Optimal bidding strategies

Your company is bidding for a service contract in a first-price, sealed-bid auction. You value the contract at $12 million. You believe the distribution of bids will be uniform, with a high value of $16 million and a low value of $3 million. What is your optimal bidding strategy with

a. 5 bidders?
b. 10 bidders?
c. 20 bidders?

Suppose the typical Florida resident has a wealth of $500,000, of which his home is worth $100,000. Unfortunately, he lives in hurricane alley, and it is believed there is a house (i.e., a loss of $100,000). However, it is possible to retrofit the house with various protective devices (shutters, roof bolts, etc.) for a cost of $2,000. This will reduce the size of loss from a 10 percent chance of loss of $100,000 to a 5 percent chance of a loss of $50,000. The homeowner must decide whether to retrofit and thereby reduce the expected loss. The problem for the insurance company is that it does not know whether the retrofit will be chosen and therefore cannot quote a premium, which is conditional on the policyholder choosing this action. Nevertheless, the insurance company offers the following two policies from which the homeowner can choose: (1) The premium for insurance covering total loss is $12,000; 0r (2) The premium for insurance covering only 50 percent of loss is $1,500. The typical homeowner has a utility function equal to the square root of wealth. Will the homeowner retrofit and which insurance policy will the homeowner buy? Will the insurance company make a profit (on average) given the homeowners choice?