Exchange Day Group C

1
Exchange Day Group C

• CS286r
• Harvard University
• 27 April 2004

2
Multiplicative Strategies

• Rothkopf (C1), Rothkopf (C2) and Rothkopf et al.
  (C3)
  
• Many bidders bidding to perform a project for one
  consumer
  
• Lowest bidder wins
• Bidders share same actual cost
• However, bidders do not know what that cost is in
  reality!

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What do Bidders Know?

• Bidders know
• Their own estimate
• Estimation Distribution - Weibull
• F(r) 1 exp(-arm), r 0
• m shape parameter
• a scale parameter
• u standard deviation of ri
• u G(12/m)-G(11/m)-1/2
• G(w)Integral(0,INF) v(w-1)evdv

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Therefore

• Pm(n-1)n1/m/m(n-1)-1
• nnumber of competing
• For example,
• u 0.12, n 3 ? P 1.175
• u 0.12, n 5 ? P 1.205
• u 0.52, n 3 ? P 2.309

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Potential Lessons For Group C

• Look at atomic items we want
• Items may exist within bundles
• Gain range of values for atomic items
• Gain range of bundles via adding items
• May come via BigButton
• May come via D (e.g., population densities)
• May be our own Weibull guess
• Given our value, sense of range, sense of size of
  competition ? shave bid

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How is C Group Organized?

• Three Teams
• Team 1 Extracting Useful Information from the
  BigButton
  
• Team 2 Using Information (lack thereof) to
  convert valuation?bid
  
• Team 3 In game strategy, how best to set/change
  upper/lower bounds

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Team 1 Extracting Info.

• Ben and Adam
• The BigButton returns a glimpse of the world we
  may live in, so what?
  
• Can BigButton be used to tell ex-ante who will
  win what for how much?
  
• How much confidence can we have in our belief?

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Team 1
From D
Team 1
MIPs Sensitivity Analysis
Big Button
World
Item Who (Confidence) A 1 10 (75) B 1 5 (50)

C 2 10 (0) D 4 3 (100)
May be 2 versions With and w/out us
Team 2
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Team 2 Constructing ICTree

• Silas, Jonathan, and Wilfred
• Group D passes C an agents true value
• But does an agent really want to pass that tree
  directly along to the proxy?
  
• Bases decision on Team 1s Return
• Team 1 may determine no useful info to work off
  of other than number of agents
  
• Can shave values AND/OR add/remove objects to the
  ICTree

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Team 2
Team 2
ICTree
May have shaved values or new items
Team 3
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Team 3 In game strategy

• Lyra and Rui
• Objective
• Maximize surplus subject to ICTree constructed by
  Team 2
  
• Team 2 constrains space for Team 3
• Team 3 ensures no submission of bids above Team
  2s shaved values
  
• Do proxy hints matter? Is LB0, UBINF really
  the best way to start?

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Team 3
Team 3
Updating Strategy
May or may not use the hints from the proxy
Proxy