DISCRETE-TIME DYNAMIC GAME MODELS FOR ADVERTISING COMPETITION IN A DUOPOLY

Advertising competition in a duopoly is modelled as a discrete time dy namic game over an infinite time horizon. Firms maximize the present v alue of their profits which depend on their own advertising strategy a nd on their market share. The evolution of market shares is determined by both firms' advertising activities. In this simple framework we co mpute a Nash equilibrium and analyse the dynamic properties of the equ ilibrium strategies and the resulting time path of the market share. I t turns out that, depending on the revenue functions and the market re sponse function, various dynamic patterns may emerge among which one c an find convergence towards a unique steady state, convergence towards one of multiple steady states, and regular or irregular pulsing strat egies.