Spring 2016 Forum (new threads)

הגשת הפרויקט

Thu, 11 Aug 2016 10:07:27 +0000

הי, איך אנחנו נדרשים להגיש את הפרויקט? אימייל?

ex2 problem5

Tue, 17 May 2016 05:53:55 +0000

Can we assume that n>k?
Thanks

ex2 problem 4

Mon, 16 May 2016 22:27:43 +0000

1. In the example we are required to give, in the case the bidder is cheating (submit multiple bids) he can lie as much as he wants (ant give some allocation not what it is really worth for him). Right?
Also, the utility in this case is calculated as v-p, when v is the value that the (chosen) allocation really worth for him, right?
2. What is the definition of Vickrey auction?
Thanks

Questions about ex 2

Mon, 16 May 2016 18:09:23 +0000

1. In question 1, can we assume the bidders have different private valuations?
2. In question 3, is "surplus" the same as social welfare?

questions about lecture 3

Sun, 15 May 2016 12:26:50 +0000

1. Definition 1 page 1 - It says (at the third line of the definition) that the equality holds for each player. Isn't that redundant, (and therefore wrong)? It seems that the equality holds only for the deviating player. (And the fact that each player can be the deviating player was already mentioned in the second line).
2. Equations (1) and (2) in page 2 - shouldn't the sum on the last operand be over all edges which are in P_i\P_i^? And therefore, shouldn't the text in the paragraph between the equations be "the last element of the second operand is canceled" (instead of the current version that says "not canceled").
3. What is the calculation that leads to the fact that the example for CE on page 5 is indeed CE?
4. I want to make sure I understand why the CCE on page 5 is CCE: In half of the profiles (in the support) player 1 shares his edge with another player, and on the other half he doesn't. Meaning, his cost expectation is 1/2*2+1/2*1=1.5 .
If player 1 deviates to the fixed strategy 0 then his cost expectation would be 1/72[6*2+6*3+3*1+9*2+3*1+9*2+36*1]=1.5 .
Is this calculation correct?
5. Inequality (4) in page 6 - Shouldn't it be equality? I mean, isn't the cost of a profile defined as the sum of the costs of all players?
6. Cost sharing games - what is the meaning of v in profile p? (the last line of the first paragraph in page 8)
7. In the potential definition on page 8 - shouldn't the last sum in this equation go from i=1 to i=p_e?
8. Lemma 16 page 10 - the lemma bounds (lower and upper bound) the potential function. Is this bound holds for all potential functions of fair cost-sharing games? Or just the one defined in page 8? And in general, is there only one potential function for each game ? (in case it exists)
9. the last equation on page 10 - Isn't the demand that outer sum goes over all edges in p^i redundant? If we want to run over all edges that were chosen (at least by one player) the demand p_e>=1 is enough. Also, it's confusing in the middle part of the equation when i has a slightly different meaning.

Thanks a lot

questions about lecture 2

Sat, 14 May 2016 20:43:57 +0000

1. What is the meaning of s_i and r_j at the of page 1 and at the beginning of page 2?
2. How problems (2) and (2') (pages 2-3) are considered to be LP? In standard LP problems the value we are trying to minimize/maximize is the dot product of the variables vector with some constant vector.
3. Does the corollary that "It is possible to compute a NE in polynomial time for every Zero-Sum game" (cor' 8 page 4) refers to 2-players games only? or to any amount of players?

Definition of VCG

Sat, 14 May 2016 14:36:01 +0000

I'm doing problem 5b and straggling to understand the definition of VCG.
VCG should be a truthful mechanism were the payment for all players (including non winners) is:
h(b_-i) - sum_j!=iv_i(w)
where:
w is the optimal allocation
b_-i is the payments of players who aren't i
v_i is the willing to pay value of i
h is a function corellated to b_-i

1.Is that the correct definition?
2.h can be anything, like h = sizeof(v_i)?
3. Does 5b should be proven for any h?

Question 5 part b

Sat, 14 May 2016 08:21:02 +0000

An answer based on Clarcke Pivot rule will suffice?

some questions regarding lecture 1

Fri, 13 May 2016 14:50:48 +0000

1. In definition 8, page 7 - shouldn't it be

(1)

\begin{align} x^{i} \in \triangle (S_{i}) \end{align}

(meaning each player has its own Delte(S_i), possibly with different vector sizes then the others)?
2. In example 1 p.8 - We assume we get NE when player 1 plays B with prob' p and O with prob' 1-p.
We can calculate p using the fact that each choice of player 2 leads to the same utility expectation, meaning E[u_2| player 2 plays B] = E[u_2| player 2 plays O]. So we have 2p+0(p-1) = 0p+3(p-1) leading to p=3/5.
Where is the mistake here?
3. Using the Brouwer fixed-point theorem - the set in the theorem is a subset of R^t. The set used to prove NE theorem is a bit more complicated. Should we look at it as a subset of R^t when t=|S_1|+..+|S_n|?
4. How is the immediate implication implies from lemma 15?
Thank you very much

Ex2 Q4

Thu, 12 May 2016 20:32:36 +0000

Is it enough to show an example of a case in which pseudonyms are utilitarian, or should we find a general pseudonyms startegy?

