Advertising, Pricing and Stability in Oligopolistic Markets for New Products

In an oligopolistic market for a new product, individual competing firms may possess a differential advantage in terms of the initial goodwill. From a business policy perspective, the question is whether the competitive market equilibrium is affected by the initial goodwill of each firm. That is, do the final market shares depend on the initial stocks of goodwill of competing firms? For a consumer nondurable or a highly depreciable durable product in an oligopolistic market, we formulate this problem as a non-zero-sum, open loop, noncooperative differential game. It is assumed that the goodwills of the competing firms adjust according to the Nerlove-Arrow capital accumulation equation, i.e., is its advertis~ng level and oi is · its goodwill decay constant. A solution to such a game (a Nash Equilibrium) is a choice of price and advertising by the competing firms such that each maximizes his own discounted profits subject to his own goodwill accumulation and given the path of the rival. We prove existence of a Nash Equilibrium _and we shoYT the conditions under which the game converges to a particular stationary point regardless of the initial conditions. That is, we show the conditions under which the final market shares do not depend on the initial stocks of goodwill of competing firms.

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