Effects of update rules on networked N-player trust game dynamics

TL;DR

This study examines how different update rules influence the dynamics of an N-player trust game on networks, revealing significant effects on trust levels, wealth distribution, and emergent spatial-temporal patterns.

Contribution

It compares various deterministic and stochastic update rules in a networked trust game, highlighting their impact on trust promotion and system dynamics.

Findings

Unconditional imitation rules maximize global wealth in harder games.

Different update rules lead to distinct spatial structures and long-term memory effects.

Stochastic rules induce low-frequency signals and fractal spatial patterns.

Abstract

We investigate the effects of update rules on the dynamics of an evolutionary game-theoretic model - the N-player evolutionary trust game - consisting of three types of players: investors, trustworthy trustees, and untrustworthy trustees. Interactions between players are limited to local neighborhoods determined by predefined spatial or social network topologies. We compare evolutionary update rules based on the payoffs obtained by their neighbors. Specifically, we investigate the dynamics generated when players use a deterministic strategic rule (i.e., unconditional imitation with and without using a noise process induced by a voter model), a stochastic pairwise payoff-based strategy (i.e., proportional imitation), and stochastic local Moran processes. We explore the system dynamics under these update rules based on different social networks and different levels of game difficulty. We observe that there are significant differences on the promoted trust and global net wealth depending on the update rule. If the game is harder, rules based on unconditional imitation achieve the highest global net wealth in the population. Besides a global perspective, we also study the spatial and temporal dynamics induced by the rules and we find important spatio-temporal correlations in the system for all rules. Indeed, the update rules lead to the formation of fractal structures on a lattice and, when the rules are stochastic, also the emergence of low frequencies in the output signal of the system (i.e., long-term memory).