You should determine a bid for Maxco and a bidding schedule for Gambit. Please submit these in an email to me (firstname.lastname@example.org) by Friday March 18, 2011. (You can fill out the last page of the case and email me the pdf version of the page, e.g.)
Here is how the case will be graded. Your Maxco strategy will be played against the Gambit strategy submitted by every other member of the class. Likewise, your Gambit strategy will be played against the Maxco strategy from each of your classmates. In each of these encounters, you earn an expected profit. Your Maxco profit is the total profit earned by your Maxco strategy, and your Gambit profit is the total profit earned by your Gambit strategy. Your Maxco profit is then compared with other Maxco profits in the class. Likewise, your Gambit profit will be compared with other Gambit profits in the class. The following formulas spell out your scores for this case:
Here is what happens when a Maxco strategy is played against a Gambit strategy. Recall that a Maxco strategy consists of a single number, whereas a Gambit strategy consists of 13 numbers, one for each of the 13 scenarios given in the case. (Assume that the true value of the oil reserve is equal to one of the 13 values given in the case, according to the given probabilities. Ignore the plus/minus ranges.) For each of the 13 scenarios, we compare the Maxco bid with the Gambit bid under the scenario, determine the winner (i.e., the higher bidder), and calculate the profit for each player (i.e., the winner’s profit is equal to the value of the oil reserve minus the winning bid, and the loser’s profit is zero). The expected profit earned by the Maxco strategy is equal to the probability weighted sum of the profits for Maxco under the 13 scenarios. Likewise, the expected profit earned by the Gambit strategy is the probability weighted sum of the profits for Gambit under the 13 scenarios.