Power Dynamics in Resource-Exchange Graph Grammars

Emergent properties in complex systems, stemming from interactions beyond specific components or events, make predicting their behaviour challenging. Graph Grammars (GGs) provide an effective framework for modeling such systems through graph rewriting rules. This paper utilises GGs to model power dynamics in a complex network of resource exchanges, innovatively incorporating group formation and dissolution to enable the study of both intra-group and inter-group dynamics in a unified setting. This approach is based on the Power-Dependence Theory (PDT) which defines power as the inverse of dependence and views group formation as a strategy to address power imbalances. In our case studies, agents, whether individuals or groups, follow a Relational Model (RM), corresponding to altruism, reciprocity, opportunism, or status. The focus of our analysis is on exploring how resource inequality influences the distribution of RMs among agents in stable states and how shared perceptions of resource values affect this impact. The analysis employs the theory of unfolding developed in [6] for conditional attributed GGs which integrates symbolic data attributes and negative application conditions (NACs) to improve expressiveness. Our primary contribution lies in applying conditional attributed unfolding to case studies involving group formation and relational constraints, providing insights into emergent phenomena such as political and socio-economic clustering. Additionally, we discuss strategies to further enhance analytical capability by incorporating complementary techniques in tandem with unfolding.