Figure 2
From: Reputation structure in indirect reciprocity under noisy and private assessment
(A) Reputations between all individuals. The image matrix \(\{\beta _{ji}\}\) is drawn, where each row represents who evaluates (j) and each column represents who is evaluated (i). Colored and uncolored dots indicate good (\(\beta _{ji}=1\)) and bad (\(\beta _{ji}=0\)) reputations, respectively. From the top, each panel indicates that individuals employ norms SJ, SS, SH, and SC, respectively. One might easily see the vertical stripes on the panels of SS and SC, which mean that various goodnesses coexist among individuals. For all the panels, computer simulations are performed with parameters \(N=100\), \(e_1=e_2=0.1\). In our computer simulations, we assume that N elementary steps of updates occur per unit time. These snapshots are taken at time \(t=100\) (sufficiently long time passed). (B) Frequency distribution of goodness, \(p_i\), at an equilibrium calculated from computer simulation results. The horizontal and vertical axes indicate goodness p and equilibrium frequency \(\phi ^*(p)\), respectively. Computer simulations are performed with parameters \(N=500\), \(e_1=e_2=0.1\). The equilibrium frequency distribution, represented by colored areas in each panel, is calculated by taking the time average of 1000 snapshots during time \(101\le t\le 1100\). Curves in black represent our analytical approximations using mixture Gaussian distribution fitting (details explained in the main text), and they show excellent fits to the results of computer simulations (see insets for minor deviations). Numbers next to each peak represent labels of each Gaussian distribution, which shall be introduced later in the main text.
