Game Theory and Strategic Behavior

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Game Theory and Strategic Behavior

• Directions 2007 Conference
• Edwin T. Burton
• June 19, 2007

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What is Going On in Academic Economics that May
be Useful?

• Not much news on the predictions front
• Next years interest rates and inflation rates are
  anybodys guess
• No one knows if the economy will be strong or
  weak
• So, what do we know or what have we learned for
  all of the effort in the last 25 years
• Interestingly, quite a bit

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Two Areas of Economics That Are Useful to the
Practical World

• Game Theory
• History dates back to 2nd World War
• Main theme that we need to understand how our
  friends and adversaries behave and how they view
  us viewing them
• Behavioral Economics (mostly Finance)
• Main theme people act in strange ways that
  may be predictable
• (We always thought that strange behavior was
  pathological or random, but recent research says
  maybe not)

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We will look at some classic situations

• Game Theory
• The Three Door Problem
• Blue Dot, White Dot the Principle of Common
  Knowledge
• Behavioral Economics
• Is This the Librarian?
• The Department Store Sale

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The Three Door Problem

• 3 doors, 1 with a prize behind it.

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This one makes people madso prepare to be mad
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The Three Door Problem

• Choose 1 door

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The Three Door Problem

• Right as youre about to open the door, the MC
  opens another door, showing its empty.

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The Three Door Problem

• Now you have the choice to keep your original
  choice or switch doors.
• Which should you choose?

?
?
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A Show of Hands?

• Most people prefer to stick with their original
  choice
• Now, think a moment
• If you stick with your original choice and I
  switch, then one of us will be right?
• So, between you and me, we have probability one
  (together) of winning
• You will win 1/3 of the time, so

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Monte Carlo Example

• You should switch doors.
• Why?

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Solution to the 3 door problem
2/3
1/3
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What do we learn from this?

• How you pose the question affects the answer you
  will get
• Pose it differently
• Would you rather pick two doors or just one door?
• Then everyone gets the right answer

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The Blue Dots

• Each person has a dot on his forehead.
• Each dot is either blue or white.
• You can see the other 2 peoples dots, but you do
  not know the color of your own dot.
• You notice that the other 2 dots are white.

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This one is hard
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The Blue Dots

• The object is to figure out what color dot is
  on your own forehead
• Neither of the first two people know the color of
  their dot.

?
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The Blue Dots

• Then someone gives everyone a hint at least 1
  of the dots is white.
• Each of the first 2 people still dont know what
  color their dot is.

?
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The Blue Dots

• Can you now figure out based on the information
  what color your dot is?

?
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The Blue Dots

• Heres what you know
• Person 1 sees your dot and Person 2s white dot.
• Person 2 sees your dot and Person 1s white dot.
• At least one dot is white.

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The Blue Dots

• Explanation
• Person 1 does not know the color of his dot.
• Therefore, he must not see 2 blue dots, otherwise
  he would know his is white.

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The Blue Dots

• Person 2 does not know the color of his dot.
• He knows the color of your dot and he sees that
  Person 1 has a white dot

?
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The Blue Dots

• Person 2 knows that there are not 2 blue dots
  because of Person 1s answer.
• Therefore Person 1 knows that there are either 0
  or 1 blue dots.

?
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The Blue Dots

• Person 1 sees your dot and still does not know
  what color his dot is.
• This means that your dot was not blue, because if
  it was Person 2 would have known that his was
  white.

?
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Didnt everyone already know that there is at
least one white dot?

• Yes, they knew that
• But, interestingly, there is a difference between
  each person knowing it privately and someone
  making the public statement there is at least
  one white dot

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So, What Did White Dot, Blue Dot Teach Us

• That sometimes a conflict can be avoided
  (resolved) by simply stating the obvious as
  common knowledge.
• Without stating the obvious, sometimes there is
  no way to resolve the conflict

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Librarian Versus Not a Librarian

• We are in a small town that is completely
  agricultural that has a library with a single
  librarian. We are looking for the librarian, who
  might be a male or a female?
• We meet lots of people wandering around town, all
  of whom seem to be farmers or part of farming
  families
• Then, we meet a demure, prim, proper lady with
  spectacles, who is carrying a book and reading
  it.
• What are the odds that this lady is the librarian?

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Is this demure, prim and proper lady likely to be
the towns Librarian? Is there a better than
50/50 chance that this lady is the towns
librarian?

• How about a show of hands.

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Of, the 5000 People in this Town, only one is a
librarian

• She is not likely to be the librarian
• The odds are one in 5,000

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What do we learn from this?

• People often ignore the broader data in favor of
  particular representative characteristic

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Heres An Experiment from Real Life

• A store is having a sale on jackets and
  flashlights (but you must buy both)
• The jacket costs 175
• The flashlight cost 15
• Now, just before you pay, the store person says
  If you walk up four flights of stairs, you can
  get that flashlight for only 10 (and the jacket
  is up there too for 175 as it is here)
• The next day, same exact experiment, except the
  store person says If you walk up four flights
  of stairs, you can get that jacket for 170 (and
  the flashlight is up there too for 15 as it is
  here

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What happens

• More than twice as many buyers will walk up four
  flights of stairs to save the 5, if the savings
  is on the 15 flashlight
• Less than half will walk up the four flights of
  stairs to save the 5, if the savings is on the
  jacket
• No difference, you end up paying 185 in either
  case by walking up four flights of stairs
  absolutely no difference in outcome
• But big difference in peoples willingness to
  walk up four flights of stairs, depending upon
  which product saves them the 5.

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What do we learn from this

• People frame their choices and separate them,
  often in irrational ways

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So, in conclusion

• We are learning more about how people make their
  choices
• We are learning more about how to resolve
  conflicts
• We are learning more about how to phrase things
  to influence decisions
• And, we are only at the beginning

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The End