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Application, Framework and Problem of Game Theory

Introduction

Game theory involves rational behavior in making decisions. It is similar to a game. A game could be interdependent and involve agents or players who try to get the best possible results from the action they choose to take. The players use a sociological or psychological viewpoint to make decisions. The final payoff depends on the action taken by all the players in the game. On the other hand the game could be non-interactive and an individual has to make a decision. The viewpoint used in a non-interactive game is rational instead of psychological or sociological. Reville defines game theory as a mathematical analysis of a situation that involves ‘conflict of interest with the intent of indicating optimal choices leading to desired outcome’ (Fong, 2005, p. 6).

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Application of the Theory

The theory was established from competitive scenarios of games such as chess, draft and so on. The games involve a number of players and each makes a decision depending on the move that the other player makes. In game theory the problems are referred to as games and the participants are called players. The techniques applied in the competitive situations are not limited to those situations. Therefore game theory deals with a problem in which the players depend on what other players do to make their strategy. An important point to note is that the main aim in the game theory is not to win but to come out with the best outcome possible, this might seem contradictory because in a normal game the aim is always to win. However this is not a typical game scenario but a concept. The main aim is to avoid the worst outcome (Fong, 2005, p.6).

Theoretical Framework

The theory is applied in many fields such as, politics, science, economics, computer science, military, evolutionary biology and so on. In life there are many situations that require interdependent decisions to be made. For example in a business environment, choosing the kind of house to live in, choosing a car to buy and so on. One has to consider the pro and cons of every decision they might make. For example when buying a house one needs to consider its location in terms of security, availability of social amenities, distance to ones place of work and many other factors. Likewise, when in a problem one needs to think strategically by using available information to make the best plan so as to get desired results. In economics there is the concept of cost benefit analysis that is used when one has to make a decision between many options. Similarly game theory uses this concept but extends to interdependent decisions. In this case decisions are made by evaluating actions of other players.

Classical Economists

John von Neumann came up with the theoretical framework of game theory during the early 1920s and 1930s and linked it to economics by highlighting its utility. In a paper he presented with Oskar Morgenstern in 1944 they looked at the games involving multi-players and the strategies they had to use to cooperate so as to make winning coalitions. This work was vital in leading to deeper understanding of game theory in economics, biological evolution, social studies and industrial standards (Emerick, 2009, ¶ 6).

Problem of the Theory

Professor Aumann also made his contribution to game theory. He gave a technical definition of the theory. It is an interaction between a number of entities who are pursing different outcomes and the games involve a strategic plan of action. He pointed out that economists have a particular theory that they apply in markets but game theory is applicable under any situation. It only calls for the understanding of incentives. For example Vickery William came up with counter-intuitive idea in auction where the bidders paid only the second highest bid. The change in strategy got the auctioneers more, than the highest bid would have; because the bidders were made to reveal their preferences more accurately (Emerick, 2009, ¶8).

Classical economists are of the notion that people should be allowed to use their own devices. This will give them freedom to make selfish choices that will result in a competitive economy. However, game theory changed this assumption using its concept of rational decisions that people make. The decisions are selfish and can be predicted by the game theory. The Traveler’s Dilemma, a game made up by Professor Kaushik Basu from Cornell University undermines the proposal of a competent economy due to selfish decisions and rational choices proposed by game theory. In the dilemma Lucy and Pete on a return journey from a holiday discovered that the airline had damaged a vase they had each bought. The airline agreed to compensate them if they wrote down the value of the vase without consulting one another. The value was to be between $2 and $100. Whoever wrote a higher value would be fined two dollars for dishonesty and the one with a lower value would get two more dollars for display of honesty. If they picked the same value it would result in compensation for that value as it would be assumed to be correct. Therefore they had to pick a value that would give them the best pay offs. In this case if they decide to pick a high value they might end up losing and they would have deviated from rational thinking. For example if Lucy picked $90 and Pete $50 she would get $48 and Pete $50. Therefore in this situation the best decision would be irrational that is picking lower value. However, most people would not choose the smallest value of $2 that the game theory predicts due to the inability to do deductive reasoning (Playing Game Theory, 2008, p.13).

