Evolving Neural Networks for a Generalized Divide the Dollar Game

Divide the dollar is a simpler version of a game invented by John Nash to study the bargaining problem. The generalized divide the dollar game is an n-player version. Evolutionary algorithms can be used to evolve players for this game, but it has been previously shown representation has a profound effect on the success of the evolutionary search. Representation defines both the genome and the move (search) operator used by the evolutionary algorithm. This study investigates how well two representations for a 3-player generalized divide the dollar game, one using a differential evolution move operator and the other a CMA-ES move operator, can find good players implemented as neural networks. Our results indicate both representations can evolve very good player trios, but the CMA-ES representation tends to evolve fairer players.