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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 ?

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  • $\begingroup$ Sounds like prisoners dilemma $\endgroup$
    – Manfred Weis
    Commented May 25, 2018 at 3:59
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    $\begingroup$ The zero-sum assumption seems unrealistic, since good content can grow the reader pool, and bad content can shrink it. $\endgroup$
    – Joel David Hamkins
    Commented May 25, 2018 at 20:42
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    $\begingroup$ Indeed. I would like to think that good content should always outweigh attempts at self-aggrandisement by orders of magnitude. Look out Tao's or Baez's blogs. $\endgroup$
    – James Smith
    Commented May 25, 2018 at 20:47
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    $\begingroup$ So you need "content" in your setup or its not a maths blog! $\endgroup$
    – James Smith
    Commented May 25, 2018 at 20:48
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    $\begingroup$ You haven't defined a game yet. In a game, there is a set of players (defined), a set of actions (more or less defined -- I guess it is the choice of which other players to connect to), and a utility function for each player mapping the actions to a utility. This is not defined -- you define utility in terms of $\{K_i\}$ but you don't define how $K_i$ depends on the actions of the players. Once you define this, the game is finite so by Nash it will have a mixed strategy equilibrium (meaning the choices of whom to connect to may be randomized). $\endgroup$
    – usul
    Commented May 25, 2018 at 21:09

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