The evolution of social institutions (e.g. institutions of political decision making or joint resource administration) is an important question in the context of understanding of how societies develop and evolve. In principle, social institutions can be conceptualized as abstract games with multiple players and rules about individual decision making and individual and joint outcomes. Here we propose a formal approach for the composition of games (e.g. Prisoner's Dilemma – PD) to model the evolution of social institutions. Following a generalized description of the approach, we describe two examples of application for the composition of PD games. We assess the impact of the composed games on the level of cooperation. We discuss the implications of the proposed approach and how it may help to develop effective models of social institution evolution.