Math behind might be interesting.

Quite recent bloggingg activity might have interesting math model. The point is that bloggers compete for subscribers and at the same time cooperate gaining subscribers from partner's blogs. Question is about existence of something like J.Nash's equilibrium strategy which should balance competition/cooperation.

Setup:

There are inet blogs, each blog has $K_i$ subscribers (=readers).

"Competition:" Blog earns $K_i/( \sum K_i )$ money. So: more subscribers blog has (relatively to other blogs) - more it earns.
Each blogger's goal is to earn more money.

"Cooperation:" Assume the following cooperation behaviour: 10 blogs make agreement and each of them recommend to its subscribers to subscribe to that 10 blogs. Assume some small percent e.g. 1% of subscribers follow that recommendation, so $.01*(K_2+K_3+...K_{10}) $ subscribers comes to blog $1$ from blogs 2,3,...10, and $.01*(K_1+K_3+...K_{10})$ comes to blog 2 from blogs 1,3,4...10 and so on.

Question: What should be optimal choice of 9 partners for your blog, if you want to maximize your profit ? Assume you can (but not obliged) offer cooperation to any 9 blogs and they have right to accept / not accept your offer.

What is the point here: if you are the largest subscriber holder - probably you should NOT cooperate with anybody since it will decrease your relative advantage, on the other hand smaller bloggers will cooperate between themselves and if you do nothing sooner or later they will overcome you. That is why you probably should also act.

We might assume that cooperation process happens at the end of each day. And money are paid at the end of each day. So there is time evolution. Probably at the end we will come to uniform distribution of subscribers between blogs. But the question what are optimal choices at each time step.

It might be model should include more assumptions to be more interesting/realistic. We should take into account that if two blogs have the same audience, then self-advertising will not help.

Question: Any improvements to the setup ?