Abstract: A new analysis method in game theory, supermodular game, is used in Bertrand model, for differentiated-product Bertrand oligopoly with general cost functions, when the strategy variable is price ato ne, the sufficient conditions are comparedfor supermodular and log-supermodular game.Although a logsupermodular game is a quasi-supermodular one, which is more general than a supermodular one, the corresponding sufficient conditions placed on the firms' profit functions are shown not to be comparable, that is one cant get one from another.When the game is neither a log-supermodular nor a supermodular one, a new monotone transformations of the firms' profit functions may make the game a supermodular one.For the special case of constant marginal production cost, counterexamples are provided.When the strategy variables are pricing and advertising effort, under usual assumptions and constant marginal production cost, the game is a supermodular one and this explains why higher prices are always associated with higher advertising levels.

Key words: Bertrand oligopoly, supermodular game, log-supermodular game, largest Nash equilibrium, smallest Nash equilibrium