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In this paper we propose an original modular extension of game theory named games network. The objective of games networks is to provide a theoretical framework which suits to modular dynamics resulting from different local interactions between various agents and which enables us to describe complex system in a modular way. Games networks describes situations where an agent can be involved in several different games, with several different other agents, at the same time. In particular, we focus on the determination of global equilibria, resulting from the composition of local equilibria for each game of the network. However, several games networks can represent the same dynamics. We define the notion of dependence between agents, which allows us to compute a games network normal form. This normal form emphasizes the elementary modules which compose the games network. Keywords: complex systems, modularity, game theory, networks, dynamics. [ABSTRACT FROM AUTHOR]

We present a game-theoretic foundation for gene regulatory analysis based on the recent formalism of rewriting game theory. Rewriting game theory is discrete and comes with a graph-based framework for understanding compromises and interactions between players and for computing Nash equilibria. The formalism explicitly represents the dynamics of its Nash equilibria and, therefore, is a suitable foundation for the study of steady states in discrete modelling. We apply the formalism to the discrete analysis of gene regulatory networks introduced by R. Thomas and S. Kauffman. Specifically, we show that their models are specific instances of a C/P game deduced from the K parameter. [ABSTRACT FROM AUTHOR]