More on schelling point

A nice defintion taken from here:

Two people are separately confronted with the following list of numbers : 2,5, 9, 25, 69, 73, 82, 96, 100, 126, 150

They are offered a reward if they independently choose the same number. If the two are mathematicians, it is likely that they will both choose 2&emdash;the only even prime. Non-mathematicians are likely to choose 100&emdash;a number which seems, to the mathematicians, no more unique than the other two exact squares. Illiterates might agree on 69, because of its peculiar symmetry&emdash;as would, for a different reason, those whose interest in numbers is more prurient than mathematical.

There are three things worth noting about this simple problem in coordination without communication. The first is that each pair of players is looking for a number that is in some way unique. The second thing to note is that there is no single right answer; the number chosen by one player, and hence the number that ought to be chosen by the other, depends on the categories that the person choosing uses to classify the alternatives. The right strategy is to find some classification in terms of which there is a unique number, then choose that number&emdash;a strategy whose implementation depends on the particular classifications that pair of players uses. Thus the right answer depends on subjective characteristics of the players.

The third point, which follows from this, is that it is possible to succeed in the game because of, not in spite of, the bounded rationality of the players. To a mind of sufficient scope every number is unique. It is only because the players are limited to a small number of the possible classification schemes for numbers, and because the two players may be limited to the same schemes, that a correct choice may exist. In this respect the theory of this game is radically different from conventional game theory, which assumes players with unlimited ability to examine alternatives and so abstracts away from all subjective characteristics of the players except those embodied in their utility functions.

Such an outcome, chosen because of its uniqueness, is called a Schelling point, after Thomas Schelling who originated the idea. It provides a possible solution to the problem of coordination without communication. As this example shows, it is relevant both to situations where communication is physically impossible and to situations where communication is impossible because there is no way that either party can provide the other with a reason to believe that what he says is true.

Even if it is impossible for the players in such a game to communicate their real demands, it may still be possible for them to affect the outcome by what they say. They could do so, not by directly communicating their own strategies (any such statement will be disbelieved), but by altering the other player’s categories, the ways in which he organizes the alternatives of the game, and so changing the Schelling points which depend on those categories.

Now, let’s apply this to spatial coordination.