By integrating these variables, the model avoids reductionist typologies and instead provides a multi-dimensional, adaptive measure of relational state. The combination of affective, cognitive, and strategic components allows the score Rij(t)R_{ij}(t) to capture emergent dynamics, hysteresis effects, and sudden shifts in relational posture.
This formalism thus offers a computationally tractable yet psychologically nuanced framework suitable for real-world simulation, predictive analytics, and relational strategy optimization.
C. Adaptation Mechanisms and Temporal Adjustments
The dynamic nature of human relationships demands not only real-time assessments of relational variables but also mechanisms for adaptation over time. Relationships are not static---they evolve through interaction, feedback, and contextual shifts. Accordingly, our model integrates temporal sensitivity and adaptive recalibration, aligning with principles from Complex Adaptive Systems (Holland, 1992) and bounded rationality (Simon). This section outlines how the model dynamically adjusts relational assessments across time tt, emphasizing hysteresis effects, memory decay, volatility detection, and tactical recalibration.
1. Temporal Sensitivity and Memory Decay
Each relational variable Vk,ij(t)V_{k,ij}(t) is not equally influential across all time points. The model applies a decay function to reflect the cognitive and emotional fading of events, such that:
Vk,ij(t)=Vk,ij(t1)ekt+Vk,ij(t)V_{k,ij}(t) = V_{k,ij}(t - 1) \cdot e^{-\lambda_k \Delta t} + \Delta V_{k,ij}(t)
where k\lambda_k is a variable-specific decay constant and Vk,ij(t)\Delta V_{k,ij}(t) represents new input. Variables such as trust and betrayal may decay more slowly than others, preserving their influence across time, consistent with neurocognitive research on memory consolidation and emotional salience.
This allows the model to balance recency and legacy, enabling agents to "forgive" over time while still retaining critical structural memory of prior events.
2. Hysteresis and Path-Dependence
Unlike linear systems, social relationships often exhibit hysteresis---the path taken matters. For example, a breach of trust may lower the relational score Rij(t)R_{ij}(t) more rapidly than a similar gain in trust raises it. This is modeled through asymmetric adjustment functions:
