Game Theory for Applied Economists - Essay Example

Game Theory for Applied Economists Game theory is one of the most famous theories in the modern era. It has been popularized by the recent usage of this theory in a number of arenas. This fact makes this theory very important from the point of view of significance. It is a very formal study of conflicts and the cooperation. This concepts come into the application whenever, the actions of multiple agents seem to be inter-dependent in nature. These agents may be in the form of a group, a form, an individual or any of them. The concepts of game theory that are inherent in it are many. It helps in the provision of a language for the formulation of a structure, analysis and the understanding of the scenarios from the view point of strategy. This is very helpful in the formulation of the necessary strategies of the business. EXAMPLES OF GAME THEORY-EARLY CONTEXT AND DEVELOPMENT One of the earliest examples of game theory can be seen in the studies of Antoine Cournot in the year 1838. It studied the example of duopoly in the context of a formal type of game and theoretical analysis. The formal theory for the games was brought into the forefront by the mathematician Emile Borel, who had the suggestion of a formal theory of the games by the year 1921.It, was further developed by the likes of mathematicians like John von Neumann in the year 1928. The field of game theory was established as an entity in its own right after the publishing of seminal book called as Theory of Games and Economic Behavior by the likes of Vo Neumann and the economist known as Oskar Morgenstern (Binmore 114). It also received a lot of fillip from the studies of mathematician John Nash who demonstrated that the finite games have any equilibrium, wherein all the players choose the option that is best for them keeping in mind the action of the fellow players. This is a fundamental unit of the design element that can be seen from the studies of these individuals. This concept of non-cooperative game theory was broadened by the application in the year 1950 and 1960’s. t has always been a central point for discussion. It has been applied to the areas of politics and war. This is one of the centralized concepts of this theory. It has also been accepted in the fields of sociology and physiology. It is also seen in the field of biology. These are some of the common points of the relationship that find mention in the development of theories. It received a lot of attention with the awarding of the Nobel Prize in the field of economics to the likes of Nash, John Harsanyi, and Reinhard Selten. At the period of 1990, it was seen that the game theory was being increasingly used in a number of the fields. It is being prominently used in for the designing of auctions. It is being designed in such a manner that there is the distribution of maximum benefits for the population. It has also developed a level of understanding in terms of the number of the division of electromagnetic spectrum to the telecommunication firms. The usage of this theory has helped in raising billions of dollars in a number of governments. GAME THEORY AND INFORMATION SYSTEMS The level of internal consistency and the basis of mathematics make it one of the primary tools of the modeling and design of many of automated processes of decision making as a part of interactive environments (Fudenberg and Tirole 173). As for example, one of the examples was setting up of efficient rules for the bidding process, websites, and the generation of tamper proof negotiation that is useful in the purchase of communication bandwidth. The automation of strategic choices is necessary for making the choices to be robust in nature. This is helpful in the avoidance of any kind of manipulation in the process of bidding and guards against any kind of abuse form any of the users. The strength of game theory comes from the process of structuring the problems in a way that all the options become clear. The process can be seen in the formal designing of a model; can be used to address the problems. The choices of the players can be explicitly analyzed by the players and the preferences for each of them can be decided. Thos model provides the decision maker with the ability to make a wider variety of decisions. It is also very helpful in making a number of decisions by keeping all the parameters in check. A model can be constructed that allows the decision maker with the ability to make a clearer and broader view of the existent situation. It can be seen as the “prescriptive” model of game theory. The basic principles of game theory have been explained with all the associated areas that the application can be found. THE DEFINTION OF GAME- A STANDARD IDEA The object of the study in game theory is a game. It can be seen as a formal model for any kind of interactive situation. There is involvement of more than one player in this theory, with only one player; it is called as a decision problem. The definition can be used for lying out of the plans, the options available at the strategic level, and the influence of the outcomes that can be seen from each of these levels. MEANING OF GAMES The object of study in game theory is the game, which 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 (Myerson 137). The formal meaning lays out the players, their preferences, their information, and the strategic actions available to them, and how these affect the outcome. There are a number of ways of classifying the games. There are various details of a game. A coalition (or any kind of cooperative game), is a high level description, that specifies the potential for each of the groups, the coalition, the description at a higher level and the specification of the payoffs for each of the groups. In a way, the