##
**Differential game models of advertising competition.**
*(English)*
Zbl 0896.90144

Summary: Differential game methodology combines two attractive features that are critical to the study of advertising competition: dynamics and multi-competitor decision making. A focused review of two decades of differential game modeling of advertising competition indicates that insights gained to date, while valuable, are of a limited nature, and research in the area needs to extend beyond present limits. Four recent studies are offered as examples of possible directions to follow in continued research.

PDF
BibTeX
XML
Cite

\textit{G. M. Erickson}, Eur. J. Oper. Res. 83, No. 3, 431--438 (1995; Zbl 0896.90144)

Full Text:
DOI

### References:

[1] | Case, James H., Economics and the Competitive Process (1979), New York University Press: New York University Press New York |

[2] | Chintagunta, Pradeep K., Investigating the sensitivity of equilibrium profits to advertising dynamics and competitive effects, Management Science, 39, 1146-1162 (1993) · Zbl 0789.90028 |

[3] | Chintagunta, Pradeep K.; Jain, Dipak C., Dynamic duopoly models of advertising competition: Estimation and a specification test (1992), working paper |

[4] | Chintagunta, Pradeep K.; Vilcassim, Naufel J., An empirical investigation of advertising strategies in a dynamic duopoly, Management Science, 38, 1230-1244 (1992) · Zbl 0775.90125 |

[5] | Chintagunta, Pradeep K.; Vilcassim, Naufel J., A dynamic equilibrium advertising investment model for oligopolistic markets: An application to the beer industry (1992), working paper · Zbl 0775.90125 |

[6] | Chintagunta, Pradeep K.; Vilcassim, Naufel J., Marketing investment decisions in a dynamic duopoly: A model and empirical analysis, International Journal of Reserch Marketing (1994), forthcoming · Zbl 0775.90125 |

[7] | Deal, Kenneth R., Optimizing advertising expenditures in a dynamic duopoly, Operations Research, 27, 682-692 (1979) · Zbl 0412.90039 |

[8] | Deal, Kenneth R.; Sethi, S. P.; Thompson, G. L., A bilinear-quadratic differential game in advertising, (Liu, Pan-Tai; Sutinen, Jon G., Control Theory in Mathematical Economics (1979), Marcel Dekker: Marcel Dekker New York), 91-109 · Zbl 0416.90040 |

[9] | Dockner, Engelbert; Jørgensen, Steffen, New product advertising in dynamic duopolies, Zeitschrift für Operations Research, 36, 459-473 (1992) · Zbl 0757.90042 |

[10] | Erickson, Gary M., A model of advertising competition, Journal of Marketing Research, 22, 297-304 (1985) |

[11] | Erickson, Gary M., Dynamic Models of Advertising Competition: Open- and Closed-Loop Extensions (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, MA · Zbl 0763.90057 |

[12] | Erickson, Gary M., Empirical analysis of closed-loop duopoly advertising strategies, Management Science, 38, 1732-1749 (1992) · Zbl 0765.90036 |

[13] | Erickson, Gary M., Advertising strategies in a dynamic oligopoly (1994), working paper |

[14] | Erickson, Gary M., Dynamic conjectural variations in a Lanchester oligopoly (1994), working paper · Zbl 0902.90015 |

[15] | Feichtinger, Gustav, The Nash solution of an advertising differential game: Generalization of a model by Leitmann and Schmitendorf, (IEEE Transactions on Automatic Control, AC-28 (1983)), 1044-1048 · Zbl 0523.90109 |

[16] | Feichtinger, Gustav; Dockner, E., A note to Jørgensen’s logarithmic advertising differential game, Zeitschrift für Operations Research, 28, B133-B153 (1984) · Zbl 0538.90043 |

[17] | Fershtman, Chaim, Goodwill and market shares in oligopoly, Economica, 51, 271-281 (1984) |

[18] | Fershtman, Chaim; Mahajan, Vijay; Muller, Eitan, Market share pioneering advantage: A theoretical approach, Management Science, 36, 900-918 (1990) · Zbl 0712.90040 |

[19] | Friedman, James W., Advertising and oligopolistic equilibrium, Bell Journal of Economics, 14, 464-473 (1983) |

[20] | Fruchter, Glia E.; Kalish, Shlomo, The \(N\)-player ad game: A closed form feedback solution (1994), working paper |

[21] | Horsky, Dan; Mate, Karl, Dynamic advertising strategies of competing durable good producers, Marketing Science, 7, 356-367 (1988) |

[22] | Jørgensen, Steffen, A differential games solution to a logarithmic advertising model, Journal of the Operational Research Society, 33, 425-432 (1982) · Zbl 0478.90042 |

[23] | Leitmann, G.; Schmitendorf, W. E., Profit maximization through advertising: A nonzero sum differential game approach, IEEE Transactions on Automatic Control, AC-23, 645-650 (1978) · Zbl 0383.90019 |

[24] | Mukundan, Rangaswamy; Elsner, Wolfgang B., Linear feedback strategies in non-zero-sum differential games, International Journal of Systems Science, 6, 513-532 (1975) · Zbl 0304.90141 |

[25] | Olsder, Geert Jan, Some thoughts about simple advertising models as differential games and the structure of coalitions, (Ho, Y. C.; Mitter, S. K., Directions in Large-Scale Systems, Many-Person Optimization and Decentralized Control (1976), Plenum Press: Plenum Press New York), 187-205 |

[26] | Rao, Ram C., Advertising decisions in oligopoly: An industry equilibrium analysis, Optimal Control Applications and Methods, 5, 331-344 (1984) · Zbl 0594.90007 |

[27] | Sorger, Gerhard, Competitive dynamic advertising: A modification of the Case game, Journal of Economic Dynamics and Control, 13, 55-80 (1989) · Zbl 0657.90031 |

[28] | Tapiero, Charles S., A generalization of the Nerlove-Arrow model to multi-firms advertising under uncertainty, Management Science, 25, 907-915 (1979) |

[29] | Teng, Jinn-Tsair; Thompson, Gerald L., Oligopoly models for optimal advertising when production costs obey a learning curve, Management Science, 29, 1087-1101 (1983) · Zbl 0522.90052 |

[30] | Thepot, Jacques, Marketing and investment policies of duopolists in a growing industry, Journal of Economic Dynamics and Control, 5, 387-404 (1983) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.