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

Figure 6

The low-degree Proposer assignment maximizes the average fitness (i.e., sum of payoffs taken over all games, see Figure 4) in a population. Here, we observe that the average fitness, , increases as decreases. We show results for BA networks with different values of and . A similar conclusion is obtained when considering DMS networks with the same parameters. Note that increasing implies that the average group size to play MUG also increases, which leads offers to be divided by larger groups (hence contributing to lower values of average payoff per game). On the contrary, increasing means that more games are played, thus contributing to an increase in accumulated fitness (taken as the sum of payoffs in all games played).