[0,1]. The “t-parameter” was 0.1. Each PhD student was given an “objective value,” uniformly chosen from [0,1]. I then ran a for loop 100 times representing 100 years. In each year, I iterated from the 0th department (“best”) to the 9th department (“worst”), calculating the “subjective value” for each student. After adding the top two students to the ith department, I dropped them from the PhD pool and then dropped the oldest two faculty members (I suppose their last decision before becoming happily emeritus). I then added 1 year to the age of each faculty member. After playing around with a few set.seeds, one sees a pattern that 70-80% of the departments become Algasis dominated, which I believe supports a steady state argument. I record these experiments in this google colab notebook, https://colab.research.google.com/drive/1Wo0rC0-zkmsMMNfDuSwXm6jcRTTUJUC2 , so it shouldn’t be too hard to play around further and in case my verbal description was not adequate. ]]>

Let’s look at just the top university. This has the advantage that it’s not influenced by the other universities. At the beginning, there’s a positive drift in the number of algasists there, which will rise roughly until it gets to the equilibrium point – until the percentage is such that the expected number of hires matches this percentage. Now, for 100% algasists we still get that the probability of hiring algasists is less then 100%, so the equilibrium is not at 100% algasists, but rather at some 0.75<A<1. Of course, we still have random fluctuations, so there's a small chance (exponentially small in the number of faculty) that there's a streak of hiring anabraists, which might cause them to become to majority, or even completely take over the department. When this happens, the value of t becomes very important – if it's small (say, less than 1/100 or so) – then there's still better chances for hiring algasists, so they will again become to majority after a short while. If t is large enough (say, 1/10), then the anabraists majority will be semi-stable (meaning it will go on for a exponentially long time). This is all due to your assumption that the new students are still 75% algasists and 25% anabraists regardless of the faculty and that their values are i.i.d.

I'm guessing that something similar also happen when looking at the entire group of universities. If you change the model slightly so that the number of students in each area is proportional to the number of faculty in this area, then the only stable states are when everyone is of the same area.

Regarding similar models in literature, I am reminded of work by Noga Alon, Michal Feldman, Yishay Mansour, Sigal Oren, Moshe Tennenholtz on "Dynamics of Evolving Social Groups" (https://arxiv.org/abs/1605.09548).

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