The N-Player Trust Game and its Replicator Dynamics

TL;DR

This paper introduces an N-player trust game and analyzes its evolutionary dynamics, revealing that trust can only be sustained if the initial population is fully trustworthy, highlighting challenges in promoting societal trust.

Contribution

It presents a novel N-player trust game model and explores its replicator dynamics, filling a gap in understanding trust evolution in social dilemmas.

Findings

Society with no untrustworthy individuals yields maximum wealth.

Even slight presence of untrustworthy individuals leads to societal collapse of trust.

Promoting trust remains challenging despite its social benefits.

Abstract

Trust is a fundamental concept that underpins the coherence and resilience of social systems and shapes human behavior. Despite the importance of trust as a social and psychological concept, the concept has not gained much attention from evolutionary game theorists. In this paper, an N-player trust-based social dilemma game is introduced. While the theory shows that a society with no untrustworthy individuals would yield maximum wealth to both the society as a whole and the individuals in the long run, evolutionary dynamics show this ideal situation is reached only in a special case when the initial population contains no untrustworthy individuals. When the initial population consists of even the slightest number of untrustworthy individuals, the society converges to zero trusters, with many untrustworthy individuals. The promotion of trust is an uneasy task, despite the fact that a combination of trusters and trustworthy trustees is the most rational and optimal social state. This paper presents the game and results of replicator dynamics in a hope that researchers in evolutionary games see opportunities in filling this critical gap in the literature.