Stability of coexistence between Simple Standing (L3) and ALLC under broader strategic competition

Determine whether the coexistence between the Simple Standing (L3) norm and unconditional cooperation (ALLC), which has been reported to be stable when competing only against unconditional defection (ALLD), remains evolutionarily stable against invasion by a broader class of strategies—including randomly cooperating mutants—within the solitary observation model of indirect reciprocity that assumes statistically independent opinions.

Background

In the solitary observation model, opinions of different individuals are statistically independent, leading the authors to show that conditional cooperation is not evolutionarily stable and that unconditional strategies (ALLC or ALLD) are best responses. Nevertheless, prior studies have suggested that a mixture of norms—specifically Simple Standing (L3) and ALLC—can coexist stably when competing only with ALLD.

The authors note they lack a general argument for the stability of such mixtures and explicitly raise the question of robustness when the strategic set expands beyond ALLD, particularly in the presence of randomly cooperating mutants who can neutrally invade under solitary observations.