A model for herd behaviour based on a spatial public goods game

Abstract

In groups and crowds, individuals have a propensity to replicate the actions of their immediate neighbours, often disregarding rational considerations. This phenomenon is known as herd behaviour, which has been extensively investigated in biological and economic contexts to comprehend the dynamics of fragile systems. Examples of herd behaviour scenarios include the bubble effect in the stock market, animal coordination, and individuals congregating together during emergency situations to avert peril. The understanding of the underlying causes and consequences of individual decision-making in crowd dynamics can mitigate the negative outcomes of these situations. Consequently, models are utilised to propose effective stock market controls and design emergency exits that enable swift responses to crises. This paper presents a spatial game that induces a level of herding in the population, whereby a multiplayer public good game serves as the platform for interaction among individuals. Herding behaviour arises when individuals shift from emulating the most successful strategy to copying the predominant strategy in their neighbourhood. The objective of the game is to investigate how the induced level of herding and the return on investment affect the total wealth, wealth distribution, and level of cooperation in the population. In summary, when herd behaviour is more prevalent, it leads to reduced cooperation and increased wealth inequality. Nonetheless, the outcome is contingent on the initial concentration of states in the simulation.