## 2 Materials and Methods
### Agent Preferences  
Table 2 summarizes all agent rule calculations in formulaic form. As shown model behavioral rules remain consistent with homophily as the total compatibility score is generated from homophily in race, attractiveness, and age with some detailed parameter estimates used in age preferences (males preferring younger female and females preferring older males). As agents are randomly selected in every turn of the model they will evaluate whether to like each other based on these attributes and comparison with a globally set threshold \(\mathcal{C}\). Generally, threshold levels determine the likelihood of a like or dislike event occurring and the resultant probabilities are detailed in Figures 3 and 4. Figure 2: Program schematic for M1 and M2 simulations. Agents in both models are allotted attributes at instantiation of the simulation. A compatibility score for each agent \(i\) is calculated for each agent \(j\) and compared to global threshold. M1 agents can choose to reject or ‘like’ other agents, where M2 agents can choose to reject, like, or message while considering reciprocal interactions. Figure 4: M2 detailed simulation schematic and logic diagram. Note \(\sum P_{M}(R,L|. )=1\) and prior \(\sum P_{M1}(L|.)=P_{M2}(L+L/M|. )\), the overall probability of receiving a like (M1) or a like or a like/Message (M2) verified in Tables 6 and 7 is maintained. Figure 3: M1 detailed simulation schematic and logic diagram. Note \(\sum P_{M}(R,L|. )=1\) while maintaining female preference for higher levels of rejection make agents and choice inclusive of compatibility score threshold. Parameter estimates are drawn from several peer-reviewed sources from within the literature on online dating. To begin, male agents were given a Gaussian preference for younger female agents where the mean difference was 3.996 years, and female agents were given a preference for older males with a mean difference of 2.046 years [79]. The compatibility score is intended to ensure that maximum score contributed by age resides at this mean, and the greater the difference from this mean difference, the lower the contribution of age to the total compatibility score. Physical attractiveness and ethnicity are based on similar principles. As we have noted, agents evaluate ethnicity and attractiveness based on the concept of homophily with much higher scores attributed when two agents of the same ethnicity or a similar attractiveness interact. We also utilized a weighing mechanism for both male and female agents as genders value attributes differently when conjoint with more attributes. The weights are multiplied by the agent-agent interaction scores then summed to yield a total score. Total compatibility score, \(S_{Total}\), is then compared to a threshold value, \(\mathcal{C}\), to determine the occurrence probability of a like or like/message relation. In line with [PERSON] et al. 's [80] study showing that males value physical features more than females, male agents were given a higher weight (\(\beta_{3}^{M}=0.4\)) for attractiveness preference than for female agents (\(\beta_{3}^{E}=0.3\)). [PERSON] et al. [81] concludes that females place greater weight in finding a potential match within their own ethnicity and so we adjusted the weighing and contribution for ethnicity to account for this (\(\beta_{1}^{F}=0.4\), \(\beta_{1}^{M}=0.3\)). Finally, the weighing of scores on age by both genders remained the same (0.3) as there was little evidence that the contribution to a total score was gender-divergent even in light of different age preferences for males (\(\mu=-4.0\)) than for females (\(\mu=2.05\)). Since our model is subject to theoretical matching system fundamentals [27], synthetic population structure and heterogeneity play an important role in model specification.