Equidistribution in Sharing Games

Games often provide a good introduction to interesting phenomena in mathematics. In this note, we examine three variations of an iterative sharing game played around a circular (or not so circular) table. More precisely, for each variation we study the tendency toward equal distribution among the players. In the first variation, the players have discrete amounts at each step. The second variation removes this restriction, and the third one considers an infinitely long table with an infinite number of players.