Final exam econ 115 practice.pdf

# Dominant strategies in the english auction wprivate

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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 -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 -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. b/t 0 and V* -probability {Vi<xV*} = x where 0<=x<=1

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-each bidder knows private value Vi, and probabilistic distribution of other values. However, she does not know the other values precisely -This assumption is easily satisfied in experiments, but not in real auctions Nash Equilibrium: bidding strategies -assumption: all agents are risk neutral Bayesian Nash Equilibrium: Bi=(N-1)Vi/N For example, if N=2, then Bi=Vi/2 If n=6 as in moblab experiment, Bi=5Vi/6 Bayesian means that there is uncertainty about other agents types NE: proof is not required at the tests First Price vs Dutch
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