For Bertrand duopoly with linear costs, we establish via a single counterexample 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, and (ii) Topkis's notion of...

We consider the issue of endogenous timing, according to the extended game of Hamilton-Sluytsky (1990), for the classical Coumot and Bertrand duopolies. We provide minimal sufficient conditions, directly on the primitives of each model (i.e. the demand and cost functions), yielding the...