Hardness of pricing loss leaders. Yi Wu IBM Almaden Research Joint work with Preyas Popat. Introduction. Example: supermarket pricing. Buy coffee and alcohol if under 15$. Buy cereal and milk if under 10$. How to price items to maximize profit?.
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IBM Almaden Research
Joint work with PreyasPopat
Buy coffee and alcohol if under 15$
Buy cereal and milk if under 10$
How to price items to maximize profit?
Buy coffee and milk if under 7$
For item pricing with items m buyers:
-approximation [Guruswami et al.]
hard[Demain et al.]
For -hypergraph pricing
4-approximaiton for graph pricing (k=2) [Balcan-Blum 06]
17/16-hard [Khandekar-Kimbrel-Makarychev-Sviridenko 09],
2-hard assuming the UGC (Unique Games Conjecture)
For highway problem
All the previous work assumes that the profit margin is positive for every item.
Profit is 40.
Profit is 50.
The seller assign a profit margin to each item and have profit with the buyer interested in set if the buyer purchase the item.
What if the production cost is 0 such as the highway problem?
The seller assign a profit margin to each item and have profit with the buyer interested in set
[Balcan-Blum 06]: The maximum profit can be log n-times more when loss leaders are allowed (under either coupon or discount model).
[Khot-Kindler-Mossel-O’Donnell-07]:assuming the Unique Games Conjecture, it is NP-hard to get better than -approximation.
Passing probability is 1/q.
The profit is then at least
Completeness c = q log q.
Then for any , suppose , then the profit is at most
Soundness is q.
We can not prove the soundness claim for this test.