2003 Volume 18 Issue 1 Pages 15-31
How often does it happen for those who meet for the first time to have an acquaintance in common? To solve this problem, we need to know the population of the society, the acquaintanceship volume, and the degree of overwraps among the acquaintances. Those problems are altogether called ‘the small world problems.’ Watts et al. (Watts and Strogatz 1998; Watts 1999) built a simulation, in which they varied the randomness of the network from regular to random, and observed when the small world phenomenon occurred. This simulation is applicable to a wide range of problems. In this paper, the finding in the anonymous one-shot PD game in small groups --- the more transitivity in trust relation, the more cooperation --- is applied to the macro or society level by using Watts' et al.'s simulation. We find that (1) as the size of the group or society increases, (2) as the number of trustee decreases, or (3) as the randomness of the trust networks increases, then the transitivity declines, which means that in such a case the cooperation ratio declines or the maintenance of social order becomes difficult. Based on this finding and the difference of the acquaintanceship volumes in Japan and US, we discuss the kinds of network structure developed in Japan and US to maintain the social order.