process of formation of the coalition is not explained. As for example, the players can be seen from multiple parties in the parliament. The strength of each of the parties is determined by a particular number of seats. Now, the game theory can be used to find out the possible combination of each of the parties, so that the desired results can be achieved. Also, it does not exclude the possibility of a group of parties voting en-bloc for a position. The cooperative game theory is used in the investigation of a cooperative game theory discussed in respect to the power being held by various players, or how much of the proceeds should be divided by the coalition (Gibbons 43). This is a situation that can be seen as a part of political science or in international relations, where the concepts of power are seen to be extremely important. This is used in discussion of the concepts of power, making it a very important part of the study. Nash had proposed the division of power among the parties depending on the strength of bargaining of involved parties (Nasar 97). The power of the parties is determined by the outcome that can be seen when the negotiations break down. This answer fits well within the framework of cooperation, but it does not take the periods of offers and counter offers into the picture. It only takes the bargaining as a part of the discussion. The non-cooperative game theory can be seen as a part of the analysis of strategic kind of choices. The process of non-cooperative theory is based on the details of ordering and also the sub sequential timing of the players. It is very crucial to the outcome of any game. It is in contrast to the non-cooperative model of Nash, where the non-cooperative model would be a process, wherein the offer period would be specified. The non-cooperative model would explicitly be a part of the process where the players make the choices out of their own interest. But, cooperation can be seen, and often arises as a part of many games, when the cooperation by any player is seen to be in the best interests of the players. There are a number of inherent assumptions in game theory. One of the assumptions is that the players are rational in nature. So, the players are seen to play in manner, where the most rational behavior is seen to be based on the outcome favored by him the most. This is also in tandem with the behavior expected from the other players. There is another model that is being developed here; this is called as the “observed behavior” model. This is based on the “descriptive” model of thought, rather than being the “prescriptive” model. STRATEGIC AND EXTENSIVE FORM OF GAMES The strategic form (also called as the normal form) is seen as the basic type of game that is a part of non-cooperative theory. A game is a part of the strategic form of each player’s strategies; and the outcomes are decided by the play-off for each of the players. The outcome of each of the players is represented by separate payoffs for each of the players, and also a number that represents how much an outcome is liked by each of the players. There is an extensive type of strategic form called as game tree, which is an exhaustive form of a game. It has the complete description of how a game is played over a period of time. There is the inclusion of action of the players, the information possessed by each of the players, the time for the resolution of any kind of uncertainty present in any situation along with the other allied factors. The extensive game form can be analyzed in a direct manner, or it can be simplified into a strategic form. The examples of each of these strategies can be explained in the following pars. They are as follows- DOMINANCE The players are assumed to be rational in nature. Thereby, each of the players has a particular strategy that they play the game with. In some of the extreme case, a player has more than one option. It can be assumed that the outcome from the option A is better than option B. So, the strategy A is said to better than strategy B in principle. So, a suitable strategy has to be given. Any rational player would not play a dominating strategy. In some games, there is an examination of strategy, where the players can choose only one of the options. As for example, it can be explained with the help of following examples. Prisoners Dilemma- There is one example of this situation that is very famous. Let us suppose, there are two prisoners who have been accused of serious crime. There is no evidence against them, except the testimony of each of the prisoners. If one of the prisoners testifies, they shall be awarded with the immunity. The other person shall serve a long time in prison. However, they both can “cooperate “with each other by not testifying against themselves. So, they will serve a short prison term. So, there are two options, one win which the prisoner can testify no matter what the other prisoner does. And, the other option is mutually beneficial wit lower individual results. So, this classical situation represents the “prisoner’s dilemma”. There are loopholes in this theory that can be seen from the point of time in this game. If the amount of time is increased, then the degree of cooperation shall also change .There would be obvious effects of other factors like security, past relationship and others. So, a unanimous decision can never be taken as a part of this decision making mechanism. The chances of a different outcome shall increase with the elapsed time. NASH EQUILIBRIUM The consideration of the dominating strategies cannot yield the precise kind of advice to the players on ways to play the game. However, in many of the games, there are no specific dominated strategies. These considerations cannot be seen as enough to have any possible outcomes or any kind of