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

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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(  ) = 1 – exp(-  m ),  > 0 m = shape parameter  = scale parameter u = standard deviation of  i u= [  (1+2/m)-  (1+1/m)] -1/2  (w)=Integral(0,INF) [v (w-1) e v ]dv

4 Therefore … P * =m(n-1)n 1/m /[m(n-1)-1] n=number of competing For example, u = 0.12, n = 3  P * = u = 0.12, n = 5  P * = 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 Big Button From D ItemWho$ (Confidence) A110 (75%) B15 (50%) C210 (0%) D43 (100%) Team 2 Team 1 MIPs Sensitivity Analysis May be 2 versions: With and w/out us World

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

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

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