Problem 3

Wed, 11 May 2016 15:30:10 +0000

Can we just use a reduction to the simple case by defining v'=v*beta?
I don't really understand the difference between the two cases.
Why does it matter that beta is publicly known?

Ex2 Q1 clarification

Tue, 10 May 2016 06:12:58 +0000

Hi,
Regarding Q1 of Ex2, can you please clarify - is this a single item auction ("Vickrey auction")?

תרגיל 2

Mon, 09 May 2016 15:23:10 +0000

היי,
אם עושים 6 שאלות בתרגיל - האם תבחרו את 5 השאלות הטובות?

Problem 5.b

Sun, 08 May 2016 09:24:07 +0000

When proving that player i can not improve his utility, can we assume the other players bid normally (meaning they bid once)?

Partner for Ex.2

Sat, 07 May 2016 12:47:30 +0000

Hey,
I'm looking for a partner for exercise 2.
Reply here if you are also looking for one.

Q3

Tue, 05 Apr 2016 12:48:29 +0000

By the hint "reduction from partition" do you mean:
The language of triples (S,S1,S2) such that S1, S2 minimize max{sum(S1),sum(S2)} among all sets S1,S2 that satisfy that their union is S?

Besides, do we need to show also membership in NP? Or only NP-hardness?

Exercise 1, question 3.2

Mon, 04 Apr 2016 21:02:07 +0000

In the question it says - "the load on the most loaded band" - by load, do you mean the sum of all bits sent by all players who chose that band?
Thank you.

Question 3 Part 7

Mon, 04 Apr 2016 20:49:36 +0000

Can we divide fractions of bits between bands? for example, can a player move 0.5 bit to a band?

Q3

Fri, 01 Apr 2016 09:26:56 +0000

1. What is the bandwidth?
2. By "the radios that use a certain band b" you mean radio users?

מספר שאלות

Thu, 31 Mar 2016 17:12:41 +0000

@@
) בשאלה 1, האם ב utility כוונה פונקציית רווח?
2) בשאלה 1 סעיף 2 הכוונה להוכיח שהגרירות בכיוון ההפוך לא מתקיימות נכון?
3) בשאלה 1 סעיף 4 - להוכיח שקילות בין שתי הגדרות הכוונה להוכיח שהגדרה אחת גוררת את ההגדרה השניה ולהפך נכון?
4) בשאלה 2 סעיף 1 - האם S ו T הן כל האסטרטגיות של שתי השחקנים או שאלה תתי הקבוצות של אסטרטגיות שמדברים עליהן (הניסוח דו משמעי)?
5) בשאלה 2 סעיף 1 - למה הכוונה ב support of the column/row stratagy - לא הגדרנו תומך לאסטרטגיה. אשמח להבהרה.
6) בשאלה 3 - יש פה מספר דברים שלא ברורים לי מהגדרת המשחק:
א) לא נתון מה רוחב הפס של כל אחד משתי ה bandים
ב) כתוב "the radios that use a certain band b…" הכוונה radio users נכון? לא הגדרנו radios בשאלה.
ג) כתוב "the radios that use a certain band b share the bandwidth of the band" - בהנחה שבסעיף ב' הכוונה לשחקנים, אז מה הכוונה ב share the bandwidth? מה רוחב הפס שלו ואיך הם חולקים אותו - שווה בשווה כי כולם משדרים רק ביט אחד כל פעם (אני מנחש - זה לא הוגדר בשום מקום) או באופן יחסי לכמות המידע שהם רוצים לשדר או הכוונה פה היא אחרת?
ד) כתוב "and all of them finish at the same time" - לא ברור למה הכוונה - שוב, קודם כל לא נתון הרוחב פס של כל band, אבל גם לא ברור למה הכוונה "מסיימים באותו הזמן" - אם שחקן A רוצה לשדר 20 ביטים ושחקן B ביט 1 - למה הכוונה ששניהם יסיימיו באותו זמן? כלומר זה שוב חוזר לעובדה שלא ברור כיצד משדרים במשחק מידע - ביט ביט, או את כל מה ששחקן רוצה לשדר בבת אחת, ומה רוחב הפס האפשרי של כל band.
@@