specific rules on playing the game. The concept of Nash equilibrium is much more general when compared to other approaches. It provides recommendation to all the players such that they cannot improve in a unilateral manner. It is based on the premise that each of the players cannot improve in a unilateral manner and each of the players follow a recommendation. If the other players are deemed to be rational in nature, the other players shall also follow the recommendations. EVOLUTIONARY GAMES There can be a different interpretation of the bandwidth game of choice when there is a large population of identical kind of players in the market. The attainment of equilibrium can be seen as an outcome of a process that is dynamic rather than being a rationally conscious in nature. The game dynamics is based on the factor that each of the strategies is enacted by a particular fraction of individuals. So, in this distribution of strategies, the individuals are having a better amount of payoff. Their population increases over a certain period of time. Thereby, the strategies that are better than others get affected over the time scale. In the case of symmetric kind of payoffs, the dynamics is controlled by the better option with higher payoffs. MIXED EQUILIBRIUM This kind of equilibrium is seen when there are chances for more than one kind of payoffs. One of the chances is a preparation for choosing a maximum and minimum kind of strategy. The usage of this strategy maximizes the worst payoffs against all the available choices of the opponents. The mixed strategy is used for the inspection with a certain level of probability. If the context of applications is taken, then randomness is also an option. EXTENSIVE GAMES WITH THE AVAILABILITY OF PERFECT INFORMATION The games in any kind of strategic format have no temporal component attached to them. In case of choice of players, the strategies are chosen simultaneously; without the knowledge of choices of other players. The other detailed form of the game is also called as a game tree. In any game with the perfect information, the players are aware of all the previously available choice of the players. Only one player moves at a time, thereby avoiding any kind of simultaneous movements. ZERO SUM GAMES In the case of players having opposing kind of interests, this kind of game is seen in the case of a two player zero sum game(or called as constant sum games). There are a number of examples of zero sum games that vary from chess to poker. Poker can be taken as an example of zero sum game, where the loss of one person is the gain of another. APPLICATION OF GAME THEORY The game theory can be applied in a number of areas. They range from the fields of biology, political science and economics. It is used to explain and understand a number of phenomenons that include the evolution and stability of sex ratios (Rasmusen 17). This has been explained as the evolutionary impact of individuals trying to increase the number of grandchildren. It is used to elucidate the concepts of selection of species. It is being used in the field of computers, like the areas of in game semantics. It is used in integrative systems an also in deciding of multi field agents. It is also used in areas like philosophy for the development of coordination games. These are the various applications of game theory. REFERENCES Binmore, Ken. Fun and Games: A Text on Game Theory. D. C. Heath: Lexington, 2001. Print. Fudenberg, Drew and Tirole, Jean. Game Theory. Cambridge: MIT Press, 1991. Print. Gibbons, Robert .Game Theory for Applied Economists. Princeton: Princeton University Press, 1992. Print. Myerson, Roger B. Game Theory: Analysis of Conflict. Cambridge: Harvard University Press, 1991. Print. Nasar, Sylvia. A Beautiful Mind: A Biography of John Forbes Nash, Jr., Winner of the Nobel Prize in Economics. New York: Simon and Schuster, 1994. Print. Rasmusen, Eric .Games and Information: An Introduction to Game Theory .Oxford: Blackwell, 2001. Print. SYNOPSIS (STUDY SHEET) The paper has dealt with a number of points that are relevant in game theory. The facts about game theory that have been discussed are highlighted below- • General introduction about game theory. The concept of game theory has been discussed from the context of different disciplines and researchers. • The early development of game theory has been explained in detail. The examples of game theory and the contributions by the scientists have been highlighted. • The game theory has been explained in tandem with the Information systems. The various areas of applications have been mentioned. • A basal idea about the definition of the term game has been given. It shall help us in developing the further premise of the paper. • Strategies and extensive forms of games have been discussed. In accordance with that, a foundation for competitive and non-competitive games has been laid. • The concept of dominance has been explained. As a part of the explanation of the concepts of dominance, the concepts like “ Prisoner’s Dilemma” has been illustrated in a lot of detail. • The definition of “Nash Equilibrium” has been spoken about in this paper. The significance of this equilibrium in determination of dynamics has been explained. • The evolutionary games have been explained. Along with that the mixed strategies have been mentioned. This is a very important area of game theory. • The games with the availability of perfect information have been discussed. This has helped in the formation of a foundation in the field of game theory. • The concept of “zero sum games “have been detailed. This gives a clear idea about the nature of certain games. • The paper concludes with the areas of application of game theory. The application is found in areas like science, biology and philosophy. Read More