Discrete time dynamic game models for advertising competition in a duopoly

Advertising competition in a duopoly is modelled as a discrete time dynamic game over an infinite time horizon. Firms maximize the present value of their profits which depend on their own advertising strategy and on their market share. The evolution of market shares is determined by both firms’ advertising activities. In this simple framework, this paper computes a Nash equilibrium and analyses the dynamic properties of the equilibrium strategies and the resulting time path of the market share. It turns out that, depending on the revenue functions and the market response function, various dyanmic patterns may emerge among which one can find convergence towards a unique steady state, convergence towards one of multiple steady states, and regular or irregular pulsing strategies.