## 2 Materials and Methods
### Agent Preferences
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Model Attribute** & **Condition** & **Value** & **Description** \\ \hline Compatibility & \(\mathcal{G}_{M}\top\mathcal{G}_{F}\) & \(S_{e}=(\dfrac{\mathcal{X}}{2})+0.5\) & \(\mathcal{X}\in[0,1]\) \\ Score (ethnicity) & \(\mathcal{G}_{M}\bot\mathcal{G}_{F}\) & \(S_{e}=(\dfrac{\mathcal{X}}{2})\) & \\ Compatibility & \(\mathcal{G}==M\) & \(S_{M}^{A}=1-(2)(|\mathcal{N}(\mathcal{A})_{cdf}|-0.5)\) & \(\mu=-3.996\) \\ Score (age) & & \(\mathcal{N}(\mathcal{A})_{cdf}=\dfrac{1}{2}[1+erf(\dfrac{x-\mu}{\sigma\sqrt{2} })]\) & \(\mathcal{X}=-3.317\) \\ Compatibility & \(\mathcal{G}==F\) & \(S_{M}^{A}=1-(2)(|\mathcal{N}(\mathcal{A})_{cdf}|-0.5)\) & \(\mu=2.046\) \\ Score (age) & & \(\mathcal{N}(\mathcal{A})_{cdf}=\dfrac{1}{2}[1+erf(\dfrac{x-\mu}{\sigma\sqrt{2} })]\) & \(\mu=2.906\) \\ Compatibility & \(S_{M}^{P}=1-(2)(|\mathcal{N}(\mathcal{P})_{cdf}|-0.5)\) & \(\mu=0\) \\ Score (attractiveness) & \(\mathcal{N}(\mathcal{P})_{cdf}=\dfrac{1}{2}[1+erf(\dfrac{x-\mu}{\sigma\sqrt{2} })]\) & \(\mu=0\) \\ Total Score & \(S_{Total}^{M}=\beta_{1}^{M}S_{e}^{M}+\beta_{2}^{M}S_{F}^{P}+\beta_{3}^{M}S_{M}^{A}\) & \(\beta_{3}^{M}=0.3\,\beta_{1}^{F}=0.4\) \\  & \(S_{Total}^{F}=\beta_{1}^{F}S_{e}^{F}+\beta_{2}^{F}S_{F}^{P}+\beta_{3}^{F}S_{F}^{A}\) & \(\beta_{3}^{M}=0.3\,\beta_{1}^{F}=0.3\) \\  & & \\ \end{tabular}
\end{table} 
Table 2: Rules applied by agents for calculation of overall compatibility (total score). Compatibility is assigned as the additive accumulation of all assigned attributes (age, attractiveness, ethnicity). Second column conveys conditions under which the rule calculation is presumed. All value calculations and parameters are assigned such that they will produce a maximum partial score of 1. Independent compatibility scores are then added to produce overall compatibility score. Description column contains parameter values chosen for a typical run. [Key: \(\top\): (same as), \(\bot\): (different from)]. In this regard, the choice of male to female agent ratios could, if chosen unwisely, create unintended consequences and artifacts in our model. Thus, we rely on [PERSON]'s work [34]: The author reports that Tinder's user base is roughly 60% male and 40% female. Though this statistic is a rough estimate drawn from non-peer-reviewed sources, we consider it a guide (and not a rule) to our implementation and model specification. As a result, we chose population proportion parameters consistent with the overall notion that there are many more males than females on dating applications at a rate of 68% men and 32% women in line with the general principle of a 2:1 ratio. Once agents are presented with a profile to evaluate, they proceed with said evaluation (\(S\in[0,1]\)) against a pre-set parameter to determine whether they will reject, like, like/message the considered agent. These threshold parameters are assigned according to the following intuitive patterns:  
* Female agents threshold for a 'like' are higher than male agents [82]. [M1 & M2]
* The probability of a 'like' when the compatibility threshold is not achieved (\((C)<S_{Total}\)) is non-zero. It is reduced but a reject, like, and like/message may still occur. [M1 & M2]
* A like with a message is still subject to the same aforementioned compatibility thresholds, but increases the probability of a reciprocal like event. [M2]
* Previous positive interactions (reciprocity) increases the probability values of like and like/message. [M2]  
All thresholds, probabilities, and decision junctures are summarized in Figures 2-4. Furthermore, while threshold levels and probabilities are homogeneous, each agent's compatibility score for every other considered agent is heterogeneous and dependent on both ego and alter's attributes. This ensures that agents' internal standard for acceptance of a potential mate are antecedents in maintaining individual and independent preferences in agent-agent interactions.