Via the AI mavens at LessWrong:
Cross-posted from my blog.
Daniel Filan
I recently read Thomas Schelling's
book 'The Strategy of Conflict'. Many of the ideas it contains are now
pretty widely known, especially in the rationalist community, such as
the value of Schelling points when coordination must be obtained without
communication, or the value of being able to commit oneself to actions
that seem irrational. However, there are a few ideas that I got from the
book that I don't think are as embedded in the public consciousness.
Schelling points in bargaining
The first such idea is the value of Schelling points in bargaining situations where communication is
possible, as opposed to coordination situations where it is not. For
instance, if you and I were dividing up a homogeneous pie that we both
wanted as much of as possible, it would be strange if I told you that I
demanded at least 52.3% of the pie. If I did, you would probably expect
me to give some argument for the number 52.3% that distinguishes it from
51% or 55%. Indeed, it would be more strange than asking for 66.67%,
which itself would be more strange than asking for 50%, which would be
the most likely outcome were we to really run the experiment. Schelling
uses as an example
the remarkable frequency with which long negotiations over complicated quantitative formulas or ad hoc
shares in some costs or benefits converge ultimately on something as
crudely simple as equal shares, shares proportionate to some common
magnitude (gross national product, population, foreign-exchange deficit,
and so forth), or the shares agreed on in some previous but logically
irrelevant negotiation.
The explanation is basically that
in bargaining situations like these, any agreement could be made better
for either side, but it can't be made better for both simultaneously,
and any agreement is better than no agreement. Talk is cheap, so it's
difficult for any side to credibly commit to only accept certain
arbitrary outcomes. Therefore, as Schelling puts it,
Each
party's strategy is guided mainly by what he expects the other to
accept or insist on; yet each knows that the other is guided by
reciprocal thoughts. The final outcome must be a point from which
neither expects the other to retreat; yet the main ingredient of this
expectation is what one thinks the other expects the first to expect,
and so on. Somehow, out of this fluid and indeterminate situation that
seemingly provides no logical reason for anybody to expect anything
except what he expects to be expected to expect, a decision is reached.
These infinitely reflexive expectations must somehow converge upon a
single point, at which each expects the other not to expect to be
expected to retreat.
In other words, a Schelling point
is a 'natural' outcome that somehow has the intrinsic property that each
party can be expected to demand that they do at least as well as they
would in that outcome.
Another way of putting this is that once we
are bargained down to a Schelling point, we are not expected to let
ourselves be bargained down further. Schelling uses the examples of
soldiers fighting over a city. If one side retreats 13 km, they might be
expected to retreat even further, unless they retreat to the single
river running through the city. This river can serve as a Schelling
point, and the attacking force might genuinely expect that their
opponents will retreat no further.
Threats and promises...
...
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