  Evolutionary game dynamics in structured populations are strongly affected by
updating rules. Previous studies usually focus on imitation-based rules, which
rely on payoff information of social peers. Recent behavioral experiments
suggest that whether individuals use such social information for strategy
updating may be crucial to the outcomes of social interactions. This hints at
the importance of considering updating rules without dependence on social
peers' payoff information, which, however, is rarely investigated. Here, we
study aspiration-based self-evaluation rules, with which individuals
self-assess the performance of strategies by comparing own payoffs with an
imaginary value they aspire, called the aspiration level. We explore the fate
of strategies on population structures represented by graphs or networks. Under
weak selection, we analytically derive the condition for strategy dominance,
which is found to coincide with the classical condition of risk-dominance. This
condition holds for all networks and all distributions of aspiration levels,
and for individualized ways of self-evaluation. Our condition can be
intuitively interpreted: one strategy prevails over the other if the strategy
brings more satisfaction to individuals than the other does. Our work thus
sheds light on the intrinsic difference between evolutionary dynamics induced
by aspiration-based and imitation-based rules.
