Salience
Tarek Rached
Overview
• David Gauthier proposes salience as a criterion for
equilibrium selection in his paper Coordination,
published in in Dialogue, 14:195-221, 1975
• 13 years later, Margaret Gilbert challenges the
validity of salience in her paper Rationality and
Salience in Philosophical Studies, 57:61-77, 1989
• Both of these are written for a philosophical
audience, although Nash and others are cited
Gauthier
• Introduces the problem of coordination
– Successful coordination requires each player to maximize utility
based on the other player’s actions
– Successful coordination will always result in an equilibrium
• Discusses the difference between explicit and tacit
coordination
– Restricts his arguments to “situations in which all [players] are
sufficiently informed about the circumstances” without allowing
communication
• Discusses optimality
– Notes that in games such as the Prisoner’s Dilemma, the optimal
outcome and the equilibirum outcome may not be the same.
– Restricts his arguments to games in which they are the same
Gauthier (cont’d)
• Omits any mention of mixed strategies, implicitly
restricting the paper to pure strategies
• Proposes a Principle of Coordination
– “In a situation with one and only one outcome which is
both optimal and a best equilibrium” the action leading
to that outcome is the rational choice
• Seeks a Theory of Rational Coordination
– By which in any situation, a single best action can be
determined
Multiple Equilibria:
An Example
• Suppose you are coming from Richmond to
Charlottesville on a bus, and I have agreed
to meet you.
• Unfortunately, once you are on your way, I
discover that there are two buses from
Richmond, one of which arrives at the
Corner, the other at the Downtown Mall.
– Which bus do you take?
– Where do I go to meet you?
Multiple Equilibria:
An Example
D. Mall
Corner
D. Mall
5, 5
0, 0
Corner
0, 0
5, 5
• 2 identical equilibria as shown
– no way to choose between them
The Problem of Multiple
Equilibria
• Suppose we both know that if we don’t meet, we would
both rather be at the Corner because you want to check out
some records at Plan 9, and I like smoothies.
D. Mall
Corner
D. Mall
5, 5
0, 1
Corner
1, 0
5, 5
• Then going to the Corner becomes the salient choice for
both of us
The Problem of Multiple
Equilibria
• Suppose instead that we both independently check the bus
schedules and find that the bus to the Downtown Mall runs
more frequently
Expected Utility
Seek
Salience
Ignore
Salience
Meet
5, 5
2.5,
50%
2.5
D. Mall
Corner
D. Mall
5, 5
0, 0
SS
Corner
0, 0
5, 5
IS 2.5,
50%
2.5
2.5,
50%
2.5
• Then going to the Downtown Mall becomes the salient
choice for both of us
What is Salience?
• The salient choice is the choice “which is
apprehended as as standing out from the
others.”
• How do we determine which choice stands
out from the others?
– External information (as seen)
– Structure of the game
• Let’s look at some more examples
A New Game
A
B
C
A
3, 3
0, 0
0, 0
B
0, 0
2, 2
0, 0
C
0, 0
0, 0
2, 2
Here, the salient solution is clear
(It’s also the best equilibrium)
A New Game, cont’d
Expected Utility
A
B
C
A
3, 3
0, 0
0, 0
B
0, 0
2, 2
0, 0
SS
C
0, 0
0, 0
3, 3
IS 2/3, 2/3 8/9, 8/9
Seek
Salience
Ignore
Salience
2, 2
2/3, 2/3
• Whereas here, it is not obvious
– Gauthier claims you would “ignore salience” by
randomizing over the 3 possibilities, I would say you
would randomize over the 2 best equilibra
– Seeking salience still a best equilbria in the right table
What’s Going On?
• Gauthier seeks to use salience as
the basis for his Theory of Rational
Coordination
• Unfortunately…
• “The apprehension of salience is
itself not, or at least not only, a
rational apprehension.” - Gauthier
Gauthier (cont’d)
• Seeks to apply his theory of salience to the
philisophical realm of act-utilitarianism
– All persons in society are rational maximizers
of individual utility
– D.H. Hodgson writes that promise keeping and
truth selling cannot be enforced in such a
society
– Gauthier applies salience to argue that they are,
in fact, encouraged
On to Gilbert’s Counterexample:
Kidnapped
• 2 players are kidnapped and separated
• Kidnapper gives them each a box with 4
buttons, each of a different color.
• Tells the captives that in 10 minutes, each
will have to press a button. If they both
press the same color button, they are free.
• Otherwise, they die.
Kidnapped (cont’d)
R
G
B
Y
R
1
0
0
0
G
0
1
0
0
B
0
0
1
0
Y
0
0
0
1
• Clearly, 4 best equilibria
Kidnapped (cont’d)
• Suppose that after the kidnapper told them about
the buttons and their impending decision, he then
tell them that he will turn on the radio.
• The radio comes on, and it’s a sports broadcast
about the Cincinnati Reds. The announcer
comments on their nice new red uniforms, the red
bleachers, and the red ketchup he just spilled on
himself.
• What then?
Kidnapped (cont’d)
R
G
B
Y
R
1
0
0
0
G
0
1
0
0
B
0
0
1
0
Y
0
0
0
1
Expected Utility
SS
Seek
Salience
Ignore
Salience
1, 1
1/4, 1/4
IS 1/4, 1/4 1/4, 1/4
• Using salience, we are led to R-R
• Fair enough
Kidnapped (cont’d)
• Suppose that after the bit on the Cincinnati Reds,
the announcer breaks in with a quick news flash
about the kidnapping, noting that one of the
captives is notoriously salience-shy.
• Red is still the salient choice, but it would now be
irrational for the captives to choose it.
Kidnapped (cont’d)
• The extreme counter-example
– Instead of the sports show, all the captives hear
is a news bulletin about the kidnapping, which
prominently mentions the fact that both
captives hate the color red.
• Red is still the salient choice, as it is distinct
from the others, but it doesn’t make any
sense to choose it.
• Salience fails because it provides no
rational criteria for “standing out”
Our previous example
•
Suppose we both know that if we don’t meet, we would both rather
be at the Corner because you want to check out some records at
Plan 9, and I like smoothies.
D. Mall
Corner
D. Mall
5, 5
0, 1
Corner
1, 0
5, 5
• We can claim that the Downtown Mall is salient by virtue
of its “standing out” as the inferior choice.
The Bottom Line
• The perception of salience itself is a nonrational process
• Even having successfully perceived
salience, it is not at all clear that it is the
rational choice
• However, it can aid real (non-rational)
players in games where knowledge of the
world around them may be a factor
Discuss