Long-run strategic advertising and short-run Bertrand competition

We model and analyze strategic interaction over time in a duopoly. Each period the firms independently and simultaneously take two sequential decisions. First, they decide whether or not to advertise, then they set prices for goods which are imperfect substitutes. Not only the own, but also the other firm's past advertisement e¤orts a¤ect the current "sales potential" of each firm. How much of this potential materializes as immediate sales, depends on current advertisement decisions. If both firms advertise, "sales potential" turns into demand, otherwise part of it "evaporates" and does not materialize. We determine feasible rewards and (subgame perfect) equilibria for the limiting average reward criterion. Uniqueness of equilibrium is by no means guaranteed, but Pareto efficiency may serve very well as a refinement criterion for wide ranges of the advertisement costs.