  Institutions and investors face the constant challenge of making accurate
decisions and predictions regarding how best they should distribute their
endowments. The problem of achieving an optimal outcome at minimal cost has
been extensively studied and resolved using several heuristics. However, these
works usually fail to address how an external party can target different types
of fair behaviour or do not take into account how limited information can shape
this complex interplay. Here, we consider the well-known Ultimatum game in a
spatial setting and propose a hierarchy of interference mechanisms based on the
amount of information available to an external decision-maker and desired
standards of fairness. Our analysis reveals that monitoring the population at a
macroscopic level requires more strict information gathering in order to obtain
an optimal outcome and that local observations can mediate this requirement.
Moreover, we identify the conditions which must be met for an individual to be
eligible for investment in order to avoid unnecessary spending. We further
explore the effects of varying mutation or behavioural exploration rates on the
choice of investment strategy and total accumulated costs to the investor.
Overall, our analysis provides new insights about efficient heuristics for
cost-efficient promotion of fairness in societies. Finally, we discuss the
differences between our findings and previous work done on the PD and present
our suggestions for promoting fairness as an external decision-maker.
