Extended Understanding of Dyadic Friendship Using Fuzzy Measures: a Simulation Approach

Friendship formation between a pair of individuals (dyads) and its dynamics is a complex phenomenon that has been extensively studied in the literature. Assortative, relational, and proximity mechanisms are the recognized social processes that are responsible for the formation of these dyadic ties. In this paper, we develop an agent-based model that derives its essence from social processes, fuzzy game theory, and social network analysis. The process of dyadic friendship formation depends on the agent's (participant's) spatial configuration, attributes affecting friendship, and interaction with other agents. To model these interactions, we use fuzzy iterated prisoner's dilemma (Fuzzy-IPD) utilizing the decision factors contributing to similar social processes. These strategies have been independently discussed in previously published studies. We, however, use them in combination to design a descriptive model with different experimental settings in an ad-hoc simulation framework. Using an integrationist approach, we blend multiple individual components of friendship formation to construct a comprehensive model. The analysis of the model thus developed reveals a possible interaction pattern responsible for the evolution of the layered associations. This paper further validates various levels of friendship ties (strong ties, medium ties, and weak ties) in social networks as reported in the published sociological studies.