Midterm Study guide econ 115.pdf

# Strategic equivalence of the dutch and first price

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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

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-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.
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• Spring '07
• wrigley
• Game Theory, Auction, Nash, Dominant strategy, auctions

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