Social Groups and Social Network Formation

This appendix provides supplementary material for the paper “Social groups and social network formation” by Bassel Tarbush and Alexander Teytelboym. This appendix presents further simulations for different parametrizations and variants of the model against the mean-field approximation results derived in the main paper. Section A presents simulations of the model described in Section 2 of the main paper for various parameter values. Section B presents simulations of the model when the link formation process is governed by preferential attachment. The preferential attachment variant of our model was discussed after Proposition 2 and in Appendix II of the main paper. Finally, Section C describes an alternative version of our model for which the mean-field approximation results derived in the main paper still apply, and we show how well our analytical results perform against simulations of this alternative model. In every section of this Online Appendix, we compare our analytic mean-field approximations against the average of 100 runs of the simulation of the relevant variant of our model, and in line with the running example in the main paper.1 That is, we restrict ourselves to 2 social categories: There are 20 type a students, 180 type b students, 50 type c students, and 250 type d students. The average over 100 runs of the simulation is shown in black, and the corresponding mean-field approximation is shown in color (q1 = 0.1 and q2 = 0.8 in blue; q1 = 0.4 and q2 = 0.4 in purple; q1 = 0.8 and q2 = 0.1 in red).2 The parameter p is varied to take the values 0.99, 0.9925, and 0.995.