# Good model to reward contributions

I hope you guys find this an interesting question. Imagine you want to implement a system that rewards people for their contributions (regardless of quality or any external assessment). What is a good model, considering the following conditions:

• It shouldn't reward people that contributes "excessively" only to gain whatever you're giving as reward. For example, if you're giving an award for 5 contributions, then you can't give that award again because of the sixth contribution.
• It shouldn't be too complex to be computationally unfeasible (although, if you know of something complex but interesting, I'd like to know about it).

As a clarification, the situation is such that you want to give a single award (instead of a variety of them).

Maybe you know some established theory dealing with this kind of stuff. Let me know if that's the case.

By the way, I searched in Google Scholar but I didn't find anything relevant.

Thanks!

-
I do not really think this can be considered a mathematical question until you're more specific about what you mean by "best." – Qiaochu Yuan Jun 9 '12 at 18:35
@QiaochuYuan Don't be distracted by "best". After all, it's not an optimization problem. I just want to read good ideas about this. – Robert Smith Jun 10 '12 at 3:44
Anyway, I changed 'best' to 'good' to avoid any confusion :-) – Robert Smith Jun 10 '12 at 3:46

Your reward function can follow the Erlang distribution for instance. If $c$ denotes the contribution, then the reward is $r(c)$ given as $$r(c) = r_{\max} \int_{x=0}^c \dfrac{\lambda^k x^{k-1} \exp(-\lambda x)}{(k-1)!} dx$$ where $r_{\max}$ is the maximum reward one can earn. This is the Erlang distribution. The parameters $\lambda$ and $k$ affect the rate of decay and the shape of the distribution respectively.