On strategic complementarity conditions in Bertrand oligopoly

Summary. For Bertrand duopoly with linear costs, we establish via a single (counter-)example that: (i) A new monotone transformation of the firms' profit functions may lead to the supermodularity of transformed profits when the standard log and identity transformations both fail to do so, and (ii) Topkis's notion of critical sufficient condition for monotonicity of a Bertrand firm's best-reply correspondence cannot be extended to rely only on positive unit costs. Received: January 16, 2001; revised version: March 20, 2002 RID="*" ID="*" This work was completed while the first author was visiting the Institute for Industrial Economics at the University of Copenhagen during Spring 2000. Their financial support and stimulating research environment are gratefully acknowledged. The views expressed here are those of the authors and should not be attributed to the European Commission. Correspondence to: R. Amir