CHAPTER

1

INTRODUCTION

1. Significance of the study

a.

Game theory, a branch of applied

mathematics that is used in the social sciences, most notably

in economics, biology, engineering, political science, international

relations, computer science, and philosophy attempts to

mathematically capture behavior in strategic situations or games, in which

an individual’s success in making choices depends on the choices of others.

While initially developed to analyze competitions in which one individual does

better at another’s expense (zero sum games), it has been expanded to treat a

wide class of interactions, which are classified according to

several criteria. Today game theory is widely used in the business for

solving situations in which there are a number of players.

b.

Countries are using the science of Game Theory to help them make

complicated strategic decisions in this highly competitive market with least

possible risk. History of Modern Game Theory is more than 50 years old and has

demonstrated an ability to generate the ideal strategic choice

in a variety of different situations, companies and industries. Principles of

game theory are applied through the use of strategy games.

c.

Game Theory is basically denoting on study of mathematical model of

differences and cooperation between intelligent balanced decision-makers. Game

Theory enables universal mathematical techniques for analyzing situation which

individuals or competitors in same segment make decision that will influence

one another’s interests. As such, game theory offers impending of essential

importance for scholars in all branches of the social science, as well for

practical decision-makers. The situation that game theories studies are not

just spare time activities, as the term game might unfortunately suggest.

Conflict analysis or interactive decision theory might be more descriptively

precise names for the subject.

2.

Applications of Game theory. A powerful tool for predicting outcomes of a

group of interacting firms where an action of a single firm directly

affects the payoff of other participating players, enables a

company to formulate their optimal strategy. It is Ideal for strategic

situations where competitive or individual behaviors can be modeled. For example:

a. Auctions

(sealed project bids).

b. Bargaining

activities (union – management negotiations).

c. Product

decisions (entry or exit markets).

d. Principal-agent

decisions (compensation negotiations, supplier incentives).

e. Supply

chain design (capacity management, build vs outsource decisions).

3.

Multiple strategy games are analyzed

to model different competitors, various payoffs and potential

strategies. The objective of these games is to deliver fol:

a. A

recommended set of strategic decisions to guide competitive behavior to a

desirable outcome, and;

b. An

analysis of how a series of possible strategic moves can predict various

competitive outcomes.

c. Various

types of games can be used and analysed based on the strategic situation, the

number of players, the amount of information available and the timing

constraints.

4. Prisoner’s

dilemma. Prisoner’s dilemma is a situation which depicts the

movements of the participants for a particular motive. Basically there are two

or more players who try to move to different segments to archive profit than

their competitors or other participants. This situation would be more clear

with the assistance of 2 by 2 matrix games. They have the minimal configuration

necessary to be a game, which are two player with each two decision

possibilities. These games can easily be examined and displayed in a matrix.

The most famous 2-by-2 matrix example in this context is the Prisoner’s

dilemma. It is one of the most interesting games which game theory has to offer

and at the same time deals with one of the most interesting thing of social

science like the interaction of individual and society. Two criminals commit a

bank robbery and are arrested by police. The police do not have sufficient

evidence to prove their crime. In this situation they use game theory to prove

it. Basically they separated them in two cells and visit each of them and offer

the same deal. If you confess and your accomplice remains silent, he gets the

full 5 year punishment and you go to free as principal witness. If he confesses

and you remain silent, you get the full 5 year punishment and he goes free. If

you both stay silent, all we can do is give you both 1 year for a minor charge,

which is illicit possession of firearms. If you both confess, you each get 4 years

1

5. Dominant Strategy. A

strategy is dominant if, regardless of what any other players do, the strategy

earns a player a larger payoff than any other. Hence, a strategy is dominant if

it is always better than any other strategy, for any profile of other players’

actions. Depending on whether “better” is defined with weak or strict

an inequality, the strategy is termed strictly dominant strategy or weakly

dominant. If one strategy is dominant, than all others are dominated. For

example, in the prisoner’s dilemma, each player has a dominant strategy. To execute the game is by categorizing two player or

competitors involving in the game and each player form the alternative strategies

to perform well. In case of two player game, the action of first player from

the rows, and the actions of the second one in the columns of given matrix. This

case is demonstrated by two players who are caught for a crime by police. Each

suspect is placed in different cells and offering to confess.

