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

TL;DR

This paper analyzes how large populations of strategic agents with conflicting incentives evolve over time, revealing conditions for consensus or oscillations and demonstrating persistent bandwagon effects in society.

Contribution

It introduces a mean field game model capturing long-term societal behaviors, including consensus and endogenous periodicity, in a strategic multi-agent setting.

Findings

Persistent bandwagoning behavior at the macro level.

Detection of endogenous periodic oscillations.

Conditions leading to consensus or oscillations.

Abstract

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 $N \rightarrow +\infty$, 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.