Practical examples of fair division algorithms being used Consider the problem of fairly sharing a homogeneous cake between two people. It is well-known that a fair division can be achieved through the divide and choose procedure: player 1 cuts the cake into two pieces and player 2 chooses a piece.

This problem can be generalized to non-homogeneous cake, more than two players, etc.

My question is: are there any concrete examples of people using the fair division procedures (such as divide and choose) that emerge as the solution to such problems in practical applications?
The easiest generalization, of envy free sharing of a heterogeneous cake between two cake eaters is quite common. My family growing up frequently used the you divide and I choose method for sharing a lone piece of dessert. Depending on what you'd accept for "concrete example", Abraham and Lot use this method to divide the land of Canaan.  A  two-stage fair division problem was used in the partitioning of Germany after World War II. The Talmud has examples of fair division rules, which though are only thought experiments, are thought to have been applied in the Jewish diaspora over inheritance matters. 

I would also argue that the marriage / matching problems of Lloyd Shapley and Alvin Roth are a form of fair division, and one that scales to very large numbers of players and applies only to multiple, indivisible "cakes. Their methods have been used extensively in real world problems of school, job, and kidney assignment.