To capture this computationally, ARZ introduces a zone assignment function:
Zij(t)=f(Uij(t),Eij(t),Mij(t),Bij(t))Z_{ij}(t) = f \big( U_{ij}(t), E_{ij}(t), M_{ij}(t), B_{ij}(t) \big)
Where:
Zij(t)Z_{ij}(t) is the zone that agent ii assigns to agent jj at time tt,
Uij(t)U_{ij}(t) is the perceived utility of maintaining the relationship,
Eij(t)E_{ij}(t) is the accumulated emotional experience (positive/negative),
Mij(t)M_{ij}(t) is the memory weight or salience of past interactions,
Bij(t)B_{ij}(t) is the bounded rationality threshold, i.e., agent ii's current cognitive-emotional capacity to process relational complexity.
Simon's view that decision-makers "construct simplified models of the world" is reflected here: rather than compute perfect game-theoretic outcomes, actors within ARZ rely on heuristic zoning, driven by moral schemas, social scripts, and strategic pattern recognition. This aligns with real-world observations---where we categorize others rapidly but flexibly, using affect-laden shortcuts, and often re-evaluate relationships not purely on logic but emotional bandwidth and shifting priorities.
ARZ advances mathematical sociology by embedding this bounded rationality engine into a formal zone-dynamic model. The model allows simulation of:
Cognitive overload scenarios (where multiple yellow-zone agents drain attention),
Emotional resilience thresholds (when agents stop reclassifying red-zone agents as yellow),
Strategic re-zoning during high-stakes interactions (e.g., post-crisis betrayal forgiveness loops).
It also allows cross-comparison between agents: why Agent A may maintain a manipulative tie for longer than Agent B due to different bounded rationality tolerances or social schema encoding functions.
In summary, ARZ offers a mathematized model of moral and strategic social perception grounded in the cognitive realism of bounded rationality. It rejects the idea of perfectly rational agents navigating static networks, and instead proposes computationally plausible, adaptively irrational agents who categorize, maneuver, and survive within layered social environments. In doing so, it forges a new bridge between the rigor of mathematical sociology and the behavioral truth of Simon's bounded decision-making.
Outline
I. Introduction
Problem Statement: Strategic ambiguity in human relations.
Limitations of existing typologies.
Our Proposition: A dynamic, formal, and strategic model.
II. Literature Review
Relational Typologies (Attachment theory, Transactional Analysis, etc.)
Trust and Betrayal Literature
Systems and Network Theory in Social Dynamics
Complexity and Adaptivity in Human Systems
III. Conceptual Framework
