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Tanima Dutta, Lovely Professional University Unit 9: Game Theory

Unit 9: Game Theory Notes

CONTENTS
Objectives
Introduction
9.1 Terminologies in Game Theory

9.2 Two Person Zero Sum Game
9.2.1 Algebraic Method
9.3 Pure Strategies: Game with Saddle Point
9.4 Two-Person-Zero-Sum Games of 2 x m and n x 2
9.5 Limitations of Games in Competition

9.6 Summary
9.7 Keywords
9.8 Review Questions
9.9 Further Readings

Objectives

After studying this unit, you will be able to:

 Understand basic terminologies used in game theory
 Familiarize with various methods solving games.
 Analyze limitations of games in competitive situations

Introduction

Game Theory was originally developed by John Von Neumann in 1928. The mathematical
relationship between game theory and linear programming was also initially recognized by
Von Newmann. However, George B. Dantiz was the person to apply the simplex method
successfully to solve a game theory problem. Von Neumann’s book entitled “Theory and Practice
of Games and Economic Behaviour”, which he authored with Morgenstern, is considered as a pioneer
work by the experts all over. It had a great impact on the development of Linear Programming
and wall’s Statistical Decision Theory.

Business decisions in a competitive situation do not depend on the decisions of the organization
alone but on the interaction between the decisions of the organization and those of the
competitors. Each firm tries to select and execute its strategies and aims to maximize its gains at
the cost of its opponents. Similarly, a competitor too rises to select the best of his strategies to
counteract his opponents again. Game theory deals with problems where actions and interactions
of competing firms give rise to conditions of business conflict. In other words, Game Theory is
a body of knowledge which is concerned with the study of decision-making in situations where
two or more rational opponents are involved under conditions of competition and conflicting
interest. It deals with human processes which an individual, a group, a formal or informal
organization or a society, is not in complete control of the other decision-making units, the
opponents, and is addressed to problems involving conflict, co-operation or both at various
levels.

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