Standard pairwise representations may fail to capture the complexity of observed collective behaviors in networked systems in many real-world applications, in- cluding ecological systems, brain cognitive processes, and social systems. This motivates the use of hypergraph representations, which capture not only pair- wise but also higher-order interactions between nodes. Traditionally, it is as- sumed that these interactions are cooperative, and several measures have been proposed to identify influential or central agents. However, in the context of so- cial networks, antagonistic relationships between individuals may coexist with collaborative ones. In this thesis project, we want to understand how an- tagonism in higher-order interactions influences collective behavior, using hypernetwork dynamics characterized by nonlinear (sigmoidal) functions.