for it to go down to 37%), and you do a favour that increases your rep with R L times a day. In the time between favors your rep declines exponentially as r(t) = r0 exp(-t/T) where r0 is your initial rep. In a steady state situation at time 1/L you finish your latest favor and get R rep, balancing the decline from the last favor: r0 exp(-1/LT) + R = r0, which gives us an equilibrium rep of r0 = R / (1-exp(-1/LT)). An approximation (valid if LT is big) is r0 ~= RLT. That is, your equilibrium rep is proportional to the sizes of your services, how often you do them and how slowly they are forgotten.
This makes sense (and might even be taken as pretty obvious). However, should you do a few big services or many small ones? Looking at the time it takes to do a service it seems to grow exponentially with the level. That makes the rate L you can perform the service decrease exponentially with favour size. So unless either the reputation reward R or the time constant increases exponentially with the level of the favour, the road to rep-riches is to do trivial things a lot. This is unlikely to work. Having exponential rewards works, but there is something strange with the idea that people will remember me saving the planet about as long as they remember that I opened the door for them. Instead (again, perhaps obviously) large favours should be remembered longer than small ones (they should have larger T).
How long should we remember big favours? The time it takes to do them and their refresh rate both are approximately exponential, and if the time constant is proportional to one of them we get a nicely balanced situation. Now small and big favours contribute about equally: if I do trivial favours all the time or if I build a habitat every few months, in both cases I end up with roughly the same equilibrium reputation. The only difference is due to how rapidly R increases with the favor level.
The rules in the rez section suggest a simple linear increase. This at first did not make sense to me: the player characters had saved the Saturn system from a seed AI, and they just got 8 rep points?! But this is actually pretty balanced. If reputation from big services decays more slowly than trivial services, its real value lies in its *stability* rather than how much it pushes your rep upwards. The trivial favours guy will lose all his stored rep if he ever lets up, while the system-saver can relax and look for other interesting things to do. A rep system that also awards enormous rep to high-level favours would create a nearly immobile "upper class" of people who have done something very good.
I have done various simulations of characters doing various mixtures of small and big favours, and the linear reward seems to have several nice properties: it is flexible (high rep people that stop doing things will eventually lose rep), it is fairly egalitarian (no gaps between classes of people) and there are rewards of doing big and meaningful things. I haven't thrown the maths at it, but no doubt a financial mathematician could have fun with a bit of stochastic differential equations and portfolio theory here. The lunar banks definitely do, and rake in profits from it.
Obviously it is not possible to run this kind of detail in the game itself (my players draw the line at differential equations as part of the house rules - yes, it is true!). So getting back to actual game system, it seems that one could have a decay rate of rep based on its level. If a character is not doing anything with a network their rep there should drop by 1 per (refresh time) x 3 or so. However, this might make very low reps rather unstable (blink, there went your 10 points in e-rep!). So maybe a gameplay compromise would be to have a lower decay rate of 1 point per month or so.
Perhaps one could even "park" one's rep by contacting a reputation manager who slows the decay by maintaining people's memories of past services.
I guess the moral is that the rep score hides an *enormous* complexity. EP rep is like PageRank, academic citation indices, Slashdot Karma points, mathematical finance and IOUs rolled into one, maintained by an infrastructure that has evolved over decades under the watchful eyes of experts, activists and gamblers. One should not take the actual number as anything but game mechanics (although there are no doubt many ways of visualizing rep scores elegantly or succinctly). But as this little essay shows, by tuning the system differently you can produce very different social outcomes.
—
