Academic journal article Atlantic Economic Journal

A Model of Optimal Advertising Expenditures in a Dynamic Duopoly

Academic journal article Atlantic Economic Journal

A Model of Optimal Advertising Expenditures in a Dynamic Duopoly

Article excerpt

PETR MARIEL [*]

This paper develops a dynamic model of oligopolistic advertising competition. The model is general enough to include predatory advertising and informative advertising as particular cases. The analysis is conducted in a differential game framework and compares the open-loop and feedback equilibria to the efficient outcome. It is found that for the informative advertising competition game, advertising levels are closer to the collusive outcomes in a feedback equilibrium. In the case of predatory advertising, expenditures are inefficiently high in a feedback equilibrium and the open-loop solution is more efficient. (JEL L13, M37)

Introduction

In this paper, a dynamic model of oligopolistic advertising competition is developed. Compared to previous literature, an important feature of this work is that the competitive and informative contents of advertising are explicitly considered, allowing advertising to have market size and business-stealing effects. When advertising effort is directed toward consumers who have not bought the product before, it has the effect of increasing total market size (providing information about the very existence of the product, its price, and general characteristics). However, when advertising is directed at a rival's clientele, it has a business-stealing effect. It increases the advertiser's market share only at the expense of competitors. In fact, the results obtained depend on the relative strength of these two factors. In their empirical analysis of the cigarette industry, Roberts and Samuelson [1988] find that advertising has a strong cooperative content. [1] In other industries, however, the business-stealing eff ect could be the relevant aspect. Slade [1995] finds that for saltine crackers, advertising is mildly predatory. For the soft drink industry, Gasmi et al. [1992] estimate a low advertising effect on market size and a strong predatory effect on market shares.

To study the problem of optimal advertising expenditure in a dynamic duopoly, a differential game framework is used and the open-loop and feedback equilibria are analyzed, the results being compared to the efficient outcome. Previous works have compared the open-loop and feedback outcomes. Fershtman and Kamien [1987] analyze a differential game of price competition assuming that price does not adjust instantaneously to its market clearing level. As the speed of price adjustment becomes instantaneous, with feedback strategies, the outcome is more competitive than in the openloop equilibrium, which approaches the Coumot equilibrium price. [2] In an advertising competition game, Sorger [1989] also finds that using feedback strategies instead of open-loop controls does not necessarily increase payoffs (see also Reynolds [1987]).

Even though the outcomes of feedback equilibria are usually less efficient than those of open-loop equilibria, the opposite result is obtained in this paper for an informative advertising competition game: advertising levels are closer to collusive outcomes in a feedback equilibrium. The intuition behind this result is that with feedback strategies, firms may take into account the stock of goodwill when deciding on their current level of advertising. Since current profits depend on past advertising by both firms, a strategy that positively depends on those stocks works as a promise to increase advertising expenses in the future, provided the opposing firm increases advertising in the current period. These strategies sustain higher advertising than the open-loop equilibrium, although the outcome does not always coincide with the joint profit maximization solution. In this present model, discontinuous strategies are ruled out so that trigger strategies, which could easily sustain collusion in a repeated game, are excluded.

For markets where advertising is mainly predatory, the results are reversed. In any Nash equilibrium, expenditures are inefficiently high and more so in a feedback strategy equilibrium. …

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