Strategic Management in Marketing: A Game Theoretic Approach

Vinod Jangid, Gaurav Sharma, Ganesh Kumar

doi:10.17762/turcomat.v12i6.5697

Abstract

In marketing, a real-world dilemma emerging between two rivals, McDonald's and Burger King, is investigated. Both firms use three strategies: discounted pricing, status quo, and aggressive commercial. In such cases, ambiguity is a determining factor. To deal with confusion in payoffs, octagonal fuzzy numbers are used. To rank fuzzy numbers, the average of odd positions, average of even positions, and quartile deviations are used. To solve the reduced modelled two competitors zero sum fuzzy matrix games, the proposed ranking methods are used. Finally, the findings are compared to current approaches that are quite similar to the proposed approach.

Highlights

Uncertain parameters are known as fuzzy numerical data, and they can be expressed by a variety of fuzzy numbers
Let A be an octagonal fuzzy number we propose some defuzzified ranking methods namely average of odd positional values in OFN, average of even positional values in OFN, Quartile deviations methods, average of the smallest possible α-cut approach for an OFN and average of the largest possible α-cut approach for an OFN to obtain a crisp value as defined as follows
It is established that competitive situations of marketing can be modeled in form of fuzzy matrix games

Summary

Introduction

Uncertain parameters are known as fuzzy numerical data, and they can be expressed by a variety of fuzzy numbers. Using a theoretical approach to fuzzy mathematics, Cevikel and Ahlataiuglu (2009) published some new solution procedures for fuzzy matrix games. They spoke about the case of linearity in fuzzy payoffs. Christi and Kalpana (2016) used trapezoidal fuzzy numbers as payoffs in fuzzy matrix games and obtained optimal value results using an average weighted approach. Yuan (1991) developed a ranking system with integral value and evaluated it using four evolutionary criteria These four requirements are fuzzy ordering rationality, robustness, fuzzy choice, representation, and distinguishability. Definition 2.2“A fuzzy set A in R is called a fuzzy number if it satisfies the following axioms:. The fuzzy payoffs gained by maximizing player is defined as,

Proposed Ranking Methods to Convert an OFN into Crisp Value

Average of the Smallest Possible α-Cut Approach for an OFN

Application in Marketing

Defuzzification Method

8.Conclusion