  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).
