3K

# GAME THEORY

Published: November 11, 2019

What is The Game Theory? History Of Game Theory Basic Concepts in Game Theory

## GAME THEORY

• 1. GAME THEORY GAME THEORY
• 2. What is The Game Theory? What is The Game Theory? In the words of mathematicians, ``Game Theory ´´ is the method of determining the most accurate strategy against conflicting possibilities. In cases where the choice of one of the competitors depends on the opponent's preference, competition occurs and the conflict starts. Special mathematical techniques have been developed to analyze conflict situations and `` THEORY OF GAMES ´´. The aim of the theory is to examine rational ways of action for the conflicting group or persons and to ensure that one of the groups wins. Each game has a purpose, the opponents' goal is to approach this goal within their means and ensure the defeat of the other side.
• 3. History Of Game Theory History Of Game Theory When John Von Neumann was in Berlin, he began to study poker. He was particularly interested in this game, because it was not only a chance factor but also a player's strategy. Within a few months, Neumann developed the ``Theory of Games´´, which brought a new field of mathematical studies. J. Neumann and his friend, Princeton University economist Morgenstern, are writing a book in 1944. It's called ``Games Theory and Economic Behavior´´. With this book, game theory takes its place in the scientific world as a true discipline. Among the scientists who contributed to the game theory, John F. Nash should be given a special place. John F. Nash developed the game theory with four works published between 1950-53, and created a concept of balance that can be used in both competitive and collaborative games. He still draws the heavy load of game theory from his Nash equilibrium.
• 4. Basic Concepts in Game Theory Basic Concepts in Game Theory Players: People or organizations that try to optimize their goals in a game. Strategies: Each player's action options. Payments Matrix: This matrix shows the gains or losses resulting from a combination of the players' choice of strategy. The elements of the pay matrix can be positive, negative, or equal to zero. If any element of the matrix is positive, the player in the column pays this amount to the player in the row. If any element of the matrix is negative, the player in the row pays the player in the column equal to the absolute value of that negative element. If the element of the matrix is zero, none of the players pay each other.
• 5. Basic Concepts in Game Theory Basic Concepts in Game Theory Complete Strategies: A single strategy pair is the outcome of the game. The result is the best possible result for each player. Exact strategies determine the game's saddle. Mixed Strategies: The situation where multiple strategy pairs determine the outcome of the game. Strategy pairs are expressed in probability values and the sum of the strategy pairs probability values that make up the outcome of the game is 1. Expected Value: The value that any player will get at the end of the game. The expected value is the sum of the probability of realization of strategy pairs and the multiplication of their values.
• 6. Basic Concepts in Game Theory Basic Concepts in Game Theory Complete Strategies: A single strategy pair is the outcome of the game. The result is the best possible result for each player. Exact strategies determine the game's saddle. Mixed Strategies: The situation where multiple strategy pairs determine the outcome of the game. Strategy pairs are expressed in probability values and the sum of the strategy pairs probability values that make up the outcome of the game is 1. Expected Value: The value that any player will get at the end of the game. The expected value is the sum of the probability of realization of strategy pairs and the multiplication of their values.
• 7. What is The Basic Logic Of Game Theory? What is The Basic Logic Of Game Theory? Whether the outcome of the game is pure strategy or mixed strategy, the solution process is carried out on the payments matrix. The solution process starts with the choice of the player from which the game is judged. If a solution is to be performed for the player representing the rows of payments matrix, the maximin method is applied, and if the solution is to be performed for the player representing the columns, the minimax method is applied. If the maxim and minimax values are equal, the game is a game with SALT STRATEGY.
• 8. Classification of Games Classification of Games
• 9. Non-Total Games Non-Total Games In game theory, it is a game where the total sum of prizes of the players in different options is not zero, in other words, the winnings of one player is not the loss of the other. All conflicts in daily life and international politics are not all zero sum. Many of these are similar to non-zero sum games. Players can have more than two. Players can either lose together or win together if they cooperate with their common interests. The fact that the two companies competing with each other by opening an advertising campaign started to earn more due to the version increase or the improvement in the foreign trade gains of the member countries after the establishment of the European Common Market are examples of the situations that may result in the benefit of all concerned.
• 10. Zero Total Games Zero Total Games They are games in which one party's loss is equal to the other party's winnings. There is an absolute victory or an absolute defeat in this kind of game. Great weight in game theory is concentrated in this type of games. As the name suggests, this game is played between two opposing players. The fact that more than two people go to a coalition and participate in the game does not change the quality of the game. If there are two coalitions permanently, the game is reduced to a two player game. The reason for the game being named as zero sum is that the sum of profit and loss obtained at the end of the game is equal to zero. Football is a game with zero sum. When one team beats the other 1-0, the other team is defeated 0-1. The sum of defeat and its value is equal to zero.
• 11. Nash Balance Nash Balance Developed by renowned mathematician John Forbes Nash, this tool is mainly based on the idea that elections determine the payoff of results. Accordingly, each individual should try to make the best choice by considering the behavior of other individuals and variables with whom he/she is in a relationship. In other words, when making a selection, it is necessary to make the most effective choice by taking into consideration the interests of the field it interacts with rather than individual interests. In other words, if all players take an action in which they get the most effective results, if the actions are done by considering the actions of other players and these choices are not harmful to the choices of other players, then this game is played with Nash equilibrium. Nash Mind Games ’film in which Nash equilibrium is discussed
• 12. Example of Prisoner Dilemma Example of Prisoner Dilemma Two suspects were taken into custody pursuant to an investigation. The police take the suspects to separate interrogation rooms and make an offer. The police have sufficient evidence and suspects have no opportunity to communicate with each other. The proposal of the police; •If both suspects remain “silent her, they will each be sentenced to 1 year imprisonment. •If the suspects testify against each other, they will both be sentenced to 2 years each. •If one suspect testifies against the other, but the other chooses to remain silent, the witness will be released but sentenced to three years of imprisonment. Question: Should the suspect remain silent, or should the other accuse?
• 13. Example of Prisoner Dilemma Example of Prisoner Dilemma Solution: The smartest choice is to remain silent. However, this rarely happens in the real world. Because usually suspects will decide in their own interests, both will be sentenced to 2 years in prison. When making the choice of the suspect, the rational one, who does not know the choice of the other party, will be to choose to remain silent, minimizing the duration of the penalty. The Prisoner Dilemma is very similar to the action of powerful countries to produce nuclear warheads. Because a nuclear war guarantees mutual destruction. According to game theory, the best thing to do is to get rid of nuclear warheads completely.
• 14. References References [1] https://tr.wikipedia.org/wiki/Oyun_teorisi [2] http://herkesicinoyunteorisi.blogspot.com [3] https://www.odevsel.com/genel-kultur/858/oyun-teorisi-ve-rekabet-oyunlari.html [4]http://acikerisim.nku.edu.tr:8080/xmlui/bitstream/handle/20.500.11776/2479/0051719_PDF.pdf?sequence=1&isAllowed=y [5] http://www.olaganustukanitlar.com/oyun-teorisi-nedir/ [6] https://nbeyin.com.tr/oyun-teorisi-nash-dengesi/