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Salience Tarek Rached
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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
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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
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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
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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?
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Multiple Equilibria: An Example D. MallCorner D. Mall 5, 50, 0 Corner 0, 05, 5 D. MallCorner D. Mall 5, 50, 0 Corner 0, 05, 5 2 identical equilibria as shown –no way to choose between them
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The Problem of Multiple Equilibria D. MallCorner D. Mall5, 50, 1 Corner1, 05, 5 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. Then going to the Corner becomes the salient choice for both of us D. MallCorner D. Mall5, 50, 1 Corner1, 05, 5
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The Problem of Multiple Equilibria D. MallCorner D. Mall5, 50, 0 Corner0, 05, 5 Suppose instead that we both independently check the bus schedules and find that the bus to the Downtown Mall runs more frequently Then going to the Downtown Mall becomes the salient choice for both of us D. MallCorner D. Mall5, 50, 0 Corner0, 05, 5 Seek Salience Ignore Salience SSMeet50% IS50% Seek Salience Ignore Salience SS5, 52.5, 2.5 IS2.5, 2.5 Seek Salience Ignore Salience SS5, 52.5, 2.5 IS2.5, 2.5 Expected Utility
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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
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A New Game Here, the salient solution is clear (It’s also the best equilibrium) ABC A3, 30, 0 B 2, 20, 0 C 2, 2 ABC A3, 30, 0 B 2, 20, 0 C 2, 2
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A New Game, cont’d ABC A3, 30, 0 B 2, 20, 0 C 3, 3 ABC A 0, 0 B 2, 20, 0 C 3, 3 Seek Salience Ignore Salience SS2, 22/3, 2/3 IS2/3, 2/38/9, 8/9 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 Seek Salience Ignore Salience SS2, 22/3, 2/3 IS2/3, 2/38/9, 8/9 Expected Utility
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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
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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
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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.
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Kidnapped (cont’d) Clearly, 4 best equilibria RGBY R1000 G0100 B0010 Y0001 RGBY R1000 G0100 B0010 Y0001
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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?
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Kidnapped (cont’d) Using salience, we are led to R-R Fair enough RGBY R1000 G0100 B0010 Y0001 Seek Salience Ignore Salience SS1, 11/4, 1/4 IS1/4, 1/4 Seek Salience Ignore Salience SS1, 11/4, 1/4 IS1/4, 1/4 Expected Utility RGBY R1000 G0100 B0010 Y0001
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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.
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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”
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Our previous example We can claim that the Downtown Mall is salient by virtue of its “standing out” as the inferior choice. 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. MallCorner D. Mall5, 50, 1 Corner1, 05, 5 D. MallCorner D. Mall5, 50, 1 Corner1, 05, 5
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The Bottom Line The perception of salience itself is a non- rational 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
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Discuss
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