Friedman's bidding model: Errors and corrections

Friedman's classic 1956 bidding model for the case in which a contractor is bidding against an unknown number of opponents applies Friedman's multiplicative model for the probability to win, which applies only when bidding against at least one opponent, to the case in which the number of opponents is zero, to which it does not apply. Thus, both the resulting general equations and the examples for the probability to win, as well as those for expected profit, are incorrect. Moreover, the example graphs offered are not true representations of these incorrect equations. The causes and consequences of these errors are described in detail and new equations are offered as replacements. Exact graphs of the incorrect equations as well as of their replacements are presented. Four new bidding models are developed by which a contractor can find the optimum bid price that maximizes expected profit when the number of opponents is unknown and could be zero. These include the case of an owner with a reserve price that leads to a distinct and novel bidding strategy.