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Table 5 Average of the convergence time for the fairness SN. ‘NA’ indicates that fairness norm is not obtained, while \(`NA^*\)’ indicates that all SNs, fairness and unfair are not obtained

From: Fairness norm through social networks: a simulation approach

Information assumption

Common knowledge P

Second-order P

First-order P

\(\text{BA}\Bigg \{\)

\(m=1\)

37

NA

\(NA^*\)

\(m=2\)

16.04

35

NA

\(m=3\)

20.31

20.17

11

\(m=4\)

24.98

24.5

31.67

Complete

Graph

17.06

17.21

17.17

\(\text{WS}\Bigg \{\)

\(p_{WS}=0\)

18.44

NA

\(NA^*\)

\(p_{WS}=0.25\)

25.15

25.67

NA

\(p_{WS}=0.5\)

39.87

51.08

NA

\(p_{WS}=0.75\)

17.55

61

NA

\(p_{WS}=1\)

36.97

29.45

NA

\(\text{ER}\Bigg \{\)

\(p_{ER}=0.25\)

17.56

17.85

19.6

\(p_{ER}=0.5\)

14.96

15.42

17.97

\(p_{ER}=0.75\)

14.93

16.48

15.76

\(p_{ER}=1\)

16.16

16.06

15.35