(a) In a second-price auction, the dominant strategy for each bidder is to bid their true valuation. This is because the highest bidder wins, but the price paid is the second highest bid. Therefore, the equilibrium strategy is for each bidder to bid their true valuation.

(b) In a second-price auction, the expected payment of a bidder with value v in [4,10] is the expected value of the second highest order statistic of two other bidders' valuations. Since each bidder's valuation is uniformly distributed in [4,10], the expected payment E[P] can be calculated as follows:

E[P] = ∫ from 4 to v (2*(v-x)/(10-4)^2) dx = v - (v-4)^2 / (2*(10-4))

(c) In a first-price auction, each bidder bids their valuation minus their expected payment if they win. Using the revenue equivalence theorem, which states that the expected payment of a bidder is the same in all auction formats, the equilibrium bidding strategy in a first-price auction is to bid:

b(v) = v - E[P] = v - (v - (v-4)^2 / (2*(10-4))) = (v-4)^2 / (2*(10-4))

Question

(a) In a second-price auction, the dominant strategy for each bidder is to bid their true valuation. This is because the highest bidder wins, but the price paid is the second highest bid. Therefore, the equilibrium strategy is for each bidder to bid their true valuation.

(b) In a second-price auction, the expected payment of a bidder with value v in [4,10] is the expected value of the second highest order statistic of two other bidders' valuations. Since each bidder's valuation is uniformly distributed in [4,10], the expected payment E[P] can be calculated as follows:

E[P] = ∫ from 4 to v (2*(v-x)/(10-4)^2) dx = v - (v-4)^2 / (2*(10-4))

(c) In a first-price auction, each bidder bids their valuation minus their expected payment if they win. Using the revenue equivalence theorem, which states that the expected payment of a bidder is the same in all auction formats, the equilibrium bidding strategy in a first-price auction is to bid:

b(v) = v - E[P] = v - (v - (v-4)^2 / (2*(10-4))) = (v-4)^2 / (2*(10-4))

Knowee AI · Accepted Answer

(a) In a second-price auction, the dominant strategy for each bidder is to bid their true valuation. This is because the highest bidder wins, but the price paid is the second highest bid. Therefore, the equilibrium strategy is for each bidder to bid their true valuation.

(b) In a second-price auction, the expected payment of a bidder with value v in [4,10] is the expected value of the second highest order statistic of two other bidders' valuations. Since each bidder's valuation is uniformly distributed in [4,10], the expected payment E[P] can be calculated as follows:

E[P] = ∫ from 4 to v (2*(v-x)/(10-4)^2) dx = v - (v-4)^2 / (2*(10-4))

(c) In a first-price auction, each bidder bids their valuation minus their expected payment if they win. Using the revenue equivalence theorem, which states that the expected payment of a bidder is the same in all auction formats, the equilibrium bidding strategy in a first-price auction is to bid:

b(v) = v - E[P] = v - (v - (v-4)^2 / (2*(10-4))) = (v-4)^2 / (2*(10-4))

Question

Solution

Similar Questions

Upgrade your grade with Knowee