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conchis comments on The Aumann's agreement theorem game (guess 2/3 of the average) - Less Wrong
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Because given what others are doing, no individual has an incentive to deviate from 0 (regardless of whether they've agreed to it or not). In contrast, if they're really trying to win, every individual agent has an incentive to deviate from 67.
ETA: You can get around the latter problem if you have an enforcement mechanism that lets you punish defectors; but that's adding something not in the original set up, which is why I prefer to consider it changing the rules of the game.
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).