The other explanation for such a choice would be selfishness and altruism. Some people may not want to let down their fellow players by making moves to earn the additional dollars. On the other hand some ignore the logic behind game theory and choose a large value because they assume the others will make similar choices. Therefore we can say that game theory has a certain weakness. People do not always choose actions as the theory predicts they would. Experiments done at the University of Virginia showed that it is very common for people to act in irrational ways according to game theory standards. In an experiment dubbed ‘travelers dilemma’ two students had to choose numbers from a given range. The two would get cash equivalent to the lower number chosen. Both would get an equal amount if they picked same numbers. The twist to the game was that whoever chose a higher number had to pay a penalty of $5. They played simultaneously and had one chance to play. This was aimed to discourage them from cooperating, if they used Nash theory each would have chosen the least in the range to avoid the penalty. However in the experiment most of the students went for the highest number to increase their outcomes. They did not get the highest payoff because the other player predicted the action the other would take and both took contractive actions therefore both missed out on a big pay off ( Coy, 2002, p.28).

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Rationality

For there to be a game the players must be economically rational. A player should be able to access outcomes, calculate courses that lead to outcomes and pick actions that are likely to yield the highest outcomes based on the actions of the players. In every game every player faces a choice. Therefore a strategy is required to enable the player know the action to take based on the actions the other players may choose to take. To illustrate this point lets us look at the 2000 scenario of four telecommunications companies. The four companies paid over £22 billion to acquire licenses to operate a third generation mobile services (3G) in Britain. The amount was high and surprised many. Economists Ken Binmore and Paul Klemperer had used game theory to design the auction. They knew that the theory would twist the rules to fit into the criteria the government had set. The criteria was; ‘to assign the spectrum efficiently, to promote competition and to “realise the full economic value”, that is, get the highest price for the Government.’ (Frary, 2009, p.55). The companies participated in the bid, and by the 150 round the best bidder was found and the final sale was an enormous figure because the game theory paid though only the government felt happy about the income.

Dominant Choices

In the game theory we have dominant choices. This means that the strategy has payoffs in spite of choices made by the other players. To explain this point, we shall look at the famous prisoner’s dilemma. In the narrative two individuals are arrested for committing the same offense. They are interrogated independently and offered three choices. One, if a prisoner confesses they get a three year sentence. Two, if only one confesses and the other prisoner remains silent he will be freed and used as witness against the other who will get ten years. Three, if both confess they will be charged with minor offence and get one year each. In this case each prisoner will see that they need to confess. This is the dominant strategy for both. It is supposed that the prisoners will use logic to make the best plan that will ensure they both get the best outcome. On the other hand if the prisoners could get a chance to communicate then they would come into an agreement that it is better to confess which has the best payoff. They cannot get this chance as the decision they are making is simultaneous. This leads us to the next point about cooperation in game theory (Fong, 2005, p.6).

Cooperation

Cooperating in a game may be beneficial to the players. This is because cooperating with other players can make sense, for example in price wars to enable competitors to continue enjoying a profit, joint tender and so on. However, this corporation can lead to cartels. The Swedish government used game theory to put an end on cartels in road surfacing tenders. In this game players need to trust one another. In the prisoners’ dilemma if the two prisoners had a chance to interact they would know the best decision to make. Hence they would make a pact and would have to trust that the other prisoner will not bail out and confess against them which would result in getting ten years. (Frary, 2009, p.55).

Conclusion

Game theory is important in our society. It guides people in making decisions. Thus people make decisions that they think are the best for them. The cooperative concept of the game can be used by countries that are making trade agreements to ensure that both countries benefit. The theory is very important in determining prices in the market thus fair competition is maintained. On the other hand game theory may be construed as a proponent of selfishness because the players always aim for the best outcomes at the expense of other players. However the game theory shows us the most likely outcomes of actions because being forewarned is better than being armed.

Reference list

Coy, P. (2002). Game Theory’s Hidden Holes. Business Week, p.28.

Emerick, N. (2009). Game theory has a host of practical applications Business Day Edition.

Fong, P. (2005). Game theory. The Globe and Mail Canada, p. A6.

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Frary, M. (2009). Game theory keeps serious company in the real world. The Times London, P. 55.

Playing Games (2008). The Irish Times, p.13.

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