In this paper, using Evolutionary Game Theory, we study the evolution of currency as an important and influential problem in the world economy by presenting three new models. In examining the evolution of two different currencies, we prove that if the parties chose either of the two currencies with a fixed probability, it will not have an impact on the evolutionary process of these currencies. Considering a new action based on either the possibility of using any two currencies or a preference between the two currencies, we illustrate their impact on the evolution-ary process of currencies. In fact, we examine the impact of different actions and strategies on the evolutionary process between the two types of currencies.
