A painting by famous painter Renoir is on sale in a first price auction . Bidders are A and B. The minimum bid is $ 1 billion , and bids must be made in minimum $ 100 million increments . If both bidders bid the same amount , the winning bidder is determined by drawing lots ( winning probability is 50 percent ) . Bidder A assesses the value of the painting at $ 1.4 billion , and bidder B assesses it as $ 1.2 billion . Create a pay - off matrix in the range of $ 1 billion to $ 1.4 billion and resolve the game .

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A painting by famous painter Renoir is on sale in a first price auction . Bidders are A and B. The minimum bid is $ 1 billion , and bids must be made in minimum $ 100 million increments . If both bidders bid the same amount , the winning bidder is determined by drawing lots ( winning probability is 50 percent ) . Bidder A assesses the value of the painting at $ 1.4 billion , and bidder B assesses it as $ 1.2 billion . Create a pay - off matrix in the range of $ 1 billion to $ 1.4 billion and resolve the game .

Expert Solution
Step 1

We are given the following bid values for A and B

Bid value of A = $1.4 billion        

Bid value of B = $1.2 billion


Here, we are assuming that aim of the bidders is to get the painting at the minimum possible cost. The incentive is to bid at each step since the probability of winning the bid would be 1/2.

Step 2

The pay-off matrix is given down below in the form of a 5X5 Table.

The values are given as $ Billion.

Statistics homework question answer, step 2, image 1

 

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