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...

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...

In a multi-commodity framework with absence of wealth effects, we prove the existence of equilibrium for Cournot oligopoly, and that the concept is completely non-ambiguous. We also obtain a uniquely defined endogenous inverse demand function, depending only on the competitive sector.