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Exchange Day – Group C

Exchange Day – Group C. CS286r Harvard University 27 April 2004. 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

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Exchange Day – Group C

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  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!

  3. 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(1+2/m)-G(1+1/m)]-1/2 • G(w)=Integral(0,INF) [v(w-1)ev]dv

  4. Therefore… • P*=m(n-1)n1/m/[m(n-1)-1] • n=number 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

  5. 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

  6. 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

  7. 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?

  8. 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

  9. Team 2 – Constructing ICTree • Silas, Jonathan, and Wilfred • Group D passes C an agent’s true value • But does an agent really want to pass that tree directly along to the proxy? • Bases decision on Team 1’s 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

  10. Team 1 Belief of Final Team 2 Team 2 ICTree May have shaved values or new items Team 3

  11. 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 2’s shaved values • Do proxy “hints” matter? Is LB=0, UB=INF really the best way to start?

  12. Team 2 ICTree Team 3 Team 3 Updating Strategy May or may not use the hints from the proxy Proxy

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