The Game Theory: Application in Strategy Making

Introduction

Game theory is utilized extensively in social sciences especially in environmental science, engineering, biased science, global associations, computer science as well as way of life. It is also considered as a branch of applied mathematics. When Game theory is applied properly, it helps individuals to make the right choices and decisions after considering the choices made by others. Initially, Game theory was made only to analyze competition and to construct strategies through which one party can make profit on the loss or expense of another (zero sum games). Throughout the years, Game theory has been much evolved and now it enables its users to make strategies on several ongoing issues of social science where the players are both human and non human.

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Traditional Game Theory makes an effort to find equilibrium in these games. Equilibrium occurs when all the players of the game have adopted a strategy that is unlikely to change. To make this possible in reality many equilibrium theories have been introduced, the most famous equilibrium game theory is the Nash equilibrium. However, all the methodologies and the concepts that have been made are also often criticized. The debate always remains the same, trying to figure out which one of the Game theories is appropriate.

A lot better employment on Game theory was completed subsequent to the liberate of the well-known volume known as Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. In 1944. Many scholars deeply studied the different theories given in the book and further developed them in the 1950’s. During the 1970’sGame Theory was applied to the concepts of biology and later on, in many academic subjects. Up till now, eight game theories have won Nobel prizes for their work in economics. The famous scholar John Maynard Smith won the Crawford Prize for applying game theory effectively in biology.

Application of Game Theories in Strategy Making

The purpose of development of Game Theories is to basically assist in strategy making and decision making during difficult situations. Conflicting situations occur when more than one decision maker having different objectives has to make a decision or a strategy using the same resources. Game Theories always have more than one player in them. The game offers a mathematical process through which an optimum strategy can be achieved enabling one player to win over another player.

A game theory is always based on following assumptions:

  1. Every player or decision maker has two to three choices available in front of him to choose from.
  2. There is always a payoff obtained at the end of the game. The payoff can be anything greater or less than zero.
  3. Every player is equipped with relevant information about the game and the opposition, he is well aware of the rules of the game and the payoffs of other players.
  4. The players are highly rational. Every player is provided two alternatives; they will choose the option they believe will give them the best strategy and greater payoff.
  5. All decision makers are provided with at least two alternatives and they choose the one that they believe will give them greater profits.

Several Game theories have been made to make the process of strategy making easy. In all these theories there are particular set of strategies that are available to the players of the game. Normally, the games are represented in two common ways:

Normal form game

Also known as strategic form game, it consists of a matrix that highlights the players, strategies and the payoffs. This game usually has two players, one takes the row and the other one chooses the column. Each player has two strategies with him that can be seen by number of columns and number of rows. The payoffs can be seen in the interior. You can see the number of payoffs received by each player in the column and the row. If the performer 1 ends and the performer 2 depart subsequently the performer 1 gets 4 while the other performer gets 2 or 3.

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Whilst a diversion is played in usual form it is unspecified that in cooperation the players should not be acquainted with everything on the subject of the measures of the other performer. If they do, then the game if played in extensive form. (Neumann and Morgenstern, 88- 96). (table x).

Extensive form game

Extensive form game makes an attempt to captivate the game according to an important sequence. Games are represented as trees, with each vertex showing the strategy chosen by the player. A row pending out of the highest point demonstrates all likely actions that a performer can obtain while the payoffs are observed at the base of the performer.

If you will see the diagram at the bottom of the report you will notice there are two players. The player 1 makes his move first and chooses either F or U. player 2 chooses A or R. like this player 1 gets a payoff of 8 and player 2 gets a payoff of 2. (Shoham and Kevin, 100- 105)

Different strategies can be made by using the below mentioned games

Cooperative or non-cooperative

A game is said to be cooperative if the players in the game have the ability to maintain binding commitments. Such as, the legal system demands the players to stay focused on their promises and commitments. While in non cooperative, no such thing is demanded.

Communication is allowed in cooperative games and is totally condemned in non cooperative games. When both the games are compared, non- cooperative game seems to create better strategies and generate better results this is mainly because Nash equilibrium is used as the basis of non cooperative games.

Both cooperative and non cooperative concepts are used in hybrid games ( John C., p. 75-78)

Symmetric and asymmetric

Under a symmetric game the players hold no importance it is the strategy that brings out the payoff. If the players are changed anytime during the game, it will not affect the payoff of the strategy in any way. Usually 2×2 games are considered to be symmetric. The most common symmetric games are prisoner’s dilemma, and the stag hunt is all symmetric games.

