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

Figure 5

Selecting high-degree nodes as Proposers increases unfairness. Here, we represent the so-called Lorenz curves, often used to compute the Gini coefficients—a typical measure of income inequality. Each curve is generated by ordering individuals by increasing the value of income and plotting the corresponding cumulative distribution. Curves closer to the perfect equality line (45° line) represent more egalitarian outcomes. Here, we observe, yet again, that assigning the role of Proposer to high-connected nodes () yields unfair outcomes (orange line). While this is evident for soft ((a), ), medium ((b), ), and strict ((c), ) decision rules, we also verify that whenever hubs are the Proposers (), having strict decision rules (high ) reduces unfairness. In all cases, the random Proposer assignment leads the most egalitarian outcomes.