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

2024-11-22

arXiv.org

AI Summary

Trust—a prosocial strategy—is evolutionarily unstable in symmetric N-player trust games, posing a fundamental challenge to understanding the emergence of multilateral trust. Method: We develop the first role-switching model wherein players dynamically alternate between investor and trustee roles; payoffs are averaged across both roles, and evolutionary dynamics are governed by standard replicator equations. Results: In well-mixed populations, trust fails to evolve spontaneously—regardless of payoff linearity—and is significantly harder to sustain than cooperation in public goods games. In structured populations, however, strong synergy emerges between nonlinear payoff structures and network topology: identical nonlinear functional forms yield qualitatively distinct evolutionary outcomes (e.g., fixation vs. extinction of trust) depending on structural properties such as degree distribution and clustering coefficient. These findings reveal a joint regulatory mechanism wherein payoff architecture and graph-theoretic features co-determine trust evolution, providing a novel theoretical framework for studying the emergence of multilateral trust in complex social systems.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Mechanism Design
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Applications and emergent phenomena

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.

Problem

• Study evolution of trust in symmetric N-player Trust Game
• Compare prosocial strategies with Public Goods Game
• Analyze impact of payoff nonlinearity and network topologies

Innovation

• Symmetric N-player Trust Game with role alternation
• Evolutionary dynamics driven by average payoffs
• Impact of nonlinear payoffs and network topologies