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Game Theory

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Allan Maglaque

on 4 February 2013

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Transcript of Game Theory

It is the scientific study of strategically interdependent decision making where several players must make choices that potentially affect the interests of the other players. Strategic Interdependence simply means, what I do affects your outcomes and what you do affects my outcomes. It is also the study of mathematical models of conflict and cooperation between intelligent rational decision-makers WHAT IS A GAME? In game theory, a game is a formal model of an interactive situation. It typically involves several players; a game with only one player is usually called a decision problem. The formal definition lays out the players, their preferences, their information, the strategic actions available to them, and how these influence the outcome. The nature of competitions against other human beings means that there are a limited number of options, some of which are more profitable than others.The purpose of studying a game is to determine which option your opponent will choose and select the option that best reacts to this and puts you at the advantage. HISTORY AND AUTHORS 1838 - The earliest example of
a formal game theoretic analysis
is the study of a duopoly
by Antoine Cournot. 1921 – 1928 - The mathematician
Emile Borel suggested a formal
theory of games,which was furthered
by the mathematician John von Neumann in 1928 in a “theory of parlor games.” 1944 - Game theory was established
as a field in its own right after the
publication of the monumental
volume Theory of Games and
Economic Behavior by von Neumann
and the economist Oskar Morgenstern.
This book provided much of the basic terminology and problem setup that
is still in use today. 1950 - John Nash demonstrated that finite games have always have an equilibrium
point, at which all players choose actions which are best for them given their opponents’
choices. This central concept of non-cooperative game theory has been a focal point of
analysis since then. 1960 - The game theory was
broadened theoretically and
applied to problems of war and politics. 1970 - Game theory has driven a revolution
in economic theory. Additionally, it has found
applications in sociology and psychology,
and established links with evolution and biology. 1994 - Game theory received special
attention with the awarding of the
Nobel prize in economics to Nash,
John Harsanyi, and Reinhard Selten. Late 1990's - Game theory has become so entrenched in society that it is being used a form of strategy in economy and politics. BASIC CONCEPTS OF GAME THEORY GAME A game is a formal description of a strategic situation. PLAYER A player is an agent who makes decisions in a game. PAYOFF A payoff is a number, also called utility, that reflects the desirability of an outcome to a
player, for whatever reason. STRATEGY In a game in strategic form, a strategy is one of the given possible actions of a player. In
an extensive game, a strategy is a complete plan of choices, one for each decision point
of the player. RATIONALITY A player is said to be rational if he seeks to play in a manner which maximizes his own
A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for each
player, which has the property that no player can unilaterally change his strategy and get
a better payoff. NASH EQUILIBRIUM ZERO-SUM GAME A game is said to be zero-sum if for any outcome, the sum of the payoffs to all players is
zero. In a two-player zero-sum game, one player’s gain is the other player’s loss, so their
interests are diametrically opposed.

A strategy dominates another strategy of a player if it always gives a better payoff to
that player, regardless of what the other players are doing.
DOMINATING STRATEGY USES OF GAME THEORY The central purpose of game theory is to study the strategic relations between supposedly rational players. Game theory allows us to quickly draw parallels from one situation to another. This will allow us to think on our feet much better and make better decisions on certain situations.

Game theoretic concepts apply whenever the actions of several agents are interdependent. These agents may be individuals, groups, firms, or any combination of these. The concepts of game theory provide a language to formulate structure, analyze, and understand strategic scenarios.

Game theory’s natural field of application is economic theory: the economic system is seen as a huge game between producers and consumers, who transact through the intermediation of the market. In economics, game theory has been used in studying competition for markets, advertising, planning under uncertainty, and so forth.

Game theory has come to play an increasingly important role in logic and in computer science. Several logical theories have a basis in game semantics. In addition, computer scientists have used games to model interactive computations. The emergence of the internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets.

The application of game theory to political science is focused in the overlapping areas of fair division, political economy, public choice, war bargaining, positive political theory, and social choice theory. In each of these areas, researchers have developed game-theoretic models in which the players are often voters, states, special interest groups, and politicians.

Game theory has influenced media in many ways. In video games, programmers use this to create artificial intelligence and to develop the game play. In game shows, it is used as a strategy to win. In movies, it is used in certain scenes or it plays a role in the plot. One of the examples is the movie “A Beautiful Mind” which is a biographical drama film based on the life of John Nash, who discovered the Nash equilibrium.

Real world games consists of a finite number of moves but mathematicians and theorists said there are infinite moves that is unknown until all the other moves are completed.

Differential games
Players have a different conflicting goals. Much like the cops and robbers.

Many-player and Population games
Random games with different players involving the population on how they will decide. It is also to see how their decision will change as individual persons
biology evolution economics population changes and switch of strategies.

In simple terms it is the use of out-of-game information or resources to affect one's in-game decisions.

Combinatorial game theory
The study of sequential games with perfect information. that is, two-player games which have a position in which the players take turns changing in defined ways or moves to achieve a defined winning condition.

Continuous game
It extends the notion of a discrete game, where the players choose from a finite set of pure strategies. The continuous game concepts allows games to include more general sets of pure strategies, which may be uncountably infinite.

Stochastic outcomes
Its like random process, because we don't know who will win or who will loose among the player's, like in businesses you don't know who will win it will randomly pop up.

Cooperative game theory it is simply coalitions of players, like in politics they join forces to make a law, Because they have only one agenda, but it has competition involve also because you will encounter a rival group or opposing group.

the difference of this to cooperative game theory, two or more individuals within the same environment with different goals. Without sharing their ideas they can make a decision. For me its like selfish decision.

The difference of this to sequential theory there's no time involve here and your doing actions that you do not think your move first, like rock paper scissors, because you both make randomly decision. It is represented by normal form or payoff matrices. It also called strategic game.

In this kind of game theory you need to know the consequences before you can make a move. This kind of game involve time like chess, backgammon. Sequential is represented by decision tree or extensive form. It is also called extensive game.
Perfect information and imperfect information
A game is one of perfect information if all players know the moves previously made by all other players. One popular game for perfect information is chess. Imperfect information is simply the opposite. Players do not know the moves made by the other players, thus limiting their information to strategize. Some examples are poker and battleship.

Symmetric and asymmetric
A symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed. One well-known game for this example is the Prisoner’s dilemma. On the other hand, asymmetric games are games where the strategies of both players are not identical.

Zero-sum and non-zero-sum
In zero-sum games the total benefit to all players in the game, for every combination of strategies, always adds to zero. Rock, paper, scissors is game that illustrates this well because one’s win is exactly the amount one's opponents lose. In non-zero-sum games, a gain by one player does not necessarily correspond with a loss by another, the outcome has net results greater or less than zero.
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