Optimal constrained bidding (Q1087118)

Consider a bidder who, subject only to a constraint on his choice of bidding strategy, will choose a strategy that maximizes his expected gross receipts. The bidder's choice of strategy may be constrained by an upper limit on exposure, an upper limit on expected expenditures, or a lower limit on expected profits. We prove that constraining the bidder only by an appropriate upper limit on expected expenditures in effect limits him to expected profit maximizing strategies; in many examples, expected profit maximizing strategies cannot be induced by solely limiting the bidder's exposure.