Mathematical Models in Marketing

Abstract

For a marketing situation, mathematical models are developed expressing the relation between net revenue and the variables that affect it. These models are extensions of the ones discussed by Mills, and Krishnan and Gupta. Mills assumed that each competitor has only one controllable variable, viz., promotional effort. Krishnan and Gupta obtained equilibrium solutions for two competitors, each having two controllable variables. This paper deals with multicompetitors and discusses four models when the market potential is independent of both price and promotional effort and when it is dependent on either or both of the controllable variables.

Understanding managers' marketing strategy choice in a collaborative competition industry

“…Strategic marketing actions can be divided into two streams of tactics. One stream is categorized as the traditional 4P elements, including product features (Ballou and Pipkin, 1980; Lane, 1980), customer cost control (Chandler and Hanks, 1994), geographic convenience (Hauser and Shugan, 1983; Kotler, 1965), and communications (Gupta and Krishnan, 1967; Fornell et al , 1984); while another one is featured as differentiation (Chandler and Hanks, 1994; Pelham and Wilson, 1996), including service superiority (Dutta and King, 1980; Hauser and Shugan, 1983), appropriate organizational support such as staffing (Shakun, 1968), customer relationship management (Payne and Frow, 2005), and vertical integration tools, e.g. e‐commerce (McGuire and Staelin, 1983).…”

Advertising Competition in a Dynamic Oligopoly with Multiple Brands

“…Early gametheoretic research (e.g. Friedman 1958, Mills 1961, Gupta and Krishnan 1967 considers static markets. More recent years have seen a number of studies involving dynamic market setting, and Erickson (2003) and Jørgensen and Zaccour (2004) provide reviews of this literature.…”

To Segment or not to Segment? An Investigation of Segmentation Strategy Success under Varying Market Conditions

“…Lane (1980) investigated the relationship between product positioning and pricing and levels of competition in oligopolistic markets with sequential entry. Friedman (1958) used game theory as a basis for a static model of advertising expenditure using different scenarios, which was later developed by Shakun who introduced interdependencies between segments, and Gupta & Krishnan (1967) who included multiple competitors and additional controllable variables. Schmalensee (1978) proposed a dynamic model of advertising expenditure in which he recognised the ongoing nature of advertising decision making.…”

“…Shakun's study (1965) indicates that the level of advertising expenditure spent selling the product of one firm proportionately influences sales of the corresponding product of the other firm, limiting the investigation to two competitors only. Gupta & Krishnan (1967) assume multiple competitors but limit the controllable variables of the firm to price and promotion, identifying conditions under which competitors with differing levels of resources should use price and promotions as their major competitive tool, depending on their respective resource levels. The knowledge gap however lies in the investigation of high levels of advertising expenditure and the most appropriate segmentation strategy for firms finding themselves in this position.…”