Optimal management of fringe entry over time

Gila E. Fruchter, Paul R. Messinger

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In this paper, we investigate the problem of a dominant company facing entry of a "competitive fringe" (smaller competitor or fringe of smaller competitors). We seek to identify pricing and advertising (or other promotional strategies) that maximize long-term profits for the dominant firm, under possible reactions of the competitive fringe. Two main situations are considered: •The firms in the fringe are price-takers, but they advertise. •The firms in the fringe are not price-takers and advertise. The possibility of a passive reaction, in the case of a very small fringe, is considered as a particular case.We assume that the rate of change of fringe sales is dynamically related to the current sales, price and advertising efforts of both the dominant firm and the fringe. The higher the dominant firm price, the faster fringe entry. The higher dominant firm advertising effort, the slower fringe entry. Fringe advertising and pricing may counterbalance these effects. Formulating a dynamic game, with the dominant firm as a leader and the fringe as a follower, we present a new methodology for providing time-invariant feedback Stackelberg equilibrium. The methodology relies on finding the relationship between the co-state variables and the state variable. The equilibrium solution is obtained in an implicit form by solving a set of two backward differential equations. To show the applicability of our solution to real situations, we use data from the U.S. long-distance market and find optimal decision rules for AT&T facing the entry of MCI and Sprint during the 1980-1990 period. The feedback equilibrium indicates that while AT&T's price is decreasing when fringe (MCI and Sprint) sales increase, the fringe price is increasing. AT&T's advertising is increasing with fringe sales while the fringe's advertising increases and then decreases. The comparison with actual behavior indicates that AT&T has adhered closer to the optimal solution in both price and advertising than the fringe.

Original languageEnglish
Pages (from-to)445-466
Number of pages22
JournalJournal of Economic Dynamics and Control
Volume28
Issue number3
DOIs
StatePublished - Dec 2003

Bibliographical note

Funding Information:
The authors thank Sean Acheson, Edward Park, and Alex Kolesch for research assistance. We also thank Gary Lilien and Suresh Sethi for helpful comments. We acknowledge the support of the Social Sciences and Humanities Research Council of Canada.

Funding

The authors thank Sean Acheson, Edward Park, and Alex Kolesch for research assistance. We also thank Gary Lilien and Suresh Sethi for helpful comments. We acknowledge the support of the Social Sciences and Humanities Research Council of Canada.

FundersFunder number
Social Sciences and Humanities Research Council of Canada

    Keywords

    • Advertising
    • Dominant firm
    • Fringe entry
    • Pricing
    • Stackelberg dynamic game

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