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Vladimir_Nesov comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Coordination determines the joint outcome, or some property of the joint outcome; possibility of defection means lack of total coordination for the given outcome. Punishment is only one of the possible ways of ensuring coordination (although the only realistic one for humans, in most cases). Between the two coordinated strategies, 67 is as good as 0.
What I wondered is what it could mean to establish the total lack of coordination, impossibility of implicit communication through running common algorithms, having common origin, sharing common biases, etc, so that the players literally can't figure out a common answer in e.g. battle of the sexes.
I'm sure I'm missing your point, but FWIW my original claim was only about the (im)possibility of coordination on a non-Nash equilibrium solution (i.e. of coordinating on a solution that is not incentive-compatible). Coordinating on one of a number of Nash equilibria (which is the issue in battle of the sexes) is a different matter entirely (and not one I am claiming anything about).