TITLE:
Equidistribution in Sharing Games
AUTHORS:
Carlos D’ Andrea, Emiliano Gómez
KEYWORDS:
Equidistribution; Iteration; Linear Transformation; Limit Distribution
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.4 No.1,
January
23,
2014
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.