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)...

This note relates to Topkis (1995). We establish via counterexample that:(i) A new monotone transformation of the firms' profit functions may lead to cardinal complementarity when the standard log and identity transformations both fail, and (ii) Topkis's notion of critical sufficient condition...