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

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Graphical Construction of Virtual Valu<strong>at</strong>ions Let X ∈ {x 1 , x 2 , x 3 , x 4 } w.p. {p 1 , p 2 , p 3 , p 4 }. (0,0) 0) p 1 p 2 p 3 p 4 (1,0) −x 1 −x 2 −x 3 −x 4
Graphical Construction of Virtual Valu<strong>at</strong>ions Let X ∈ {x 1 , x 2 , x 3 , x 4 } w.p. {p 1 , p 2 , p 3 , p 4 }. (0,0) 0) p 1 p 2 p 3 p 4 (1,0) −x 1 −x 2 −x 3 −x 4
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 and 8: Outline 1 Review of revenue optimal
Page 9 and 10: Model A Bayesian framework The valu
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: Graphical Construction of Virtual V
Page 23 and 24: Graphical Construction of Virtual V
Page 25 and 26: 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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