Equidistribution in Sharing Games

Carlos D’ Andrea, Emiliano Gómez

Departament d’àlgebra i Geometria, Universitat de Barcelona, Barcelona, Spain.
Department of Mathematics, University of California, Berkeley, Berkeley, USA.

DOI: 10.4236/ojdm.2014.41003                

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.

Keywords

Equidistribution; Iteration; Linear Transformation; Limit Distribution

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[2]	G. Latouche and V. Ramaswami, “Introduction to Matrix Analytic Methods in Stochastic Modeling,” 1st Edition, PH Distributions, ASA SIAM, 1999.