Question
Answer the following about designing strategyproof games, in which players are incentivized to be truthful about their preferences. For 10 points each:
[10e] No strategyproof rule exists for performing this process non-dictatorially among more than two alternatives, the Gibbard-Satterthwaite theorem. Limitations on systems for this process are described by Arrow’s impossibility theorem.
ANSWER: voting
[10m] Description acceptable. In order to strategyproof a sealed-bid auction, in which contestants do not know each others’ bids, the winner pays this price for the item won, rather than the amount they bid themselves.
ANSWER: second highest bid [accept second price auction; accept answers indicating the second highest bid plus some small amount]
[10h] The generalized second-price auction is not strategyproof when there are multiple items for sale, so companies like Facebook opt for these other auctions to sell ad space. In these auctions, bidders pay their externalities.
ANSWER: VCG auction [or VCG mechanism or Vickrey-Clarke-Groves auction]
<VD, Social Science>
Summary
| 2023 ARCADIA at UC Berkeley | Premiere | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at Carleton University | Premiere | Y | 3 | 13.33 | 67% | 67% | 0% |
| 2023 ARCADIA at Claremont Colleges | Premiere | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at Indiana | Premiere | Y | 5 | 18.00 | 100% | 80% | 0% |
| 2023 ARCADIA at RIT | Premiere | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at WUSTL | Premiere | Y | 3 | 16.67 | 100% | 67% | 0% |
| 2023 ARCADIA at Duke | Emory, Duke, Yale | N | 4 | 12.50 | 75% | 50% | 0% |
| 2023 ARCADIA at Emory | Emory, Duke, Yale | N | 4 | 12.50 | 75% | 50% | 0% |
| 2023 ARCADIA at Imperial | Imperial | N | 5 | 16.00 | 100% | 60% | 0% |
| 2023 ARCADIA at Maryland | Maryland, Online | N | 3 | 10.00 | 67% | 33% | 0% |
| 2023 ARCADIA at Ohio State | Ohio State, Texas | N | 3 | 13.33 | 67% | 67% | 0% |
| 2023 ARCADIA Online | Maryland, Online | N | 3 | 20.00 | 100% | 100% | 0% |
| 2023 ARCADIA at Texas | Ohio State, Texas | N | 3 | 13.33 | 100% | 33% | 0% |
Data
| Berkeley B | Berkeley C | 10 | 10 | 0 | 20 |
| Stanford A | Berkeley A | 10 | 10 | 0 | 20 |
| Ottawa B | McDouble West-Carleton | 0 | 10 | 0 | 10 |
| Toronto | Ottawa A | 10 | 0 | 0 | 10 |
| Waterloo | Ottawa C | 10 | 10 | 0 | 20 |
| Auxiliary Lofthouse Cookie University | I will play anything with a buzzer in front of me | 10 | 10 | 0 | 20 |
| Chicago A | Vanderbilt | 10 | 10 | 0 | 20 |
| Indiana | Chicago B | 10 | 10 | 0 | 20 |
| Illinois A | Illinois B | 10 | 10 | 0 | 20 |
| Purdue A | Notre Dame B | 10 | 0 | 0 | 10 |
| Notre Dame A | Purdue B | 10 | 10 | 0 | 20 |
| Cornell MATLAB | Cornell R | 10 | 10 | 0 | 20 |
| Syracuse+Rochester | RIT | 10 | 10 | 0 | 20 |
| Squidward Community College | Missouri B | 10 | 10 | 0 | 20 |
| Missouri A | WUSTL H2O | 10 | 10 | 0 | 20 |
| WUSTL XYZ | SIUE | 10 | 0 | 0 | 10 |