Promoting Fair Proposers, Fair Responders or Both? Cost-Efficient Interference in the Spatial Ultimatum Game

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.