Sotheby’s has acquired a new Rothko painting and it has decided to auction it. There are...

Sotheby’s has acquired a new Rothko painting and it has decided to auction it. There are two anonymous art-lover bidders of the painting, we will refer to them as Bidder A and Bidder B to protect their anonymity. In this auction format, Bidder A and Bidder B simultaneously submit a written bid for the Rothko painting. However, the auction has a weird twist. Sotheby’s requires that Bidder A must submit an odd number (in millions of US dollars) between 1 and 9 (that is, the bid must be 1, 3, 5, 7, or 9) and Bidder B’s bid must be an even number between 2 and 10 (that is, the bid must be 2, 4, 6, 8 or 10). The bidder who submits the highest bid wins the Rothko and pays a price equal to her bid. The winning bidder’s payoff equals his valuation of the item less the price she pays, whereas the losing bidder’s payoff is 0. Assume that Bidder A has a valuation of 7 (million US dollars) and that Bidder B has a valuation of 8 (million US dollars).

a) (10 points) Write down the strategic form of this game.

b) (10 points) Find all of the Nash equilibria of the game you wrote in part a.

Show every step of your calculations

Expert Solution

Rahul Sunny answered 9 months ago

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