Evolution of trust in the N-player trust game with the margin system

Abstract

Investigations into trust behavior between investors and trustees using trust games have gained significant attention in recent years. However, understanding the process of trust evolution remains challenging. The margin system, widely employed in the financial industry as an economic and behavioral incentive mechanism, aims to maintain order in financial markets and protect participants' rights and interests. Despite its extensive use, the precise influence of the margin system on trust evolution dynamics remains unclear. To address this gap, we propose an N-player trust game model that incorporates a margin system within an infinite well-mixed population. In our model, a third-party institution collects a proportionate amount of margin from trustees, which is returned upon fulfilling their obligations but forfeited otherwise. By utilizing replicated dynamic equations, we find that implementing the margin system can establish a stable coexistence state between investors and trustworthy trustees, representing a significant advancement in trust evolution. Additionally, an intriguing finding arises from our observation of an inverted U-shaped relationship between the magnitude of the attraction domain for coexistence and the coefficient of the margin. This suggests that excessively high margin proportions can discourage trustees' participation, while excessively low proportions may fail to effectively deter dishonest behavior. Optimal margin proportions can effectively promote trust evolution.