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January  2005, 1(1): 1-19. doi: 10.3934/jimo.2005.1.1

Advertising competition with market expansion for finite horizon firms

F. M. Bass 1, , A. Krishnamoorthy 2, , A. Prasad 1, and  Suresh P. Sethi 3,

1. 

School of Management, University of Texas at Dallas, Richardson, TX 75083-0688, United States, United States
2. 

College of Business Administration, University of Central Florida, Orlando, FL 32816-1400, United States
3. 

School of Management, The University of Texas at Dallas, Richardson, TX, 75083-0688, United States

Received  May 2004 Revised  December 2004 Published  January 2005

Firms that want to increase the sales of their brands through advertising have the choice of capturing market share from their competitors through brand advertising, or increasing primary demand for the category through generic advertising. In this paper, differential game theory is used to analyze the effects of the two types of advertising decisions made by firms offering a product in a dynamic duopoly. Each firm's sales depend not only on its own and its competitor's brand advertising strategies, but also on the generic advertising expenditures of the two firms. Closed-loop Nash equilibrium solutions are obtained for symmetric and asymmetric competitors in a finite-horizon setting. The analysis for the symmetric case results in explicit solutions, and numerical techniques are employed to solve the problem for asymmetric firms.
Keywords: Optimal control, Marketing, Advertising, Dynamic duopoly., Differential games.
Mathematics Subject Classification: 90B60, 49N70, 49N90, 49J20, 91A2.
Citation: F. M. Bass, A. Krishnamoorthy, A. Prasad, Suresh P. Sethi. Advertising competition with market expansion for finite horizon firms. Journal of Industrial & Management Optimization, 2005, 1 (1) : 1-19. doi: 10.3934/jimo.2005.1.1
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