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Asymmetric games on the other hand are those games in which different strategies are applied for different players. At times, it is possible that both the players are working on same strategy but still the game is asymmetric. For example, see the table y below, you will see that both the strategies used by the players are the same still the game is asymmetric. (P. Dasgupta and E. Maskin, p.145). (table Y)

Zero sums and non-zero sum

Under a zero-sum game the benefit is not restricted to one player. Each time a new strategy is introduced, a player benefits at the expense of another player. Poker is the best example of zero- sum player, where the player wins only when its opponent loses. Some other popular games utilizing the zero sum strategy are board games like chess.

Non- zero sum games are the ones in which the outcome is either greater than or less than zero, and it is not necessary that a player gains with the loss of another. (Bowles, p.55-58). (table Z)

Simultaneous and sequential

Under a simultaneous game, both the players keep on revising their strategies to make the other player unknown about their next action. Sequential games are those games in which the player has some idea of the strategy that will be applied by the other player, and then he makes his strategy accordingly. In this scenario, even little information would work for the strategy making.

In the direction of demonstrate simultaneous playoffs usual form is utilized and to represent sequential games extensive form is used.

Perfect information and imperfect information

Another important game that players usually play to device strong strategies is the perfect information game. In this the players make their strategy after deeply studying all the strategies made by their opponents in the past. In this they know all about their possible actions in the future. The strategies coming out of perfect information are extremely beneficial and they always give the player a strong outcome.

Infinitely long games

These games are won only those who have constructed a winning strategy for themselves and are able to display it properly in a set of appropriate actions and movers. The player wins only when his moves are completed. The secret to success in these games is to keep on bringing changes in your strategy so that your opponent is unable to predict your course of actions. (Gale, D. and F. M. Stewart, p.175).

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Uses of Game Theory in Academic Disciplines

Game theory was first introduced in economics to develop deep understanding of economic behavior existing in markets, consumers and firms. Later on, the use of game theory was also made in other academic disciplines like sociology, psychology and politics.

Game theory has also been used to identify the animal behavior by Ronald Fisher in the 1930s. And, the use of of Game theory in environmental science was at length completed by John Maynard Smith inside his volume Evolution as well as the Theory of Games.

Apart from all this, Game theory has also been used to analyze and explain ethical and normative behavior. Different theories have come out which define ways to apply good and proper behavior.

Political science

Within political science game theory has been used to appreciate plus analyze fair separation, following financial system, community option, war negotiate, optimistic political hypothesis in addition to communal choice hypothesis. All these areas have been deeply studied by scholars and researches and have been implemented with interesting Game theories.

Some of the early game theories invented were in the year 1957 by Anthony Downs in his book under the name of An Economic Theory of Democracy. In his book, he has explained how the politician candidates can use hotelling firm location model to create policies and impressive ideologies. Some of the new work completed on Game theories as a biased science is by Steven Brams, George Tsebelis, Gene M. Grossman as well as Jeffrey S. Banks, David Austen-Smith and Elhanan Helpman.

Many game theories have been invented that define ways of attaining democratic peace. The game-theoretic explanation defines the benefits of keeping promises and means of getting rid of disputes. (Anthony, p. 98-100)

Economics and business

Since many years, game theory has been a significant part of economic and business studies. Applying game-theoretical explanation in economic phenomena’s is the favorite act of economists. Some of the places where games theory is effectively applied are auctions, bargaining, duopolies, fair division, oligopolies, social network formation, and voting systems. Mostly, in all the game theories efforts are made to achieve equilibrium and rationality by creating several solution concepts. Nash equilibrium is applied in non-cooperative games. With the Nash equilibrium all the players can invent their set of strategies and attain payoff on them, the payoffs are usually in the form of money.

Biology

In biology the outcome received from game theory is related to fitness. The best part of application of game theory in Biology is that it does not pay much attention to equilibrium or rationality rather it deals with the evolutionary forces.

The first ever use of Game theories was made to understand the evolution of sex ratios, claiming it is an act done by individual’s whishing to increase their number of grandchildren.

The biologists have made use of the evolutionary game theory and the ESS to understand how animals communicate amongst each other. Many signaling games and several communication games have been invented to analyze the communication process between animals. Biologists have also invested the game of chickens to study the fighting behavior of the animals. Many researchers are of the view that game theories are more applicable on biology than economics. Maynard Smith in his book Evolution and the Theory of Games said that game theory defines the natural phenomena’s better than the upcoming market trends. (Maynard Smith, John, 142),

Computer science and logic

Game theory is repeatedly used in logic and computer science. Many of the theories have game semantics in them. Computer scientists with the help of game theory have also invented many interactive computation systems and online algorithms. The most interactive game was invented by Ben David in 1994 defining k-server problem, a game with moving costs and request-answer games. Yao’s principle is another game theoretical dame that defines computational complexity of randomized algorithms, and especially of online algorithms. (David, Borodin, Karp and Wigderson, A., 75).

