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

Figure 4

On top of decreasing the average level of proposal in the population, , we found that attributing the role of Proposer to highly connected nodes decreases the level of fairness and equality within the population. Here, we use scatter plots to observe the average payoff obtained per game, , for individuals with a certain degree (horizontal axis). (a, d) A low-degree Proposer assignment scenario (); (b, e) random—and degree-independent—role attribution (); (c, f) a high-degree Proposer assignment scenario (). Each gray cross represents a node in a degree- space; the orange line represents the mean taken over all nodes with a certain degree. (a–c) and (d–f) . High , i.e., high-degree Proposer assignment, implies that highly connected nodes earn (approximately) five times more payoff per game than low-connected nodes (c). This effect is alleviated for higher ; for , highly connected nodes earn (approximately) three times more payoff per game than low-connected nodes (f).