Modular decomposition of complex interactions using games networks

In this paper, we describe a modular game theoretical framework: the theory of games networks. Games networks extend non cooperative game theory by allowing agents to participate to several games simultaneously, what make possible the description of local interactions between agents. The theory enables us to formulate global interaction behaviors as composition of local interactions. This puts the emphasis on the way to decompose a game (viewed as a global structure of interactions) into a network of smaller games (viewed as local structures of interactions). The question of decomposition is significant for the understanding of complex systems whose dynamics is based on interactions between agents, such as biological networks. We describe an algorithm for this decomposition which modifies the network structure --- how agents are connected to games --- while preserving its dynamics --- identified by games network equilibria (Gne) which extend the notion of Nash equilibria to games networks. Games within the decomposed network represent basic building blocks whose interactions may explain how the system works.