Using a market share attraction structure of advertising competition and following a supermodular game approach, this article demonstrates for an asymmetric oligopoly, the directional impact of changes in model parameters on the marketing controlled variables of all rivals (advertising budgets) and the operations controlled variables of all rivals (ordered quantities). Importantly, the various changes are examined analytically, empirically and numerically in both non-dominated and dominated asymmetric oligopolies. In this regard, the results indicate that firms in a dominated oligopoly (one firm of market share larger than or equal to 50%) behave differently compared to firms in a non-dominated oligopoly (each firm of market share less than 50%) in response to changes in model parameters. Furthermore, changes in model parameters are investigated in terms of their relative influential impact on a variety of equilibrium measures. In this regard, the findings indicate that for the analyzed model the marketing parameters exert much more influence on the equilibrium measures than the operations parameters. Additionally, a change in the mode of competition from non-cooperation (oligopoly) to cooperation (joint ownership) dictates that strong asymmetric firms (of favorable marketing and operations parameters) continue advertising (but at lower levels) and weak asymmetric firms (of less favorable parameters) cease advertising altogether. 
On modeling the advertising-operations interface under asymmetric competition