Custom versus fashion: path-dependence and limit cycles in a random matching game

A pairwise random matching game is considered to identify the social environments that give rise to the social custom and fashion cycles. The game, played by Conformists and Nonconformists, can generate a variety of socially stable behavior patterns. In the path-dependence case, Conformists set the social custom and Nonconformists revolt against it; what action becomes the custom is determined by “history.” In the limit cycle case, Nonconformists become fashion leaders and switch their actions periodically, while Conformists follow with delay. The outcome depends on the relative share of Conformists to Nonconformists as well as their matching patterns.