The Bennati-Drăgulescu-Yakovenko (BDY) game is an agent-based simple exchange game that models a basic economic system. The BDY game results in the agents' wealth following a Boltzmann-Gibbs distribution. In other words, the result of the game is many "poor" agents and few "wealthy" agents. In this paper, we apply several tax and redistribution models to study their effect on the population's wealth distribution by computing the resulting Gini coefficient of the system. We find that income taxes, both flat and progressive, that evenly redistributed taxed monies do little to change the Gini coefficient from the Boltzmann-Gibbs distribution. However, income taxes that are redistributed to the poorest agents can significantly lower the Gini coefficient, resulting in a more evenly distributed wealth distribution. Furthermore, we find that a very small wealth tax can lead to significant decreases in the Gini coefficient.