Climb on the Bandwagon: Consensus and periodicity in a lifetime utility model with strategic interactions

What is the emergent long-run equilibrium of a society where many interacting agents bet on the optimal energy to put in place in order to climb on the Bandwagon? In this paper we study the collective behavior of a large population of agents being either Left or Right: the core idea is that agents benefit from being with the winner party, but, on the other hand, they suffer a cost in changing their status quo. At the microscopic level the model is formulated as a stochastic, symmetric dynamic game with $N$ players. In the macroscopic limit, as N goes to infinity, we obtain a mean field game whose equilibria describe the "rational" collective behavior of the society. It is of particular interest to detect the emerging long-time attractors, e.g. consensus or oscillating behavior. Significantly, we discover that bandwagoning can be persistent at the macro level: endogenously generated periodicity is in fact detected.

What is the emergent long-run equilibrium of a society, where many interacting agents bet on the optimal energy to put in place in order to climb on the Bandwagon? In this paper, we study the collective behavior of a large population of agents being either Left or Right: The core idea is that agents benefit from being with the winner party, but, on the other hand, they suffer a cost in changing their status quo. At the microscopic level, the model is formulated as a stochastic, symmetric dynamic game with N players. In the macroscopic limit as N ->+infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N \rightarrow +\,\infty $$\end{document}, the model can be rephrased as a mean field game, whose equilibria describe the "rational" collective behavior of the society. It is of particular interest to detect the emerging long time attractors, e.g., consensus or oscillating behavior. Significantly, we discover that bandwagoning can be persistent at the macrolevel: We provide evidence, also on the basis of numerical simulations, of endogenously generated periodicity.