Remember, “fairness” itself is not always a focal point, and even if it is a focal point there can still be plenty of others. Nash bargaining & co involve a symmetry assumption, independence of irrelevant alternatives (or some substitute for it), etc. These are elegant mathematical assumptions, and they are sometimes intuitive focal points in real negotiations, but not always. Symmetry, in particular, is very often not a realistic condition in bargaining (and not just because players have different BATNAs, which Nash already accounts for). Also, in practice utility functions are not observable, and the “no substantive communication” issue means that I can’t trust what the other player claims about their utility/BATNA (though of course mechanism design can counterbalance this problem sometimes).
I agree in general, though afaik there is just no really rigid theory for what constitutes a focal point—it can be anything that is salient. If you let people play in a lab and give them game matrices with multiple equilibria with identical payoffs, then coloring one equilibrium can make it focal point; but in reality many things can seem salient. Maybe it’s somehow built into our genetic and cultural code what we coordinate on—e.g. what’s best for “all” or what’s best for “our group” etc. (IIRC, Ken Binmore suggests something along the lines of “Evolution makes us find Nash bargaining solutions fair” in the book Natural Justice, but I don’t remember what his evidence is to support that.)
Concerning symmetry and Nash: you can model the Nash bargaining solution asymmetrically, but of course it’s unclear whether that helps. Models like Rubinstein’s are elegant but not really realistic in their assumptions and neither in their implications.
Remember, “fairness” itself is not always a focal point, and even if it is a focal point there can still be plenty of others. Nash bargaining & co involve a symmetry assumption, independence of irrelevant alternatives (or some substitute for it), etc. These are elegant mathematical assumptions, and they are sometimes intuitive focal points in real negotiations, but not always. Symmetry, in particular, is very often not a realistic condition in bargaining (and not just because players have different BATNAs, which Nash already accounts for). Also, in practice utility functions are not observable, and the “no substantive communication” issue means that I can’t trust what the other player claims about their utility/BATNA (though of course mechanism design can counterbalance this problem sometimes).
I agree in general, though afaik there is just no really rigid theory for what constitutes a focal point—it can be anything that is salient. If you let people play in a lab and give them game matrices with multiple equilibria with identical payoffs, then coloring one equilibrium can make it focal point; but in reality many things can seem salient. Maybe it’s somehow built into our genetic and cultural code what we coordinate on—e.g. what’s best for “all” or what’s best for “our group” etc. (IIRC, Ken Binmore suggests something along the lines of “Evolution makes us find Nash bargaining solutions fair” in the book Natural Justice, but I don’t remember what his evidence is to support that.)
Concerning symmetry and Nash: you can model the Nash bargaining solution asymmetrically, but of course it’s unclear whether that helps. Models like Rubinstein’s are elegant but not really realistic in their assumptions and neither in their implications.