Eliciting Fairness in N‐Player Network Games through Degree‐Based Role Assignment

Abstract

From social contracts to climate agreements, individuals engage in groups that must collectively reach decisions with varying levels of equality and fairness. These dilemmas also pervade distributed artificial intelligence, in domains such as automated negotiation, conflict resolution, or resource allocation, which aim to engineer self-organized group behaviors. As evidenced by the well-known Ultimatum Game, where a Proposer has to divide a resource with a Responder, payoff-maximizing outcomes are frequently at odds with fairness. Eliciting equality in populations of self-regarding agents requires judicious interventions. Here, we use knowledge about agents’ social networks to implement fairness mechanisms, in the context of Multiplayer Ultimatum Games. We focus on network-based role assignment and show that attributing the role of Proposer to low-connected nodes increases the fairness levels in a population. We evaluate the effectiveness of low-degree Proposer assignment considering networks with different average connectivities, group sizes, and group voting rules when accepting proposals (e.g., majority or unanimity). We further show that low-degree Proposer assignment is efficient, in optimizing not only individuals’ offers but also the average payoff level in the population. Finally, we show that stricter voting rules (i.e., imposing an accepting consensus as a requirement for collectives to accept a proposal) attenuate the unfairness that results from situations where high-degree nodes (hubs) play as Proposers. Our results suggest new routes to use role assignment and voting mechanisms to prevent unfair behaviors from spreading on complex networks.

Catalysing cooperation: the power of collective beliefs in structured populations

“…We use a degree-based scheme to choose the node for introducing the mutant 43 . The probability of being chosen is given by p j ¼ e αk j = P i2N e αk i Fig.…”

Social diversity reduces the complexity and cost of fostering fairness

“…Fairness has a deep impact on decision-making and individuals often prefer fair outcomes over payoff-maximising ones [1,2]. For example, fairness concerns emerge and play a crucial role in group interactions, when agents must decide upon outcomes possibly favouring different parts unequally [3]. These concerns arise in many domains -hybrid collectives of humans and machines [4], wildlife management [5], conflict resolution [6] or enforcing global climate change actions [7][8][9], just to name a few.…”

Network topology and movement cost, not updating mechanism, determine the evolution of cooperation in mobile structured populations

“…As our interactions can occur in groups of arbitrary size, we use multiplayer games, which are otherwise similar to those considered in other models. Evolutionary graph theory often uses multiplayer games, though interacting groups do not emerge naturally from their interactions as in our framework, but often involve all players neighbouring a particular individual as in [ 51 ].…”