Follow the Leader Steady State Analysis of a Dynamic Social Network

A social pyramid is show to be the unique steady state social structure when agents gain utility from being early adopters of subsequently popular trends. The environment is related to a majority game, but introduces the importance of the timing of adoption. Utility derived from making a popular choice independent of timing is demonstrated as essential to support the hierarchy. The proposed environment is relevant to a number of settings in which leadership and timing of decisions are important or where being perceived as a trend setter is rewarded. The leadership position can be self-reinforcing. For a professional critic, for example, a cult-ofpersonality can dictate popular tastes, such as in art, food, and wine markets. A social hierarchy can also apply to the introduction of new products or ideas including academic research and financial market analysts.