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Game theory is a theoretical analysis or strategic decision making tool in which the economic agents produce outcomes by making strategic interaction among them. Mainly Game theory is the interdisciplinary approach for the study of human behavior, which involves mathematics, economics and other social and behavioral science. Game theory, computational theory and so many other contributions related to game theory was founded by the great mathematician John von Neumann. He also wrote the first book on game theory that was "The theory of games and economic behavior" with the cooperation of the great mathematical economist of that time Mr. Oskar Morgenstern. Game theory is mainly used for strategic decision making process between the two or more players and its descry

7iuibes how their strategic decision making process affects the other participants. One of the major applications of game theory is that it provides strategy for how to make business and government decision and for real world application.

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Prisoner's dilemma is the highly used game theory strategy in the social science. It helps in develop the strategy of how to maintain the balance between the cooperation and competition in business, in politics and in social settings. The prisoner's dilemma has also applicable for making strategy for economics and business. According to Adam smith prisoners dilemma appears when each individual in the game will be more concern about their private interest and not able to promote the collective interest in the group. Taking the example of the two firms Pepsi and coke, which are selling similar products? Each firm having their own decision about the pricing strategy and they both will always try to utilize their joint market power when they both increase their price.

Suppose when while making high price , each get a profit of ten million dollar per month. In this situation if one firm seta a lower price than other, then that particular firm having lower price will be able to get more of customer from the rivals and automatically it profit will be rises than the other firm. Suppose its profits rises to twelve million and that of rivals' falls to seven million dollars. On the other hand if both the firm Pepsi and coke sets the low price strategy both will get the profit of nine million dollars. So in this case the conclusion can be drawn is that the lower price strategy leads to the prisoner's confession and the high price strategy leads to the prisoners to keep silent. If we consider the first strategy as the cheating and the later one as the cooperation, then the cheating is the dominant strategy of each firm upon the others and the later one is considered as the cooperation. So finally it can be concluded about by taking the consideration of the two firms Pepsi and coke is that cheating is the dominant strategy for any firm and when both will cheat is the worst situation than that of when both will cooperating(econlib,4th January).

## Dominant strategy Game

If a player in a game chosen the same strategy for each of the different combination of strategy the player might face the new strategy, which is called as dominant strategy for the particular player in that particular game. This is happens when an individual player evaluate the strategy combination he may face and try to choose the strategy which will gives the best payoff to that particular individual.

Dominant Strategy Equilibrium:Â

If in a particular game each player has the same dominant strategy and they play also the same dominant strategy then that combination of dominant strategy with respect to the payoffs of that particular game is called as the dominant strategy equilibrium for that particular game. For example in the prisoners dilemma game to confess is a dominant strategy and when two player confess combine that situation called as the dominant strategy equilibrium (Faculty.lebow, 24th June 1999).

## Assumption of Game theory

Game theory mainly used in strategic decision making process during the conflict situation by mathematical analysis. It helps in develop an finest strategy by mathematical process in the face of a rival who has his own strategy. For developing the optimum strategy following assumptions can be developed.

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(1) Every individual decision makers or players should be available with two or more well specified choices or sequences which is called as plays.

(2) The second basic assumptions for game theory is that each possible combination of plays available to each player should be lead to a proper end state for the game that is might be the result of the game win, lose or draw which helps in terminate the game successfully.

(3) The third assumptions states that there should be a specified payoff for each player associated with each end state of the game, which means the sum of payoffs for all players will be zero in every end states.

(4) The most important assumption is that every decision maker must have the perfect knowledge of the game and about his position in the game.

(5)The last assumption sates that all decision makers involved in the game should be rational or balanced, which means each player given two separate alternatives and they select the one best alternative that give them the greater payoff(Cleamc11,N.D).

## Literature review

Game theory represents a set of strategy that is used in the process for decision making in the situation of competition and conflict as well as cooperation and interdependence under specific rules. It mainly represents the situation in which two participants get the choices of action by which each individual may gain or lose depending upon the strategy chosen by the other participants. The final results of the game can determined by the analyzing the strategies adopted by all the participants. There is also situation of uncertainty because no participants aware about what other participants going to decide. There are various types of game theory adopted by different economist which gives different strategies. Some are like

Two person zero some games - Its mainly used by the military strategists. In this game one must gain and others loose.

Many person game - Its mainly used to study the economic behavior.

Prisoners dilemma - Its mainly used in the conflict situation of political theory and union negotiations. In this type two players or participants have choose their action of strategy without communicating without communicating with each other to cooperate or betray(Business dictionary,23rd April 2012 ).

Except these there are two main branches of game theory considered that is cooperative and non cooperative game theory .

