In general, a focal point is needed when you have to choose something without being able to explicitly coordinate on it (and when there are multiple equilibria). Here the families do coordinate—they negotiate.

Negotiation was actually one of the central topics in Schelling’s original book on the topic. The problem is that, in a negotiation, there’s an effect similar to not-being-able-to-coordinate. There are multiple Nash equilibria, but players prefer different equilibria. Each player will say whatever seems most likely to make their preferred equilibrium happen, but other players know they will say those things, so the “communication” actually has zero information content (at least with respect to which-equilibrium-to-choose). This means players must coordinate on an equilibrium, despite generally discounting everything the other players say about which equilibrium to choose. Thus, the Schelling point becomes relevant—e.g. borders are drawn along rivers, even without any “sense of fairness”.

That is very interesting. I have not read Schelling’s book, and having worked a lot with and/or read things applying Nash’s bargaining solution as an axiomatic version of bargaining and Rubinstein-like alternating-offers games over the years, it seemed to me that agreeing on sharing rules should be considered distinct from uncoordinated behavior. In this sense, I do buy the point that a river can be an “agreement focal point”, but only if it is roughly in the middle. It seems to me that the fairness focal point would be a 50:50 split, and using a river instead is a pragmatic deviation from that, because of the fact that the river is a barrier and any crossing and violation of the agreement can be observed easily. I doubt that you could “shift the focal point” by damming because that constitutes such a violation, and then the focal point becomes non-cooperation. (Concerning the incomplete contracts I mentioned: In practice not even that will work, because when the other side sues you, a judge would probably rule against you but that may depend on the legal system.)

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.

Negotiation was actually one of the central topics in Schelling’s original book on the topic. The problem is that, in a negotiation, there’s an effect similar to not-being-able-to-coordinate. There are multiple Nash equilibria, but players prefer different equilibria. Each player will say whatever seems most likely to make their preferred equilibrium happen, but other players

knowthey will say those things, so the “communication” actually has zero information content (at least with respect to which-equilibrium-to-choose). This means players must coordinate on an equilibrium, despite generally discounting everything the other players say about which equilibrium to choose. Thus, the Schelling point becomes relevant—e.g. borders are drawn along rivers, even without any “sense of fairness”.That is very interesting. I have not read Schelling’s book, and having worked a lot with and/or read things applying Nash’s bargaining solution as an axiomatic version of bargaining and Rubinstein-like alternating-offers games over the years, it seemed to me that agreeing on sharing rules should be considered distinct from uncoordinated behavior. In this sense, I do buy the point that a river can be an “agreement focal point”, but only if it is roughly in the middle. It seems to me that the fairness focal point would be a 50:50 split, and using a river instead is a pragmatic deviation from that, because of the fact that the river is a barrier and any crossing and violation of the agreement can be observed easily. I doubt that you could “shift the focal point” by damming because that constitutes such a violation, and then the focal point becomes non-cooperation. (Concerning the incomplete contracts I mentioned: In practice not even that will work, because when the other side sues you, a judge would probably rule against you but that may depend on the legal system.)

Remember, “fairness” itself is not always a focal point, and even if it is

afocal 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 aresometimesintuitive 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.