Philosophy

Game theory is also commonly used in the concepts of philosophy. In the past two papers of W.V.O. Quince and Lewis that came out in 1970’s made extensive use of game theory in their research. The technique of coordination games introduced in these research papers was later on used by many philosophers like Lewis, Grim, Kokalis, and Alai-Tafti et al. In 2006, Bicchieri developed theories of social norms that deeply defined Game theories in accordance with Nash equilibria. These theories were basically a mixture of mixed-motive game into a coordination game.

In ethics, many researches have been made efforts to define the war going on inside a person regarding morality and self interest. The theories made for ethics have highlighted the importance of cooperation. Several theories like evolutionary game theory have been used to define the changes taking place in a person’s attitude on experiencing several animal behaviors. Some of the games supporting these theories are Prisoner’s dilemma, Stag hunt, and the Nash bargaining game.

Criticism of Game Theory

It is true that game theory is applicable in many situations; still game theory is criticized on several points. It has been pointed out many times, that game theory is of help only when you are trying to assume realistic behavior and also only when, all the actions done are rationalized as self-interest acts.

A major difficulty faced with game theory is that the theory states the players have to know the entire action plan of its opponent. The player should be aware of all the factors and variables that can create an impact on the strategy and the outcome. This is realistically not possible.

Game theory targets rationality. In the traditional game theories we see that the players have been asked to maximize their payoff every possible way in name of rationality. The players are not supposed to stop their counter attacks no matter how harmful they may prove to the other player. However, in some modern game theory models like cooperative games we see that both the players are motivated to keep a cordial relationship with each other. But again, this is criticized on the basis of rationality. How can you cooperate with your opponent when you are taught in the initial phases of the game to win the game by taking advantage and misleading your opponent?

One thing that game theory teaches us is to loose the game initially. Like this, you will come to know how you’re opponent acts and the strategies he applies. During the previous one – shot game the opponent revealed his outcome and full knowledge of strategies devices. Utilizing this information, you can devise a strategy that can lead to the doom of the opponent.

Under the cooperative game theory, the players are asked to reveal maximum information about their strategy. At times when players are unwilling to do so, one of the players manipulates them to reveal information. With this information, any of the players can create their own leading strategy resulting in deep loss of other players. The players often become so self-centered they do not only make you loose the game but also create a negative impact on your reputation.

Is it rational to trick your player into giving information and then devising a strategy against him?

Conclusion

Through this report we have seen that game theory studies different ways through which strategies can be applied by the players to produce effective outcomes with respect to the needs and demands of those players. The importance of game theory has expanded to a great extent throughout the years from being used in economics and businesses to biology and physiology. With the application of game theories many successful strategies can be made and huge profits can be earned.

References

Anthony, Downs. “An Economic theory of Democracy”, New York: Harper, 1957.

Bowles, Samuel. “Microeconomics: Behavior, Institutions, and Evolution”, Princeton University Press, 2004, ISBN 0691091633.

David, Gale and Michael, F. Stewart. “Infinite games with perfect information; Ann Math Studies, 1953.

Dasgupta, Partha and Maskin, Eric. “The existence of equilibrium in discontinuous economic games; The Review of Economic Studies”, 1986.

John, Harsanyi. “An equilibrium point interpretation of stable sets; Management Science”, 1974.

Shoham, Yoav and Leyton-Brown, Kevin. “Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations”, New York: Cambridge University Press, 2009, ISBN 978-0-521-89943-7.

Shai, Ben. Allan. Borodin, Richard. Karp, Goc. Tardos and Wigderson. “On the Power of Randomization in On-line Algorithms“, 1994. Web.

Von Neumann, John and Morgenstern, Oskar. Theory of games and Economic Behavior, John Wiley Science Editions, Princeton University Press, 1964.

Weibull, Jorgen. “Evolutionary Game Theory”, Cambridge MA; MIT Press, 1995.

Appendix

Table X

Player 1
chooses Left
Player 2
chooses Right
Player 1 4, 3 1, –1
chooses Up
Player 1 0, 0 3, 4
chooses Down

Normal form or payoff matrix of a 2-player, 2-strategy game

Table Y

E F
E 1, 2 0, 0
F 0, 0 1, 2
An asymmetric game

Table Z

A B
A –1, 1 3, –3
B 0, 0 –2, 2
A zero-sum game
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