Figure 1: The schematic illustration of playing PGGs.

(a) The focal player (red node) participates in 4 different groups of PGGs (α, β, γ and δ). Group α is centred on the focal individual and the other groups β, γ and δ are centered on the focal player’s neighbors, respectively. The payoff of the focal player stems from participating in four groups of PGGs. The solid links represent direct interactions among players. (b) The focal player 1 (red node) has one direct link with player 2 (blue node) and one indirect interaction (dashed line) with player 3 (gray node) due to their common neighbor (player 2). In this situation, the focal player 1 belongs to 2 different groups of PGGs (one self-centered PGG and the other PGG centered on player 2) and the payoff of player 1 will be affected by the action of player 3. (c) If the indirect interaction between player 1 and 3 in (b) is changed to a direct interaction, the focal player 1 will participate in 3 different groups of PGGs (one self-centered PGG and the other two groups centered on player 2 and 3, respectively), rendering the player 1’s payoff different from that in (b).