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15.040 Game Theory for Managers Professor David McAdams

Urn Game

We will play the Urn Game next class. As preparation, please think about the game,

answer the two questions at the bottom of this page, and turn in this sheet to the TA at

the beginning of next lecture.

Description of Urn Game:

󰂃 “Urn W” has two white balls and one yellow ball

󰂃 “Urn Y” has one white ball and two yellow balls.

󰂃 The TA flips a coin and picks up Urn W if Heads and Urn Y if Tails.

󰂃 Students are invited – one at a time – to pick a ball from the chosen urn and then

guess whether it’s Urn W or Urn Y. The class gets to learn each student’s guess BUT

NOT what type of ball the student saw. The chosen ball is then put back into the urn.

󰂃 Payoffs: You “WIN” if you guess correctly and “LOSE” if you guess incorrectly.

How would you play?

What would you do in the following two situations? Please briefly explain your answers.

1. You are the third person to pick a ball. The first person and the second person

both guessed “Urn W”. You draw a yellow ball.

Would you guess “Urn W” or “Urn Y”?

2. You are the tenth person to pick a ball. The first seven people each guessed “Urn

W” while the next two people each guessed “Urn Y”. You draw a yellow ball.

Would you guess “Urn W” or “Urn Y”?

Your Name: __________________________

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MIT-SCIENCE-Lectures-q12_ltl_cotifl

MIT-SCIENCE-Lectures-q12_ltl_cotifl

24.400

Proseminar in philosophy I

Fall 2003

Language, Truth, and Logic

1. Enlarge the punctures in the principle of verification, as explained in the main text of

LTL. Does Ayer succeed in patching them up in the Introduction? (See the attached

review by Church.) Is any kind of verificationism plausible?

2. (a) Are arithmetic and logic analytic?

(b) Is is true that there is “no way of proving that the existence of a god, such as the

God of Christianity, is even probable”?

3. “‘I can only know that I have personal experiences, not that anyone else has’.—Shall

we then call it an unnecessary hypothesis that anyone else has personal experiences?—

But is it an hypothesis at all?” What is Ayer’s answer?

“The Concept of Truth in Formalized Languages”

0. (a) Polish notation has no parentheses. The relative scopes of connectives and

MIT-SCIENCE-Lectures-studentinfo

MIT-SCIENCE-Lectures-studentinfo

14.20 information

1. 󰀃First and Last Name (using whatever nickname you wish to be called by)

2. 󰀃Course & Year: 3. 󰀃e-mail address: 4. 󰀃Previous microeconomics courses:

5. 󰀃Any industry experience (summer jobs,etc.)?

6. 󰀃Any market or company behavior you would especially like to learn about?

7. 󰀃Team preferences: list up to 2 other students in the course with whom you would like to be teamed if possible. We will try if possible to match at least one, but can’t guarantee a match.

MIT-SCIENCE-Lectures-feb192002

MIT-SCIENCE-Lectures-feb192002

TheBayesianCentralLimitTheorem,

withsomeintructionson#1(e)ofthesecondproblemset

WehaveseenBayesformula:

posteriorprobabilitydensity=constantpriorprobabilitydensitylikelihoodfunction.··

The“BayesianCentralLimitTheorem”saysthatundercertaincircumstances,theposterior

probabilitydistributionisapproximatelyanormaldistribution.Actuallymorethanone

propositioniscalled“theBayesianCentralLimitTheorem,”andwewilllookattwoof

them.

Firstversion:SupposeΘisdistributedaccordingtotheprobabilitydensityfunctionf

Θ(θ),

and

X

1,X

2,X

3,......[Θ=θ]∼i.i.d.f

X1[Θ=θ](x)|

|

i.e.,X

1,X

2,X

3,...areconditionallyindependentgiventhatΘ=θ,andf

X1[Θ=θ](x),asa

|

functionofxwithθfixed,istheconditionalprobabilitydensityfunctionofX

1giventhat

Θ=θ.Supposetheposteriorprobabilitydensityfunctionf

Θ[X1=x1,...,Xn=xn]iseverywhere

|

twice-differentiable,foralln.

Letc=theposteriorexpectedvalue=E(ΘX

MIT-SCIENCE-Lectures-lec_7_1

MIT-SCIENCE-Lectures-lec_7_1

Ingo Schulze

East German.

In Simple Stories, he

returns to his hometown of Altenburg, a small community located in the former East

Germany.

The 29 anecdotal tales in Simple Stories range from the years immediately after the

fall of the Berlin Wall through the end of the decade,

as the citizens of Altenburg deal with

the particulars of their newfound freedom.

Q: does it satisfy as a novel?

Q: how to describe the narrative form?

He frequently brings back key characters in later

chapters as a means of clarifying earlier events:

Q: can you diagram the relationships among the characters?

(ernst, martin, andrea, holitschek (someone end up living with her)

The psychiatrist in chapter five,

turns out to have been responsible for the death of the wife

of the unemployed art historian met in chapter 4...