In this post I continue my exploration of the [1]. This time let us consider what happens if the users who were matched are replaced by a random sample from the population. Will only the least and most attractive ones remain unmatched?
Well, at least it was as productive on Physics of Risk blog. Though with less focus with quite a few assorted posts. In a few a bit longer series of posts we have taken a look at three papers I have found interesting. [1] inspired few posts on traffic. [2] inspired couple posts on biology. Exploration of [3] continues in series of posts on dating apps.
Fig. 1:The number of posts written in English and still available on this iteration of Physics of Risk. The wide bars represent total number of posts for each year since 2010, while the narrower bars represent a number of posts with 'Interactive models' tag.Once again, at the time of writing this post, I still do not have an idea what we will have in store for 2023. Obviously, we will finish dating apps series. And then we will have a few more assorted posts?
In this post I continue my exploration of the [1]. In this post I will consider what happens if the users decide to dropout from the app as soon as they are matched with somebody.
In this Numberphile video Dr. Emily Riehl introduces stable marriage problem.
Practical applications of Gale-Shapley algorithm are much less romantic. Variations of the algorithm is used to, for example, optimize assignment of users to servers in content delivery networks. Similarly optimal matchings are often need in economic and management sciences. In fact, L. Shapley was awarded Nobel Memorial Prize in Economics in 2012 (together with A. Roth) for the theory of stable allocations. One of the most well known examples of this is matching graduating medical students to their first hospital appointments.
In this post I continue my exploration of the [1]. Yet here I will slowly start moving away from the course of the original manuscript.
The original manuscript [1] also explores unbiased decision model. In the unbiased model users make decision only based on the attractiveness of the recipient. For some reason I do not feel that unbiased decisions are realistic (though only the data can tell this) and thus I will not explore the unbiased model.
The original manuscript is also concerned with another important feature of the dating apps: visibility of the users. It is not likely, but still somewhat possible, that I will also follow in this direction.
Still this post is within the scope of the original manuscript, as when reading it I wasn't able to understand whether static or dynamic model is considered. So here I present you a dynamic biased decision model.
Physics of risk, complexity and socio-economic systems.