Economic theory of game has its three main major branches such as decision theory, general equilibrium theory and mechanism design theory.

Decision theory - This theory mainly used in the process of decision making in a conflict situation, which gives an idea about how suitable information can be acquired before taking a decision. This theory mainly focuses on preferences and formation of beliefs.

General Equilibrium theory- It is the branch of game theory which deals with trade and production and high numbers of individual consumers and producers. It is mainly used to analyze the macroeconomic and other broad based economic policies such as monetary and tax policies. .

Mechanism design theory- Mechanism design theory is different from game theory about the consequences of different types of rules. Mainly game theory used the riles that has given and decided prior but in mechanism design theory it asks about the consequences of different types of rules (Dklevine, N.D).

## Application of game theory

Game theory used to develop strategy about how business and government decision can be made. For example by the help of game theory economist able to analyze antitrust policy, tariff wars and auctioning behavior. Game theory mainly comprises three basic elements these are

The players

The strategies available to each player

The last element is the payoffs of each player receives.

Payoff matrix - The above three elements summarize together in a table and it is called as the payoff matrix. A payoff matrix is a matrix which describes the payoff of each player for the combinations of the strategy given to the players or chosen by the players. The discussion continue about the pay off matrix by taking the example of two companies Pepsi and coke and their advertising strategy in terms of payoff matrix.

## COKE

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80, 80

120, 45

45, 120

100, 100

Here in the above table the first two numbers in the square in the horizontal line represents the payoff of the row player that's here for coke and the second two numbers in the vertical line represents the payoffs of the column player that's here we consider for Pepsi company.

Description about the game - Here in this game

(i)There are two players participating that is Pepsi and Coke. The strategy available to each player is that Pepsi being the row player can either choose advertise or don't advertise strategy and coke being the column player can either choose the advertise or don't advertise strategy

(ii) The payoff received by each player are

If Pepsi choose advertise and coke choose advertise strategy then both will earns 80.

The second payoff is that if Pepsi choose advertise strategy and coke choose don't advertise then Pepsi earning 120 and coke earning 45.

Other case Pepsi earns 45 if it chooses doesn't advertise and coke earns 120 when it chooses the advertising strategy.

While Pepsi and coke both earns 100 when they both choose don't advertise strategy.

Dominant strategy for this Game -

Dominant strategy is the best strategy followed by one player apart from the strategy followed by the other one.

Dominant strategy for Pepsi -

In this game with the two players Pepsi and coke the dominant strategy for Pepsi is to choose advertise. Because Pepsi earns more by choosing the advertising strategy apart from the strategy chosen by the coke.

Pepsi earns 80 by choosing advertise while coke chooses advertise which is greater than for earning by choosing don't advertise for Pepsi.

While Pepsi earning 120 by choosing advertise while coke don't advertise, which is good and greater for Pepsi than earning 45 by choosing don't advertise.

Dominant strategy of coke -

Here the dominant strategy for coke is also to choose the advertise. This is because coke earning more by choosing advertises regardless what strategy Pepsi choose.

Coke earns 80 by choosing advertise which is greater than 45 for coke by choosing don't advertise while Pepsi choosing advertise.

One more profit coke gaining is that when Pepsi chooses don't advertise coke earning 120 by choosing advertising which is greater than earning 100 from choosing the don't advertise strategy(Scribd,2012).

## Conclusion

Game theory is strategic analysis and decision making tool which plays an important role in economic analysis by the various economists. The concept behind game theory is very exciting because the principles for game theory are simple but its applications are very important especially in taking interdependent decision and almost any effort and effective decision taken by the self interested agents and cooperate agents. The most interesting game in the game theory is communication where so many layers of strategy are possible. The application of game theory extended to design probable commitments, threats or promises and to asses proposal and statement offered by others.

## Criticism and Future Direction

There are many criticism regarding game theory has been reviled by different researchers and economist. First of all game theory sometimes judged to have failed , because some game gives solution and some games unable to provide any solution and those who provides solution ,sometimes provide too many solutions for a single problem which creates confusion. According to Bacharach (1976) the failure of game theory to give a definite or particular solution does not implies the flow of inadequacies in the theory. He states that it's the natural thing and we cannot expect unique and rational answers all the time in a complex irrational world. Aumann (1987) stated that" Game theory itself has no moral content and it makes no moral recommendation, it is ethically neutral".

On the whole the game theory has a bright future which has been proved by the recent development of game theory in economics that is the discovery of new Nash equilibria(such as Markov equilibrium used to study the common resource problem), enhancement of equilibrium concepts ( for example the stability concept used to study signaling in markets) and discovery of evolutional game theory which is an exciting and new field in studying social conditioning and behavior selection(Jamus.name, 1999).