Consider the following situation. Engineers working for the government of Mexico have recently discovered an offshore...

 

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Consider the following situation. Engineers working for the government of Mexico have recently discovered an offshore area potentially rich in oil and gas. To raise revenue, the Mexican government decides to auction off drilling rights to private companies. The auction is structured as a first price sealed bid auction. First price means the highest bidder will win the auction. Sealed bid means the bidders submit bids simultaneously and secretly - no bidder knows what its rivals have bid until the auction is over and the winner is declared. Three companies formally enroll in the auction and prepare to submit their bids: Exxon, Shell, and Pemex. a) You are hired as a consultant for Exxon to help them prepare their bid. Due to the sealed bid structure, the bids of Shell and Pemex can be thought of as continuous random variables. They are denoted B shell and B Pemex respectively. Using the notation of a joint cdf, write down a simple formula for the probability Exxon will win the auction if it submits a bid of 80 million dollars. b) Suppose your strategic analysis of Shell and Pemex leads you to believe that their bids will be independent in a probabilistic sense. Furthermore you believe that FB Shell (70m) = 0.4 and FB Pemex (70m) = 0.6. Given this information, what is the probability Exxon will win the auction if it submits a bid of 70 million dollars? Activate Windows Consider the following situation. Engineers working for the government of Mexico have recently discovered an offshore area potentially rich in oil and gas. To raise revenue, the Mexican government decides to auction off drilling rights to private companies. The auction is structured as a first price sealed bid auction. First price means the highest bidder will win the auction. Sealed bid means the bidders submit bids simultaneously and secretly - no bidder knows what its rivals have bid until the auction is over and the winner is declared. Three companies formally enroll in the auction and prepare to submit their bids: Exxon, Shell, and Pemex. a) You are hired as a consultant for Exxon to help them prepare their bid. Due to the sealed bid structure, the bids of Shell and Pemex can be thought of as continuous random variables. They are denoted B shell and B Pemex respectively. Using the notation of a joint cdf, write down a simple formula for the probability Exxon will win the auction if it submits a bid of 80 million dollars. b) Suppose your strategic analysis of Shell and Pemex leads you to believe that their bids will be independent in a probabilistic sense. Furthermore you believe that FB Shell (70m) = 0.4 and FB Pemex (70m) = 0.6. Given this information, what is the probability Exxon will win the auction if it submits a bid of 70 million dollars? Activate Windows

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