Implementation, Honesty, and Common Knowledge


Hitoshi Matsushima


We investigate the unique implementation problem of social choice functions (SCFs) from ethical and epistemological concerns. According to Matsushima and Noda (2020), we consider the possibility that in higher-order beliefs there exists an agent who is honest, that is, motivated by intrinsic preference for honesty as well as material interest. We assume only weak honesty in that an honest agent is mostly motivated by material interests and even tells a white lie. We show a very permissive result that any social choice function is uniquely implementable in Bayes Nash equilibrium if “all agents are selfish” never happens to be common knowledge. Hence, any SCF is uniquely implementable even if all agents are selfish and “all agents are selfish” is mutual knowledge. Importantly, any ethical SCF is uniquely implementable whenever “all agents are selfish” never happens to be common knowledge while it is never uniquely implementable otherwise.