Custom Versus Fashion: Hysteresis and Limit Cycles in a Random Matching Game - Kiminori Matsuyama (Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, 1991)
This paper considers a simple pairwise random matching game in the society populated by two groups of agents: Conformists and Nonconformists. Depending on the relative frequencies of intergroup and intragroup matchings, the best response dynamics show three types of asymptotic behaviors: global convergence, hysteresis and limit cycles. In the hysteresis 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.
Keywords: 330; Best response dynamics; Bifurcation; Equilibrium refinement; Evolutionary process; Hysteresis; Limit Cycles; Perfect foresight; dynamics; Strategic complements and substitutes