Political elites are the foundation of contemporary representative democracies. This reality highlights the unique scientific and practical significance of studies on political elites. The paper presents a non-standard research approach. Some aspects of using evolutionary game theory models to study the evolution of cooperative behaviours among representatives of political elites are presented. To that end, two models of 2 × 2 games were developed: a single-population and a two-population model. The first one assumes the existence of interactions between representatives of the same population, while the second focuses on interactions among individuals from two different populations. The analyses used two interaction schemes: Stag Hunt and Chicken. Standard replicator dynamics was employed to describe the evolutionary process. The results of the analyses are presented in a graphic form in phase diagrams. The presented approach should be treated as a supplement to traditional research approaches used in social sciences rather than as an alternative.