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"? ]]>

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

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

"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.

]]>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

]]>Please contact me at achiyaj at gmail dot com ]]>

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

Ben

]]>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?

]]>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

]]>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

]]>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. ]]>