By: julia on Abel Soares Siqueira

Re-posted from: https://abelsiqueira.com/blog/2018-09-04-the-dollar-game-from-numberphile/

I just watched The Dollar Game –
Numberphile, in which a game involving graphs is presented.
I recommend you watch the video for complete information.

The game involves a graph with integer values on its nodes, positive and
negative. For instance, the following graph:

Each node corresponds to a person, the node value is the amount of
money that person has, the edges are the people that person can give or
take money from.
The objective of the game is to have everyone have a non-negative amount of money.
In each move of the game, one person decides to give or take money,
however, that person either takes 1 dollar from each of their connections,
or gives 1 dollar to each one.