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

Figure 2

Example of group formation and Proposer selection based on the degree. Each node and its neighborhood define an interaction group. In the figure, node plays in 5 groups and its fitness results come from the payoff sum after playing in all those groups. In general, a node plays in a number of groups equal to its degree plus one. For each group, the payoff is calculated after one individual is selected to be the Proposer. Proposer selection depends on the degree of each individual in the group, and a parameter controls this dependence (see the Materials and Methods section). To exemplify this process, the inset graph represents the probability of each individual— (high degree), 1 (medium degree), and 2 (low degree)—to be selected as a Proposer when playing in the group centered on , as a function of .