At the last part of the renegotiation section in Pearce (1992), I found the interesting description about Matsushima (1990) "Structure of Renegotiation in Infinitely Repeated Games" mimeo, Stanford University.

I cannot end this catalogue without mentioning an intriguing paper by Matsushima (1990). His idea is that just as an equilibrium specifies what will happen if its "instructions" are not obeyed, societies have metacodes indicating what happens when a social convention (equilibrium) is breached. The ensuing analysis is highly ingenious; to my astonishment, Matsushima emerges from a jungle of infinite sequences of social conventions and breaching rules, with an existence result. I will not try to explain the motivation for the solution concept; on that score, despite some enjoyable discussions with the author, I remain mystified.
(Pearce (1992), p.166)

By the way, I could not find Matsuhima's paper; he does not seem to have published the paper, and Stanford does not have the working paper either. If you know something about this paper, pleaes let me know. (maybe I should ask him directly)