Level-Agnostic Representations of Interacting Agents

The study of the interactions among intentional agents, with rationality being the main source of intentional behavior, requires mathematical tools capable of capturing systemic effects. Here, we choose an alternative toolbox based on Category Theory. We examine potential level-agnostic formalisms, presenting three categories: PR, G, and an encompassing one, I. The latter allows for representing dynamic rearrangements of the interactions among different agents. Systems represented in I capture the dynamic interactions among the interfaces of their sub-agents, changing the connections among them based on their internal states. We illustrate the expressive power of this formalism in four different instances, providing practitioners with a toolbox for representing cases of interest and facilitating their modular analysis.