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Instability of group formation through indirect reciprocity under imperfect information and implementation error

Indirect reciprocity is a key mechanism behind the evolution of cooperation. Oishi et al. analytically showed the formation of two exclusive groups under the KANDORI assessment rule in the case of perfect information and no implementation error, regardless of the population size $N$. Here, we numerically show the formation of many exclusive groups under the JUDGING assessment rule in the same case. Introducing degrees of exclusive groups, we numerically examine the stability of the group formation under imperfect information and implementation error.