# Emotional Dynamics in Social Interactions: A Multi-Strategy Synergy Model
## 2 Multi-Strategy Driven Emotional Evolution Model
### Model Construction
#### 2.2.1 Emotional Regulation Strategy  
An emotional regulation strategy \(S(t)\) is a weighted combination of three sub-strategies: social comparison discrepancy, strategic self-positioning, and emotional resonance enhancement, that is  
\[S(t)=w_{1}S_{1}(t)+w_{2}S_{2}(t)+w_{3}S_{3}(t),\]  
where  
* \(S_{1}(t)\) represents the social comparison discrepancy strategy, which involves evaluating one's emotional state relative to others. In social interactions, people often assess their emotional state by comparing themselves with others. According to Social Comparison Theory [2], this comparative behavior is a universal psychological phenomenon in humans, serving as a way to gain self-awareness and regulate emotions through comparisons with others. When individuals perceive their emotional state as falling short of a desired level, they can adopt strategic actions to bridge this gap. Specifically, the intensity of an individual's emotional regulation strategy is directly proportional to the emotional gap. When an individual's emotional state \(E(t)\) falls below a predefined threshold \(E_{\text{high}}\), the emotional gap widens, causing the individual to seek the attention and support of the group through self-deprecation. The intensity of this strategy can be modeled by the following mathematical expression: \[S_{1}(t)=\mu\left(1-\frac{E(t)}{E_{\text{high}}}\right)^{+},\] (1) This formulation explicitly captures the dynamic relationship of the social comparison discrepancy strategy. The larger the emotional gap, the stronger the intensity of the strategy. * \(S_{2}(t)\) denotes the strategic self-positioning strategy, which focuses on adjusting one's emotional state based on self-assessment and positioning within the group. In social settings, people actively modify their self-presentation to shape others' perceptions and feedback. This is known as Strategic Self-Positioning, which involves altering one's behavior or communication style to meet social expectations or achieve specific goals. The strategic self-regulation theory [9] explains that individuals adjust their strategies based on situational demands, to manage their emotions and achieve social objectives. These behaviors are dynamic and evolve with the context to help people adapt to different social and emotional situations. During emotional regulation, strategic self-positioning is when people adjust their self-presentation based on their current emotions and social goals. For example, someone might act humbly to seek support when needed, or appear confident to receive positive feedback at other times. The strength of this strategy can be represented by a dynamic function, which is provisionally formulated in this paper as \[S_{2}(t)=\
u\left(\sin\left(\frac{2\pi t}{T}\right)\right)^{+},\] (2) This form can be customized and does not necessarily require the use of periodic functions. * \(S_{3}(t)\) captures the emotional resonance enhancement strategy, which aims to amplify emotional alignment with the group. In social interactions, the emotional resonance enhancement strategy is a key mechanism. It allows individuals to elevate their emotional states by synchronizing with others' emotions. Empathy research shows that emotional resonance involves both understanding others' emotions cognitively and sharing/responding to them emotionally. This strategy boosts the interaction between group feedback and an individual's emotional capacity space, thereby intensifying the individual's emotional experience. In the process of emotional regulation, this strategy is manifested in individuals using group feedback to enhance their emotional states. When the group provides positive feedback in response to an individual's emotional expression, the individual's emotional state is further elevated, thereby achieving enhanced emotional resonance.