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7. Private value auction (optimal bidding strategy) You and another bidder are the only two bidders at a private value auction. Both of you are assigned a value that is randomly drawn from a uniform distribution. This private value for the prize is equally likely to be any penny amount between $5.00 and $20.00. After finding out your own private values, each of you would select a bid. You know that the other person will bid the exact amount of his/her private value. If the other person's bid turns out to be lower than your own bid, then you would earn the difference between your private value and your bid. If the other's bid were higher, then you would earn nothing. Suppose both of you are risk neutral, derive your optimal bidding strategy. (16 points) 7. Private value auction (optimal bidding strategy) You and another bidder are the only two bidders at a private value auction. Both of you are assigned a value that is randomly drawn from a uniform distribution. This private value for the prize is equally likely to be any penny amount between $5.00 and $20.00. After finding out your own private values, each of you would select a bid. You know that the other person will bid the exact amount of his/her private value. If the other person's bid turns out to be lower than your own bid, then you would earn the difference between your private value and your bid. If the other's bid were higher, then you would earn nothing. Suppose both of you are risk neutral, derive your optimal bidding strategy. (16 points)