Abstract
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.
Highlights
Suppose you have n persons seated around a circular table, each having an even number of dimes
We leave the details of the proof to the reader. Another interesting problem is to determine the number of iterations needed to reach equidistribution in terms of the initial data
Equidistribution is achieved at the 16-th iteration
Summary
Suppose you have n persons seated around a circular table, each having an even number of dimes. If the minimum amount is strictly smaller than the maximum amount, after the step, either the minimum amount will have increased, or else the number of players having the minimum amount will have decreased. Together, these observations imply that after finitely many steps, the maximum and minimum amounts will coincide. We leave the details of the proof to the reader Another interesting problem is to determine the number of iterations needed to reach equidistribution in terms of the initial data (see Figures 1, 2 and 3). 3-D graph of the discrete sharing game with 10 players and with initial distribution as shown In this example, equidistribution is achieved at the 16-th iteration.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
