Non-Negative Quantity Constraints and the Duration of Punishment

In an oligopoly supergame, firms face an obvious technological constraint: the positivity of their production quantities. WE show that Lambson's (1987) result on "security-level punishment", that the single-period punishment makes the firm's discounted participation condition just bind, holds only in a Bertrand supergame with perfect substitutes. In general, the sustainability of collusion by means of single-period penal codes hinges critically upon the degree of supermodularity in the stage game, as well as upon the positivity constraints on prices and/or quantities.