Consider a private value auction with 2 bidders. The auction is carried out as a second...

Consider a private value auction with 2 bidders. The auction is carried out as a second price sealed bid auction where in case of a tie between the bidders, the winner is selected by a coin toss. The seller has valuation of the good of zero and will accept any bid at or greater than zero. Each bidder knows his/her own valuation, v, and does not know the valuation of the other bidder. It is common knowledge that the bidder valuations are drawn from the following distribution: The valuation is a realization from the following set of values {0.25, 0.5, 0.75}. Each realization is equally likely.

State a dominant strategy equilibrium of the auction by starting the bidding strategies of each bidder as a function of the bidder’s valuation.
What is the expected revenue of the seller? (For this work out the 9 different possible value realization combinations for the bidders. Each one has probability 1/9 of being realized. Work out the revenue to the seller in each case and take the average. Possible value realization combinations are (v1, v2) = (0.25, 0.25), (v1, v2) = (0.25, 0.5), and so on...).

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Rahul Sunny answered 1 year ago

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