Mathematics and Computer Science, Volume 1

10Solution of Matrix Games With Pay‑Offs of Single‑Valued Neutrosophic Numbers and Its Application to Market Share Problem

Mijanur Rahaman Seikh and Shibaji Dutta*

Department of Mathematics, Kazi Nazrul University, Asansol, India

Abstract

Single-valued neutrosophic numbers (SVNNs) are an immensely convenient tool to counter imprecise circumstances in real-life problems containing indeterminacy. The objective of this chapter is to explore matrix games (MGs) where the pay-offs are assumed as SVNNs. A solution methodology has been derived using the notion of the score function (SF) of SVNNs. First, we formulate two neutrosophic mathematical programming problems to obtain optimal strategies. The SF of SVNNs is used to transform these problems into two crisp equivalent problems, which are solved to get the optimal strategies. A market share problem is illustrated to express the rationality and applicability of the presented method. A comparative study with an existing work analyzes the superiority of the performed method.

Keywords: Game theory, single-valued neutrosophic numbers, score function, market share problem

10.1 Introduction

Game theory has engaged largely in competitive decision-making systems. In reality, many situations are uncertain due to the imprecision of facts, asymmetric information, and conflict of interest between opponents in the same field of business. However, the pay-offs may not be expressed precisely due to uncertainty in game situations.

In the literature, ...