Numberphile: Stable Marriage Problem

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.

Dynamical model of dating apps

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.

Statistical physics of dating apps?

Previous summer I have stumbled upon an interesting manuscript [1], which explores dating app dynamics (?) from the perspective of statistical physics. I am not sure about the "dynamics" part, as to me it appears to be more "static" than "dynamic", but nevertheless the manuscript caught my attention and I would like to discuss some related questions in the next few posts.

In this post we will take a look at static interpretation of the "biased decisions" model from the manuscript [1].