Notice that in a market s.t. all agents have unit demand valuation functions- if there is an allocation (not necessarily and a matching) that yields SW of value v, there is also a

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW2 - Q3 ]]>

I think one should assume that there are no outgoing edges in G_I from vertix j if j was not sold under OPT.

This makes the graph well defined and makes it possible to prove the theorem.

Is this an acceptable assumption ?

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW2 - Q3 ]]>

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW2 - Q3 ]]>

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Forum thread: H2 q1 ]]>

Maybe it was confusing in this context, but in the previous answer I was talking about unit demand functions

I hope it is clearer now.

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Forum thread: HW 2 - Q 3A4 ]]>

צרו קשר דרך:

mendelsohn@mail,tau,ac,il

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Forum thread: Looking to switch presentation date ]]>

OPT is defined as "OPT (i.e. maximum weighted matching)" - In the definition of a "matching" in graphs that I'm familiar with, no node can be matched twice. In the context of markets, it means that each player gets at most one item.

If I understand correctly, we usually assume that an allocation in a unit-demand market is a matching (i.e. each player gets at most one item, which is more restrictive), and we can assume this without loss of generality because the value of each set is determined by only one item.

Reading your answer, it seems like that you assume players can get more than one item in OPT. Is this the definition of a "matching" we should work with?

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW 2 - Q 3A4 ]]>

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW 2 - Q 3A4 ]]>

Also, in this question we assume all valuations are unit-demand, which means that adding or removing items to a set of price 0 and value smaller than the value of the set doesn't change the set's utility.

An extreme example of this will be items of value and price 0, but in the context of the question, all unsold items which are of smaller value compared to agent i's set pose this problem as well.

Because adding and removing such items doesn't change the utility of agent i's set, I don't understand how their demand set can only have a single, unique set. I can always generate another, different set by adding/removing such an item.

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW 2 - Q 3A4 ]]>

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW 2 - Q 3A4 ]]>

Consider items of price 0. Because we prove the prices are Walrasian, all unsold items will be such items.

For any set of items in the demand set, you can add / remove items of price 0 without changing its utility. This means if there are unsold items, there are multiple sets in the demand set, contradicting what we need to prove.

Can we assume the uniqueness is "up to elements of price 0"?

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW 2 - Q 3A4 ]]>

Please contact me at: yotam.nitzan@gmail . com

Forum category: Discussions / Spring 2018 Forum

Forum thread: Looking to switch presentation date ]]>

Does anyone present on the 6.6 and wants to switch with us?

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Forum thread: Looking to switch presentation date ]]>

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Forum thread: H2 q1 ]]>

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Forum thread: q3b ]]>

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW2 - Q3 ]]>

I managed to prove that the greedy algorithm indeed outputs a correct result for a demand query, however I'm having trouble proving poly(m) time. In each iteration the algorithm needs to compute v(j|S) for items, and we were taught that computing v(j|S) requires computing a demand query several times. Given at worse case the greedy algorithm needs to compute v(j|S) when |S| = m-1, I realized that computing v(j|S) using the greedy algorithm as demand query oracle will result in infinite recursion, since computation of v(j|S) will require computing demand query over items set S + {j} which is the full item set. How should I proceed?

Thanks,

Eldar

Forum category: Discussions / Spring 2018 Forum

Forum thread: H2 q1 ]]>

or assume worst case as in assume the best poosible SW in the arrival order (which is the worst case when trying to show SW is low)

Forum category: Discussions / Spring 2018 Forum

Forum thread: q3b ]]>

Tie breaking can be arbitrary. Assume worst case option (this should help you).

Forum category: Discussions / Spring 2018 Forum

Forum thread: q3b ]]>

"For each pair of items j, j', let the weight of the edge (j, j') in G_I be v_i({j}) − v_i({j'}),

where i is the agent that was matched by M to j."

What happens if j was not matched to any agent in M ?

This case isn't defined explictly.

Can one assume that it means j has no outgoing edges ?

Thanks.

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW2 - Q3 ]]>

Is it enough to show an example that will work for any static prices where the prices are different?

I think I have an example - but it breaks when all prices are equal.

Also, can we assume how players break ties? does it happen in an arbitrary order? or can we determine the tie breaking for every player as part of his valuation function?

Thx

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Forum thread: q3b ]]>

Please contact me at achiyaj at gmail dot com

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Forum thread: HW 2, q4 ]]>

For example, can the first buyer decide to just buy everything if it is good for him?

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Forum thread: HW 2, q4 ]]>

Ben

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Forum thread: HW1 q4.1 ]]>

The result Im getting is:

$E[u_i + r_j] \ge \frac{1}{2} - \frac{1}{2e^2}$

is it possible? or am i wrong somewhere?

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW1 q1 ]]>

Can you clarify the meaning of the claim?

Is the claim that there exist combinatorial auctions (with specific valuations) in which a bidder can earn higher utility by submitting multiple bids.

Or is the claim that there are combinatorial auctions in which under any adversarial valuations by the other bidders, submitting multiple bids is a dominant strategy for the bidder.

Thanks

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Forum thread: HW1 q4.1 ]]>

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Forum thread: HW 1, q2 ]]>

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Forum thread: HW 1, q2 ]]>

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Forum thread: HW 1, q2 ]]>

If so, contact me - moc.liamg|nroh.inoy#moc.liamg|nroh.inoy / 0502758710

Yoni

Forum category: Discussions / Spring 2018 Forum

Forum thread: Looking for partner for HW ]]>

Can we assume we know the bidders bid regarding any sub-group of their prefered packages?

For example, if the auction is for fruits, and some bidder gave a bid for a package of {apple, banana}, did he also gave a bid for just an apple (and just a banana) ?

Thanks

Itay

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Forum thread: HW 1, q2 ]]>

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Forum thread: HW 1 question 4 section 1 ]]>

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Forum thread: Hw1 q1 ]]>

To my understanding it can be, e.g. a unit-price demand auction case where auction designer assumes builders are interested in one item only while in fact they may wish for more than one.

Forum category: Discussions / Spring 2018 Forum

Forum thread: HW 1 question 4 section 1 ]]>

I'm not sure I understand your question, omega notation is indeed a lower bound.

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