Consider three bidders who have private values that are independently and uniformly distributed between 0 and 100. Suppose that these values happen to be v1 = 30, v2 = 90, and v3 = 10. Then the equilibrium price in the second-price auction is:

Question

BlackTom AI · Accepted Answer

In a second-price auction, also known as a Vickrey auction, each bidder submits a sealed bid without knowing the bids of the other participants. The highest bidder wins, but the price paid is the second-highest bid. This auction format encourages truthful bidding as a dominant strategy because the winner pays the second-highest bid, not their own, eliminating the incentive to bid below their true value.

Given the private values v1 = 30, v2 = 90, and v3 = 10, the bidders will submit bids equal to these values if they follow the dominant strategy of bidding truthfully. Thus, the bids will be b1 = 30, b2 = 90, and b3 = 10.

The highest bid is b2 = 90, so bidder 2 wins the auction. However, the price paid is the second-highest bid, which is b1 = 30. Therefore, the equilibrium price is 30.

Comparatively, the other options fail because:
- '20' is not a bid submitted by any of the bidders; thus, it cannot be the second-highest bid.
- '60' is also not a bid submitted by any of the bidders and is irrelevant to the given values.
- '90' is the highest bid, not the second-highest, and thus cannot be the equilibrium price in a second-price auction.

Therefore, the correct answer is '30', as it is the second-highest bid among the truthful bids submitted by the participants.

Consider three bidders who have private values that are independently and uniformly distributed between 0 and 100. Suppose that these values happen to be v1 = 30, v2 = 90, and v3 = 10. Then the equilibrium price in the second-price auction is:单项选择题

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