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 ?

What blogging type I am talking about. That happened recent 1-2 years in messenger Telegram, where blogs called "channels". Top channels now up to 500K subscribers and are like a small mass-media. Bloggers often use the trick described above to increase their audience. One may look at https://zen.yandex.ru/media/id/5ae4970ebce67e5cd9f4d664/moi-pobeg-v-tamtam-5b0856c200b3dd18a15d8772 to know how all that works.

Now another messenger TamTam is doing the same and you are welcome to math blog: https://tamtam.chat/math20

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 ?

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 ?

What blogging type I am talking about. That happened recent 1-2 years in messenger Telegram, where blogs called "channels". Top channels now up to 500K subscribers and are like a small mass-media. Bloggers often use the trick described above to increase their audience. Now another messenger TamTam is doing the same and you are welcome to math blog: https://tamtam.chat/math20

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 ?

What blogging type I am talking about. That happened recent 1-2 years in messenger Telegram, where blogs called "channels". Top channels now up to 500K subscribers and are like a small mass-media. Bloggers often use the trick described above to increase their audience. One may look at https://zen.yandex.ru/media/id/5ae4970ebce67e5cd9f4d664/moi-pobeg-v-tamtam-5b0856c200b3dd18a15d8772 to know how all that works.

Now another messenger TamTam is doing the same and you are welcome to math blog: https://tamtam.chat/math20

Let me try to describe what nowadays happens in some part of inet blogging: it seems to me that there might be interesting math behind that. Might be some game theory approach should be used since on the one hand blogs are competing with each other for subscribers (=money), on the other hand they should act cooperatively in order to increase number of subscribers (making cross advertising).

Hope some equilibrium between competition-cooperation might exists providing optimal solution. The question would be what is that optimal "strategy".

Setup:

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

Blog earns $K_i/( \sum K_i )$ money.

So: more subscribers blog has (relatively to other blogs) - more it earns. So the goal is it increase number of subscribers.

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 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.

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 ?

What blogging type I am talking about. That happened recent 1-2 years in messenger Telegram, where blogs called "channels". Top channels now up to 500K subscribers and are like a small mass-media. Bloggers often use the trick described above to increase their audience. Now another messenger TamTam is doing the same and you are welcome to math blog: https://tamtam.chat/math20

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 ?

What blogging type I am talking about. That happened recent 1-2 years in messenger Telegram, where blogs called "channels". Top channels now up to 500K subscribers and are like a small mass-media. Bloggers often use the trick described above to increase their audience. Now another messenger TamTam is doing the same and you are welcome to math blog: https://tamtam.chat/math20