Taylor. Na, Amy. Hong, Brian. Sang, Luck Yoon

What is the Game Theory? intelligent rational decision-makers Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.” -according to the “naver dictionary” Game Theory

What is the Game Theory? By using : 1. the players of the game 2. the information and actions available to each player at each decision point 3. the payoffs for each outcome. to predict the outcome of interactions between people and f ff find out the best profit one can make while considering others’ situations.

HISTORY Backgrounds +Who ; J JJ John von Neumann +When ; Why / how it was made ; John von Neumann published it on the paper

HISTORY development 1950 Developed extensively in the 1950 by many scholars. Jean Tirole The Nobel Memorial Prize in Economic Sciences went to game theorist Jean Tirole in Crafoord Prize John Maynard Smith was awarded the Crafoord Prize for his application of game theory with biology.

3 forms -extensive form a time sequencing of moves. used to formalize games with a time sequencing of moves. In this picture, 1. each vertex of the tree represents a point of choice for a player. 2. The lines out of the vertex represent a possible action for that player.

3 forms -Characteristic function form decides the payoff of each unity.

3 forms -normal form usually represented by a matrix which shows the players, strategies, and payoffs For example, there are two players, one chooses the row and the other chooses the column. Each player has two strategies, which are specified by the number of rows and the number of columns.

Practical uses in life Economies and business Political science Biology Computer science and Logic

Major method used inmathematical economics and business for modeling competing behaviors of interacting agents. Applications include a wide array of economic phenomena and approaches, such as auctions,bargaining, mergers etc. Economics and business

f focused in the overlapping areas of fair division,political economy, public choice, war bargaining. I In each of these areas, researchers have developed game-theoretic models in which the players are often voters, states, special interest groups, and politicians. Political science

Game theory has been used as a model to understand many different phenomena. It was first used to explain the evolution of the approximate 1:1 sex ratios. Biology 1:1 sex ratios are a result of evolutionary forces acting on individuals who could be seen as trying to maximize their number of grandchildren. Biologists have used evolutionary game theory and the ESS to explain the emergence ofanimal communication. The analysis of signaling games and other communication games has provided insight into the evolution of communication with animals.

Logical theories have a basis in game semantics. Computer science and logic Computer scientists have used games to model interactive computations. Also, game theory provides a theoretical basis to the field of multi-agent systems. Game theory has played a role in online algorithms. In particular, the k-server problem, which has in the past been referred to as games with “moving costs” and ”request- answer games”.

Strategy The strategy concept is a move. It is an actio n taken by a player at some point during the pl ay of a game. For example, chess. A strategy on the other hand is a complete al gorithm for playing the game, telling a player w hat to do for every possible situation of the ga me. A strategy profile is a set of strategies for all players which fully specifies all actions in a gam e. In game theory, the definition of the strateg y sets is an important. The game theorist can us e knowledge of the overall problem to limit the strategy spaces, and ease the solution.

Mixed strategy Mixed strategy is an assi gnment of a probability to each pure strategy. This makes player to ra ndomly choose a pure s trategy. Since are conti nuous, there are infinit ely many mixed strategi es available to a player.

Pure Strategy Two-person Zero-sum game A specific move or action that a player will follow in every possible attainable situation in a game.

MINI GAME Prisoner’s dilemma The prisoner’s dilemma is a central issue in game theory that displays how it is possible for two people not to cooperate with each other even if it is each person’s best interest to do so. Suppose the police arrest two individuals suspected of committing a crime. The police do not have enough evidence to convict both criminals and separate both prisoners in two rooms and offer each the same deal. If one confesses while the other remains silent, the confessor goes free and the other receives a ten-year jail sentence. If both remain silent, they each go to jail for one year on a lesser charge. If they each confess, they both go to jail for five years.

In this situation, it is in both prisoners’ interests to cooperate with each other and both want to avoid the ten-year sentence.However, since neither prisoner knows what the other will choose, it would be irrational to cooperate unilaterally because of the chance that the other will defect. Since the goal is to avoid the maximum sentence, each prisoner should choose to confess because he will either go free or go to jail for five years, each of which is preferable to going to jail for ten years. The prisoner’s dilemma is important because it shows that for people to be perfectly rational actors, they cannot trust the other players in the game, regardless of the greater good they may achieve by cooperating. The way to solve

THE STORY: John Nash It is about John Nash who won the Nobel Prize in economics with game theory. optimize their outcomes Nash put some structure around how players in a "game" can optimize their outcomes. In this tutorial, we use the classic "prisoner's dilemma" to highlight this concept. predicting the outcome Game theory is always concerned with predicting the outcome of games of strategy with having complete information. Movie