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.
[1] G. Z. Chang and T. W. Sederberg, “Over and Over again,” New Mathematical Library, 39. Mathematical Association of America, Washington DC, 1997. xiv+309 pp. ISBN: 0-88385-641-7.
[2] G. Latouche and V. Ramaswami, “Introduction to Matrix Analytic Methods in Stochastic Modeling,” 1st Edition, PH Distributions, ASA SIAM, 1999.