**Game Theory**

What is it?

-Game theory is a study of strategic decision-making on whether you will win

- With penalty kicks, the shooter hits the ball hard and fast, the goalie has to make their decision of where to dive for the ball the same time the player hits the ball. Because of this, the game is based on probability and maximizing your chances based on your opponent.

-Tic-Tac-Toe also follows a similar pattern as you have to make your move based on what your opponent will do/has done

- any time a game includes 2 or more players and a prize or consequence, game theory can be used.

Pyschology

Psychology is based on choices of people and how it is driven by what they feel. Game theory often helps solve why people do what they do. For instance, a lady has a house cleaner, regardless of how good a job the cleaner does the lady tips her the amount of money the cleaner would have expected for. Without game theory you would wonder why someone would do a foolish thing like that, but then you take into account the ladies beliefs, regardless of tipping. The lady always feels guilty when she lets people down, and to her, keeping her cleaner happy but giving her what she doesn’t deserve overrules the guilt she would have felt.

Philosophy

The way humans developed over time and peoples

development in their morality is credited much to

Game theory. Game theory in philosophy dates back

as far as Plato’s studies. For instance with drinking and

driving, 40 years ago it was common and was more of

a worry of getting caught by the police than putting someone

or yourself in danger.Governments or people who really

just want to get the message across to change people's

beliefs on drinking and driving, they look at what

strategy would work the best. For instance, scientific

studies on impairment of driving, or advertisements

constantly everywhere, so people can’t run away

from it and really start to question how dangerous

drinking and driving is. The main focus is to truly

change everyone’s moral beliefs on what is right

and what is wrong, like how it is wrong to go up

to a stranger and beat them up,these morals have

been engraved into our brain.

Politics

Game theory has commonly been applied to the world of politics. It overlaps in many areas of politics like war-bargaining, economics, and social choice strategy., The players used in game theory represent voters, states or provinces, or opposing politicians. Suppose a politician is running for election. He is trying to maximize his votes to win and is going to offer the people what they would want most. Certain things like reducing taxes, that can also be bad with less money going into the government is often a dilemma. It is studied to find the popularity of the votes where it helps you as a politician the most. This is a prime state used to accomplish with game theory.

Cooperative Game Theory

Cooperative game theory is when groups of players have to make strategic decisions, overall becoming a consenus decision, making strategic game more hard.It is much less of teams versus other teams, and more of a whole of one team who are individually trying to maximize their own game while still having to agree with everybody.

Non cooperative Game Theory

Game theory is branched into two different concepts; Cooperative and Non-Cooperative game theory. The more common, and more beneficial branch of game theory is non- cooperative game theory which we will further explain in this page. To define non-cooperative game theory, it is much like its name that is, based on a single person’’s decision without consulting or working with someone else. Although the decisions you make are independent, the game you are playing often is quite the contrary from independent. Non-cooperative game theory are strategic decisions based on your opponents optimal moves are. Non-cooperative game is often used not just in games and become beneficial in the real world. An example is non-cooperative game used in sports like penalty kicks in soccer or a batter-pitcher duel. Anything where your opponents moves and your moves can affect you or help you INDIVIDUALLY is an example of non-cooperative game theory.

Uses of Game Theory

Game theory was originally created for the use of it in economics. But the uses of game theory that could be applied to a wide variety of aspects in life and schooling quickly developed. Soon after Game theory was expanded in the social sciences and was found in politics, philosophy, and even psychology. Game theory was also applied in biology and the study of animal behaviour. In this report we will research each use of game theory and how it was applied.

How to Apply Game Theory

History

-The very first hint of game theory is dated back to thousands of years where it was founded in the writings of Talmud and Sun Tzu

-official founder of game theory; John Van Neumann. In 1944, Van Neumann, in collaboration with Oskar Morgenstern; a mathematical economist wrote the breakthrough book on game theory called “The Theory of Games and Economic Behaviour”

-Josh Nash created the basis of the field of game theory. After game theory was made an official mathematical theory

-Game theory can be laid out in various graphs to organize and better solve all possible outcomes

-This diagram displays your

start position in a game ( in this

diagram, the start of a game of

tic-tac-toe) and each possible

move you can make branches

out and then branches into

more options of your opponents

possible moves after your choice.

Payoff Matrix

A Payoff Matrix lay out all possible

outcomes for what you decide to do in a game, compared to the other player(s) possible outcomes as based on your decision or vice versa.

An Example

An example of cooperative

game theory is a negotiation

business contract, between

the employees, and the employer

. Although it seems as an

opposition of the employers

and the employee it isn't.

At the end of the day, they'll

have to come together and

make an agreement, it was

a group decision that really

is meant to benefit everybody.

Putting It in Action

Let’s say the employee’s want more vacation days but the employer can't afford his business to be short-staffed for so long. Instead of an argument between yes and no, compromising plays a factor. Compromise then gives the employee’s the vacation days they want but also doesn’t put the employers business under fire. The employer would then agree to more vacation days as long as a certain number of those days they have to put in a certain amount of hours of work online. The employees then must decide whether it is smarter to just have the same amount of vacation days or take the compromise, and that is where game theory comes into play.

Nash Equillibrium

Nash equilibrium is a vital state to know about in game theory, named after it’s inventor, John Nash. The state nash equilibrium is when you cannot gain anymore in the game as long as

your partners decision remains

unchanged. An example of a nash

equilibrium is when neither

opponent is worse off or better

off. Below is an example of

two separate nash equilibriums

and as you can tell they have

a pattern of both being matched

numbers.

Step 1: Put all outcomes into a graph of your choice, (payoff matrix, game tree) we will be using a payoff matrix by labelling you on one side and your opponent on the other, with divisions for each possible move,confess or don’t confess. ex.

Step 3:

Now assume 100% that the other suspect was going to keep quiet and look at your options.

Since no time in jail is better than 2 months in jail it would be better to confess

Step 2:

Now put in all outcomes based on what box is lined up with your box.

Based on Jim Harvey's speech structures

Game tree

We will use a common use of game theory played in a realistic game called Prisoner’s Dilemma

The game:

- you and another suspect are arrested

-police caught you selling drugs, but suspect you of an armed robbery from last week.

- The police needs you or the other suspect to rat out the other

-interrogate each of the suspects in separate rooms offering a compromised sentence if they confess and their partner doesn’t.

If they both confess: 8 months in jail

-both deny: 2 months in jail for drugs

-one confess and one deny: no time for the rat and a year for the one who kept quiet.

confess

don't confess

opponent

confess

don't confess

you

confess

don't confess

confess

don't

confess

opponent

you

-8,-8

0,-12

-12,0

-2,-2

0,-12

-2,-2

don't confess

confess

don't confess

you

Step 4:

Now suppose that the other suspect was 100% going to confess, what would your best move be?

since 8 months in jail is better than a year in jail, it s better to confess.

confess

confess

don't confess

you

-8,-8

-12,0

Conclusion

Now since in both scenarios it is better to confess, no matter what the other suspect does, your optimal move is to confess.

Now you know how to solve Game Theory!