Once upon a time, two families fought a bloody feud over the border of their properties. After many years of escalation, neither family could afford to continue the fight. They both wanted to negotiate a truce, but the original issue still had to be settled: where was the border of their lands to be drawn? They needed a Schelling point, so they settled on a river which ran roughly through the middle of their territories.
For a short time, there was peace.
Soon, though, a clever couple from one of the families hatched an idea. Each morning, they walked down to the river and dropped a few large stones into it. Before long, half a dam had built up on their side of the river. The water was driven toward the opposite bank, which was steadily washed away. Over time, as the river ate away the opposite bank, the couple extended their dam further, and so the river’s course was gradually pushed sideways. The couple’s family gained territory, while the opposed family lost it.
At this point, the story diverges, and many versions of the tail are told.
In one version, the couple push too fast. Soon the river has moved deep into the territory of the other family, and the family responds by attempting to break the dam. Violence escalates, and the feud breaks out anew - but peace is even harder to come by, now, since the river has been permanently destroyed as a Schelling point.
In another version, the push is slow. The couple bequeaths the task of dam-building to their children, and to their childrens’ children, and the river shifts slowly over the course of generations. With each generation, the resources of the couple’s descendants grow, and their family grows with it - while the resources of the opposed family slowly dwindle. Nobody ever takes much note of the river’s slow drift, until eventually the opposed family dies out altogether.
In most versions of the tale, the river’s movement is quickly noticed, but a return to violence is deemed unacceptable. Instead, the opposed family begins dropping rocks of their own. Soon both families are dumping rocks on their respective sides of the river, building up dams, aiming to drive the water against the opposite bank. This bloodless but expensive feud escalates. Along some sections of the river, each side expands until the two dams clash in the middle, blocking the flow of the whole river, and water backs up and bursts the banks. That doesn’t stop the dam-building - rather, each side builds tall walls alongside their dams, in hopes of flooding the other family’s land while preserving their own. The two families quickly bankrupt themselves in an arms race to build the tallest walls along their respective riverbanks.
Word goes out of the strange practices, the two families pouring all their resources into a competition of great dams and flood-walls. Travellers passing through town stare in bemusement, and wonder what strange force would lead the families to waste so much resources on a minor stream through the woods.
Moral(s) of the Story
I see two main takeaways to this parable. First, Schelling points can be moved by changing the underlying territory. The river's course can be physically moved. This generally costs some real resources (e.g. building the dams); modifying the world is rarely free.
Second, when players compete to move a Schelling point, they often end up in an all-pay auction: all players spend the resources required to move the river, but only the player with the "highest bid" (i.e. tallest dam) gains anything from the competition. In general, all-pay auctions often lead to all players spending more than the value of winning: at any point, either family can gain by building their dam just a bit taller, even long after their dam-building expenditures far exceed the value of the land.
This applies to most of the "strategic negotiation"-style situations where Schelling points play a prominent role, and in particular I see the parable of the dammed as a prototypical model of politics. Politics is an all-pay auction, in which "bidders" (i.e. anyone spending time/resources on political influence) compete to move Schelling points. The Schelling points which people compete to move include obvious things like laws, but also more subtle Schelling points like social norms.
I like the story as illustrating inefficient fighting over resources and entitlements. However, I am not sure your interpretation of moving focal (or Schelling) points works?
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. As a fairness norm, I'd guess that choosing the middle of the river works because the river "ran roughly through the middle of their territories". When one conflict party afterwards manipulates the river, the river becomes useless as a border, and trust is destroyed (ending 1), or one conflict party just does not notice what happened and seemingly has limited attention or limited information (ending 2), or the destruction of trust again leads to wasteful fighting (ending 3). Endings 1 and 3 can be interpreted as the "bad" Nash equilibrium of a repeated game. Standard game theory does not offer convincing solutions for why one of the possible equilibria (cooperate or don't) is chosen, so focal points may be part of the answer, but then the river is not the focal point; rather, "cooperation" is the focal point.
Since the parties agreed to use the middle of the river as the border and then one of the parties had the idea to manipulate it, the story may illustrate a problem of incomplete contracts.
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 "Evolu... (read more)