Strategic equivalence of the dutch and first price

Info icon This preview shows pages 5–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Strategic equivalence of the dutch and first-price auctions Strategic equivalence b/t Dutch and first-price auctions; -first-price auction, bids are submitted to the auctioneer -Winner=player with highest bid B -Price=highest bid among all B Dutch auction, bid B represents prie when player i is willing to stop the auction if it has not been stopped before, so the bids are not submitted, but still need to be chosen by all players -winner=player w/highest bid B -price=highest bid among all B Conclusion: dutch and first-price auctions are represented by the same game -equilibria in the 2 auctions must be the same, avg revenues must be the same Dominant strategies in the english auction w/private values -all reservation values private; no dependence on values or signals of others -each bidder has a dominant strategy = to quit when price equals to Vi -if he quits earlier, he loses the chance to get Vi-p>0
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
-if he waits longer, he risks to get Vi-P<0 Strategy is dominant bc it’s always best choice for agent i regardless of what other bidders choose to do Dominant strategies in the second-price auction w/private values -bidders w/private values have a dominant strategy in the second-price auction, too -strategy is to bid the true private value Bi = Vi Dominant strategy equilibria -if values are private, English and second-price auctions both have equilibria in dominant strategies -equilibria in 2 auctions deliver the same outcome: -winner=bidder with the highest value Vi -price = second highest value among all Vi The two auctions always produce the same revenues! Second price vs english -English auction produces behavior very close to theoretical predictions -most subjects quit when current price exceeds their reservation value -auction rules motivate rational decisions and requires little learning -Second-price auction produces some overbidding relative to the dominant strategy(avg, ppl bid about 10% above their private values) -dominant strategy is not obvious, learning is slow bc overpayments are relatively rare and small (within 10%) -behavioral explanation: there may be some extra utility derived from winning the auction -rules matter even when game theory predicts the same outcomes Equilibria in the dutch and first-price auctions 2 observations: -no dominant strategies (Vi=100, best bid depends on bid of other players. If M<100, best choice for player i is to bid M plus a small increment) -Strategic Equivalence: 2 auctions have same set of strategies, same payoffs. Expect 2 auctions to produce same outcomes Auctions with private values -in Dutch and first-price auctions, there exists NO dominant strategies, yet NE can be found -each NE strategy is best choice against the equlibria strategies of other agents -unlike dominant strategy, NE strategy need not be best choice against all strategies that opponents can possibly use Lecture 21 -To find NE in the dutch and first-price auctions, one needs to assume probability distributions of reservation values -simplest assumption is: private value Vi of agent i has an independent and uniform distr.
Image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern