Feedback competitive advertising strategies with a general objective function

G. Fruchter; G. M. Erickson; S. Kalish

doi:10.1023/a:1017567805831

Feedback competitive advertising strategies with a general objective function

G. Fruchter, G. M. Erickson, S. Kalish

School of Business Administration

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max-min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.

Original language	English
Pages (from-to)	601-613
Number of pages	13
Journal	Journal of Optimization Theory and Applications
Volume	109
Issue number	3
DOIs	https://doi.org/10.1023/a:1017567805831
State	Published - Jun 2001

Bibliographical note

Funding Information:
1This research was supported by the Technion V.P.R. Fund and by the N. Haar and R. Zinn Research Fund. 2We would like to thank Professors Arkadi Nemirovski and Leonid Gurvits for very valuable and constructive suggestions and to Professor Shlomo Maital for Ref. 24. 3Senior Lecturer, School of Business Administration, Bar-Ilan University, Ramal-Gar 52900, Israel; currently with Hong Kong University of Science and Technology. 4Professor, Marketing and International Business, School of Business, University of Washington, Seattle, Washington. 5Senior Lecturer, Leon Recanati Graduate School of Business Management, Tel Aviv University, Tel Aviv, Israel.

Funding

1This research was supported by the Technion V.P.R. Fund and by the N. Haar and R. Zinn Research Fund. 2We would like to thank Professors Arkadi Nemirovski and Leonid Gurvits for very valuable and constructive suggestions and to Professor Shlomo Maital for Ref. 24. 3Senior Lecturer, School of Business Administration, Bar-Ilan University, Ramal-Gar 52900, Israel; currently with Hong Kong University of Science and Technology. 4Professor, Marketing and International Business, School of Business, University of Washington, Seattle, Washington. 5Senior Lecturer, Leon Recanati Graduate School of Business Management, Tel Aviv University, Tel Aviv, Israel.

Funders	Funder number
Technion V.P.R. Fund

Keywords

Differential games
General objective function
Isaacs equation competitive advertising
Marketing
Nash equilibrium strategies
Saddlepoint feedback strategies
Subgame perfect equilibrium

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10.1023/a:1017567805831

Cite this

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title = "Feedback competitive advertising strategies with a general objective function",

abstract = "We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max-min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.",

keywords = "Differential games, General objective function, Isaacs equation competitive advertising, Marketing, Nash equilibrium strategies, Saddlepoint feedback strategies, Subgame perfect equilibrium",

author = "G. Fruchter and Erickson, {G. M.} and S. Kalish",

note = "Funding Information: 1This research was supported by the Technion V.P.R. Fund and by the N. Haar and R. Zinn Research Fund. 2We would like to thank Professors Arkadi Nemirovski and Leonid Gurvits for very valuable and constructive suggestions and to Professor Shlomo Maital for Ref. 24. 3Senior Lecturer, School of Business Administration, Bar-Ilan University, Ramal-Gar 52900, Israel; currently with Hong Kong University of Science and Technology. 4Professor, Marketing and International Business, School of Business, University of Washington, Seattle, Washington. 5Senior Lecturer, Leon Recanati Graduate School of Business Management, Tel Aviv University, Tel Aviv, Israel.",

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AU - Kalish, S.

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AB - We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max-min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.

KW - Differential games

KW - General objective function

KW - Isaacs equation competitive advertising

KW - Marketing

KW - Nash equilibrium strategies

KW - Saddlepoint feedback strategies

KW - Subgame perfect equilibrium

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ER -

Feedback competitive advertising strategies with a general objective function

Abstract

Bibliographical note

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Keywords

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