The evolution of donations on scale-free networks during a COVID-19 breakout

Abstract

Abstract Having a large number of timely donations during the early stages of a COVID-19 breakout would normally be considered rare. Donation is a special public goods game with zero yield, and it has the characteristics of prisoners’ dilemma. This paper discusses why timely donations in the early stages of COVID-19 occur. Based on the idea that donation is a strategy adopted by interconnected players on account of their understanding of the environment, donation-related populations are placed in social networks and the inter-correlation structure in the population is described by scale-free networks. Players in donation-related groups are of four types: donors, illegal beneficiaries, legal beneficiaries, and inactive people. We model the evolutionary game of donation on a scale-free network. Donors, illegal beneficiaries and inactive people learn and update strategies under the Fermi Update Rule, whereas the conversion between the legal beneficiaries and the other three strategies is determined by the environment surrounding the players. We study the evolution of cooperative action when the agglomeration coefficient, the parameters in the utility function, the selection strength parameter, the utility discount coefficient, the public goods discount coefficient and the initial state of the population in the scale-free network change. For population sizes of 50,100,150 and 200, we give the utility functions and the agglomeration coefficients for promoting cooperation. And we study the corresponding steady state and structural characteristics of the population. We identify the best ranges of selection strength K, the public goods discount coefficient α and the utility discount coefficient β for promoting cooperation at different population sizes. Furthermore, with an increase of the population size, the Donor Trap are found. At the same time, it is discovered that the initial state of the population has a great impact on the steady state; thus the Upper and Lower Triangle Phenomena are proposed. We also find that population size itself is also an important factor for promoting donation, pointing out the direction of efforts to further promote donation and achieve better social homeostasis under the donation model.