Non‐Negative Quantity Constraints and the Duration of Punishment

Luca Lambertini () and Dan Sasaki

The Japanese Economic Review, 2002, vol. 53, issue 1, 77-93

Abstract: In an oligopoly supergame, firms face an obvious technological constraint: the positivity of their production quantities. Applicability of single‐period optimal punishment hinges critically upon the degree of supermodularity in the stage game, as well as upon the positivity constraints on prices and/or quantities. If both prices and quantities are constrained to be positive, then the relevant multi‐period punishment prescribes securitylevel payoffs (where individual rationality binds) when and only when the game is perfectly supermodular, i.e. is either a Bertrand supergame with perfect substitute products or a Cournot supergame with perfect complement products. JEL classification numbers: D43, L13, C72.

Date: 2002
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Working Paper: Non-Negative Quantity Constraints and the Duration of Punishment (1998)
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