The case study has shown that Alpha somewhat leans towards the polycentric hiring approach, meaning that foreign subsidiaries are staffed locally to a certain extent, but some limitations such as hiring costs have also been mentioned in the text.
Ultimately, I would think that the geocentric hiring approach would be the best solution in the long-run, if we're talking about having the best people to manage in each locations, regardless of their nationality. However, I do also believe that this is the most costly approach, as candidates with talent will seek higher salary and the position will be highly competitive (because people from any country can apply), meaning that the HR department have to process all the applications. I think currently only a huge company would be able to do this, but with the improvement of the AI, this method may be available to smaller firms in the near future.