This paper proposes a new framework to model institutions and institutional change. It shows how moral agents, who strive to cooperate with others, can form institutions that facilitate cooperation. The framework makes it possible to model informal as well as formal institutions as games played by moral agents: when the quality of the government is low and agents are not willing to use its services they will create informal institutions that allow them to cooperate outside the official channels. It is also possible to conceptualize institutions as inclusive or extractive and model institutional change as a consequence of the choice of moral agents among available institutions as time unfolds. With a series of examples of clientelistic networks, the paper shows that the framework can be useful for understanding how and why such networks form and persist. The framework can be used to model any interactions among moral agents, thus giving rise to a wide variety of possible institutional settings.