I think you’re missing a very large confounding factor. To be useful, the common knowledge must be true (or at least must lead to preferred equilibria). It doesn’t matter if you agree on the decision, but you’ve agreed based on an incorrect payoff matrix.
This goes pretty deep in making it difficult to move the equilibrium—lots of individuals with different (or even the same, but with mistaken beliefs) payoff matrices are trying to convince each other to believe things that move them to a different square.
I think you’re missing a very large confounding factor. To be useful, the common knowledge must be true (or at least must lead to preferred equilibria). It doesn’t matter if you agree on the decision, but you’ve agreed based on an incorrect payoff matrix.
This goes pretty deep in making it difficult to move the equilibrium—lots of individuals with different (or even the same, but with mistaken beliefs) payoff matrices are trying to convince each other to believe things that move them to a different square.