Figure 1

Stationary states are shown, by the corresponding action matrices (left in the each panel) and the schematic diagram of clustering structure (right). Elements of action matrices are shown with white (cooperative) and black (not cooperative) pixels. Diagonal pixels are gray since they are not defined. Matrices shows are sorted to make their structure easier to see. Circles in schematic diagrams represents clusters of players. Arrows show players in which cluster are cooperative to players in which cluster. The fraction of the size of each cluster over total population is shown in each circle. The $p$ which appears in the fractions is the initial trust probability. These stationary states are analytically derived in Supplemental Material [15].Reuse & Permissions

Figure 2

Four possible opinion matrices after a revision. Elements of opinion matrices are shown with white (good) and black (bad) pixels. Elements irrelevant with the donor and the recipient do not affect, therefore they are shown with grey pixels. (1), (2), (3), and (4) correspond to the situation that all the players regard the donor as good, the all regard the donor as good, the all have the same opinion on the donor and on the recipient, and the all have the opposite opinions on the donor and on the recipient, respectively. Note that diagonal elements are also defined since they are not action matrices but opinion matrices.Reuse & Permissions

Figure 3

Opinion matrices of players who form (1) one opinion group or (2) two opinion groups with size ratio $p:1-p$. Opinion matrices are shown with white (good) and black (bad) pixels. Matrices in right hand side are results of sorted to make their structure easier to see.Reuse & Permissions