Why should we model two-person random interactions in everyday human activity? If we had to how would we model such interactions? This thesis tries to understand how individuals will behave in 2-person everyday interactions as such interactions comprise a substantial part of our everyday lives. It starts to answers these questions by reviewing Adam Smith’s concepts of selfishness (self-interest) and altruism (benevolence) in his books, An Inquiry into the Nature and Causes of the Wealth of Nations (1776) and The Theory of Moral Sentiments (1790) to put this research into context. This literature review is extended to strong reciprocity that develops on the ideas of selfishness and altruism and explains how punishment can impact such behaviour. Game theory and complex system are used to develop the 2-person random interaction model (2PRIM) in order to explain the evolutionary dynamics of selfishness, altruism and strong reciprocity within such interactions. Previous two-person models have not simulated random interactions with strong reciprocity. Results show that selfishness increases rapidly in such interactions and punishment has little or no impact in such situations. However, an increase in the return on selfishness, common or public good or cost of competition in 2PRIM can have a similar impact as strong reciprocity in such two-person random interactions.