6. Classification of

game theory. There are basically three types of games

classifications. It is always in the best interest of all countries to avoid

the collision and If they have to avoid the collision each of them has three

strategies:

a. move

right

b. move

left

c. maintain

direction

7.

Methodology. The tactic for collection of data and its analysis is methodological and

permits more flexibility then quantitative research. The data is gathered in

textual format on the basis of observations and interactions with the

participants.for instance through

participant observation, in-depth interviews and focus groups. It is not

converted into numerical form and is not statistically analyzed.

8. Research questions

a.

Game-theoretic Understanding of India-Pakistan Relations?

b.

Is Game theory useful to bring Crisis

Stability

c.

Can Pakistan and Indian find resolution of Kashmir dispute through Game

Theory.

CHAPTER

2

LITERATURE REVIEW

9.

The

scientific hypothesis of Game theory was developed by John von Neumann and

Oskar Morgenstern (1944). For explanations to be talked about later,

impediments in their numerical system at first made the hypothesis pertinent

just under uncommon and constrained conditions. This circumstance has drastically

changed, in ways we will analyze as we come, in the course of recent decades,

as the system has been extended and summed up. Refinements are as yet being

made, and we will survey a couple of exceptional issues that lie along the

propelling front edge of these improvements. Nonetheless, since 1970s it has

been conceivable to state with certainty that Game hypothesis is the most

imperative and helpful device in the analyst’s pack at whatever point he/she

faces circumstances in which what considers one specialist’s best activity (for

her) relies upon expectations about what one or more players will do, and what is considered as their best

actions (for them) similarly rely upon expectations about him/her.

10.

Notwithstanding the way that Game hypothesis has

been rendered numerically and coherently precise just since 1944, diversion

theoretic experiences can be found among analysts backpedaling to antiquated

times. For instance, in two of Plato’s messages, the Laches and the Symposium,

Socrates reviews a scene from the Battle of Delium that a few observers have

translated Game hypothesis.

11.

Long before game theory had come along to

show analysts how to think about this sort of problem systematically, it had

occurred to some actual military leaders and influenced their strategies. Thus

the Spanish conqueror Cortez, when landing in Mexico with a small force who had

good reason to fear their capacity to repel attack from the far more numerous

Aztecs, removed the risk that his troops might think their way into a retreat

by burning the ships on which they had landed.

12. Some time before Game hypothesis had come

along to demonstrate to experts generally accepted methods to consider this

kind of issue efficiently, it had jumped out at some genuine military pioneers

and impacted their systems. Subsequently the Spanish vanquisher Cortez, when

arriving in Mexico with a little power who had justifiable reason to fear their

ability to repulse assault from the far more numerous Aztecs, expelled the risk

that his troops may think their way to retreat by burning the ships on which

they had arrived made use of game theory in the war.

CHAPTER

3

RESEARCH

METHODOLGY

13. Research Methodology. This

portion of study will elaborate the modality of the study and the type of

research methodology used in this study. This chapter will describe the study’s

population, sampling, philosophy and will also explain the methods and

approaches used to conduct this research. Moreover, in this chapter, the

research design will be carefully studied as well as the sampling techniques

and instruments used in this study

14. Research Philosophy. So as to comprehend the dispute on the Game theory,I

drew many qualitative readings trusting on evocative data based on past

abstracts and assertions by each of the

applicant countries. For sustenance my report I searched help from manifold

sources.

15.

Research

Design. The research design for this Individual Research

paper is appended for developing a conceptual framework. The foremost step was

to carry out an in depth analysis of previous literature review on the topic.

In order to make a review of previous studies or data on concern issue,

different academic databases were used and number of scholarly articles were

read. Besides this, different books, journals related to the topic were

reviewed. The data for all this was all gathered from secondary sources in

order to gain imperative information prevalent to the aforementioned concern.

16.

Population

of the study. All-out effort and strive were made for finding and consulting

impartial, authentic and diverse sources for gaining authentic information on

the mentioned subject. Sources of Wikipedia are used

1K. Yasukawa,”Game theory, Science direct,http://www.sciencedirect.com/topics/neuroscience/game-theory Accessed date 12 Oct 2017