History Purpose And Varieties Of Game Theory

Introduction

It is defined as a means of mathematical analysis of conflicts of interest to reach the best possible decision-making options under the circumstances given to obtain the desired results. Its applications in many fields of social science, as well as in logic and computer science.

In the beginning, it was handles zero-sum games, in which one person's gains result in losses for the other entrant.

Nowadays, game theory applies to a wide domain of behavioral relations, and is now way for the science of logical decision making in humans, and computers. John von Neumann and John Nash, as well as economist Oskar Morgenstern are the pioneers of the game theory.

History

There is talk that the beginning (theory of the game) began at the hands of the Jews in the Babylonian Talmud (0 - 500 AD).

And also, some writings by some people such as James Waldegrave (1713 AD) in his letter to Pierre-Remond de Montmort, which he sent to Nicolas Bernoulli accompanied by a discussion of what James Waldegrave wrote.

Augustin Cournot’s (Researches into the Mathematical Principles of the Theory of Wealth) (1838 AD) which is a limited version of the Nash equilibrium.

And also, the book of Francis Yessidro Edgorth (1881 AD), an article on the application of mathematics in moral sciences.

The theory of Zermelo (1913 AD) is the first theory of game theory published by E. Zermelo in his paper (Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels) which spoke about strategies for chess.

Game theory was no longer an independent scientific field until John von Neumann (1944) and Oskar Morgenstern published their Theory of Games and Economic Behavior, which contributed to making game theory an area of independent study.

John Nash give us a big contribution in four papers between (1950-53). first two papers, he makes balance point N- Person Games and non-cooperative games and these two papers known to us as the Nash equilibrium. proposed Nash in Nash equilibrium the study of cooperative games via their reduction to non-cooperative form. he founded axiomatic bargaining theory in his other two paper the Bargaining Problem and Two-Person Cooperative Games. proved the existence of the Nash bargaining solution and provided the first execution of the Nash equilibrium.

Near the end of this decade (Late 50's) came the first studies of repeated games. The main outcome to show at this time was the Folk Theorem. This states that the equilibrium results in an infinitely reiterated game concur with the practical and strongly individually rational results of the one-shot game on which it is based. synthesis of the theorem is obscure. (1988) Drew Fudenberg and David Kreps's A Theory of Learning, Experimentation and Equilibria, which attack the learning problem (how agents learn the equilibrium) of the Nash equilibrium.

Game types

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Game theory distinguishes between several forms of games, depending on the number of players and the conditions of the game itself.

Cooperative / Non-cooperative

The Solitaire is an individual game, where there is no real conflict of interest, because the only interest here is the individual's own interest. In this game, luck or chance is the basic structure of the game, depending on the mixing of the cards and on what the player has of good papers distributed randomly. Although probability theory is concerned with individual games, it is not one of the favorite subjects in game theory, since there is no opponent who adopts an independent approach that competes with the options of the other player.

Symmetric / Asymmetric

In the theory of games, we tell a game what it is a symmetrical game when it comes out playing a particular strategy depends only on other strategies used, not on who plays out. If it is possible to change the players' identity without changing the exit strategies, the game is symmetrical. Parity can be achieved in different varieties.

Zero-sum / Non-zero-sum

If the total profit-output at the end of the game is zero, the game is zero sum, and in these games the amount or probability of the profit is exactly equal to the amount or probability of the loss, which is equivalent to the term economic parity analysis which expresses access to the point of loss and no loss or no production And no depreciation. In 1944, Von Neumann and Oskar Morgensten showed that a total zero-sum person could be expanded to a N +1 person in a zero-sum game, so the N + 1 games could be generalized from the special case of zero-sum binary games. One of the most important issues raised in this area is that the principles of maximization and reduction apply to all zero-sum binary games. This term is known as the reduction-maximization problem. It was proven by Newman in 1928, and others proved to be multi-layered.

General and applied uses

The application of the theory of games is wide and multiple. The authors of the theory von Neumann-Morgenstein have pointed out that the effective tool of game theory must be closely related to economics and consumer behavior. Economic models, especially the market economy model, the perfect competition market is ideal for testing game theory hypotheses, the strong use of gaming theory in the Operations Research Department, which deals with issues of maximizing profits and reducing costs. Game theory is also closely linked to sociology and is widely used in politics. According to the views of many scientists, Quantum physics and many applications to explain human cognition and thought patterns is illogical.

What game theory still has going for it

1. It is a terrific way to describe the structure of many multi-person decision making scenarios, especially certain types of market competition with fixed technologies and firms, collective action, and more. This is true whether or not one applies equilibrium concepts. (I heard Schelling say that the best thing about game theory was the invention of the extremely useful game matrix.)

2. The methodological assumption that a social phenomenon can be understood as an equilibrium of an underlying game allows for numerous insights to be gleaned by constructing what one considers to be the game being played. This makes more sense if the phenomenon exhibits some type of stability (see 5 below), yet many phenomena have such stability, and equilibrium analysis is tailor made for those cases.

3. There is a blossoming literature on the game theory of social networks–both games played on networks and games of network formation. A social network provides a mathematical way to structure interaction in games that fits nicely into standard game theoretic analysis. I think examples from this literature will soon make their way into standard game theory textbooks, which is a good sign of acceptance in the profession.

4. People just don’t conform to the axioms of rational choice. This is not a death blow to game theory because classical game theory will always provide important a normative benchmark. However, until the models more accurately reflect actual decision making, game theory as descriptive analysis will always be constrained. Some changes could be quite simple to make, e.g., incorporating Prospect Theory or quasi-hyperbolic discounting and then doing standard equilibrium analysis. Some changes would be more ambitious, e.g., drawing upon research in neuroscience to better capture new insights into how the mind works when making decisions.

5. Despite #2 above, many important economic and social phenomena are best thought of as out-of-equilibrium phenomena, e.g., think of markets adapting to new technologies or cultural change. We have well-known tools from evolutionary game theory that provide ways to study some out-of-equilibrium interactions. But I see the need for a more general “dynamic game theory” (distinguished from equilibrium analysis of games with timing) of which evolutionary game theory would be a subset. There’s much to learn about out-of-equilibrium dynamics. Some transitions from one equilibrium to another, even if ever reached, are chaotic.