MODEL OF GOCO COMPETITION WITH UNCERTAINTY
This appendix provides the underlying mathematical calculations for the model of GOCO competition with uncertainty discussed in Chapter Five. When the operator of Iowa AAP does not know the exact costs of its competitors, it must calculate a bid that trades off higher profits when it wins the production contract against an increased probability that it loses the contract because one of its competitors enters a lower bid. Thus, it calculates a bid that maximizes expected profits. Suppose the operator of Iowa AAP knows that it can LAP 100,000 artillery shells at a cost of $100 per shell, but it thinks its competitors' costs are uniformly distributed between $110 and $130 per shell.
Let b stand for Iowa AAP's bid in the production contract competition and E[[.pi]] stand for its expected profits. When there is one other competitor, Iowa AAP wins the contract with the probability that its bid is less than its competitor's costs, or 1 – (b – 110)/(130 – 110), which can be rewritten as (130 – b)/20. Therefore, Iowa AAP chooses b to maximize
The first-order condition for the profit-maximizing bid iswhich has a solution of b = 115. If Iowa AAP bids $115 per shell, it wins the production contract with probability (130 – 115)/20 =. 75. Thus, expected