On Revenue Optimal Combinatorial Auctions - IFP Group at the ...

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Model N buyers, multiple items. The bundles desired by the buyers are publicly known. Each desired bundle has the same value for a buyer. A buyer is a winner if he gets any one of his desired bundles.
Model A Bayesian framework The value of a buyer n: A realization of a discrete random variable X n . X n ∈ {xn 1 , xn 2 , . . . , xn Kn }, where 0 ≤ xn 1 < xn 2 < . . . < xn Kn . p i n P(X n = x i n), assume p i n > 0. One-dimensional private information: Beliefs: The exact realization of X n is known only to buyer n. X n ’s are independent across the buyers. The probability distributions of X n ’s are common knowledge.
Page 1 and 2: On Revenue Optimal Combinatorial Au
Page 3 and 4: What Makes It Hard? Private values:
Page 5 and 6: Our Contributions Most of the liter
Page 7: Outline 1 Review of revenue optimal
Page 11 and 12: The Components of an Auction .Bid v
Page 13 and 14: The Constraints First, focus on one
Page 15 and 16: Geometric Interpretation Let A 0 (
Page 17 and 18: Simplifying the Constraints A payme
Page 19 and 20: Graphical Construction of Virtual V
Page 27 and 28: The Optimal Auction Problem Extendi
Page 29 and 30: Simplifying OAP Revenue(π) maximu
Page 31 and 32: The Maximum Weight Algorithm (MWA)
Page 33 and 34: Outline 1 Review of revenue optimal
Page 35 and 36: Some Questions How different is a r
Page 37 and 38: Revenue vs Efficiency - Example 1 T
Page 43 and 44: Revenue vs Efficiency - Example 3 E
Page 45 and 46: Quantifying Efficiency Loss For an
Page 47 and 48: Worst Case ELR Computation - Exampl
Page 49 and 50: Worst Case ELR Computation - Exampl
Page 51 and 52: ELR Bound - Single Item Auctions wi
Page 53 and 54: Limitations of General CAs Implemen
Page 55 and 56: Why Study Single-Minded Buyers Mode
Page 57 and 58: Extending the Model to Single-Minde
Page 59 and 60:
Does It Work? Buyer 1 Buyer 2 1 1/2
Page 61 and 62:
Does It Work? Buyer 1 Buyer 2 1 1/2
Page 63 and 64:
The Sufficient Condition Hazard rat
Page 65:
Concluding Remarks A revenue optima
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