To Be a Truster or Not to Be: Evolutionary Dynamics of a Symmetric N-Player Trust Game in Well-Mixed and Networked Populations

TL;DR

This paper introduces a symmetric N-player Trust Game to study trust evolution, revealing that trust struggles to evolve in well-mixed populations but can be influenced by payoff structures and network topology in structured populations.

Contribution

It proposes a novel symmetric N-player Trust Game with role alternation and analyzes how payoff nonlinearity and network structure affect trust evolution.

Findings

Trust does not evolve in well-mixed populations regardless of payoff nonlinearity.

Nonlinear payoffs significantly impact trust evolution in structured populations.

Network topology influences the success of prosocial strategies in the game.

Abstract

Trust and reciprocation of it form the foundation of economic, social and other interactions. While the Trust Game is widely used to study these concepts for interactions between two players, often alternating different roles (i.e., investor and trustee), its extensions to multi-player scenarios have been restricted to instances where players assume only one role. We propose a symmetric N-player Trust Game, in which players alternate between two roles, and the payoff of the player is defined as the average across their two roles and drives the evolutionary game dynamics. We find that prosocial strategies are harder to evolve with the present symmetric N-player Trust Game than with the Public Goods Game, which is well studied. In particular, trust fails to evolve regardless of payoff function nonlinearity in well-mixed populations in the case of the symmetric N-player trust game. In structured populations, nonlinear payoffs can have strong impacts on the evolution of trust. The same nonlinearity can yield substantially different outcomes, depending on the nature of the underlying network. Our results highlight the importance of considering both payoff structures and network topologies in understanding the emergence and maintenance of prosocial behaviours.