The Game theory is one of the branches of applied mathematics which formally studies the ways in which outcomes are yielded by strategic interactions among agents which are economic in nature. The outcomes are produced with reverence to the utilities of those agents and they might not have been deliberated for by any of those agents. The game theory conception is relevant whereby the feat of various elements are co-dependent. The elements may be firms, groups, individuals or either of these factors combined. The Game theory usually endeavors to scientifically and more so mathematically to explain actions in premeditated scenarios where a person triumphs at the expense of others. Game theoretic concepts offer a language to devise, structure, analyze and understand situations that are tactical.The game theory of economics is usually a lot useful to settings with fewer players because every player choice is of importance to his opponents. For instance, when the number of companies in a market is small, it will have a huge impact on the market price and for that reason it is not logical for every company to take the set market prices. This theory was introduced by Neumann and Morgenstern who argued that most problems in economics should be evaluated as games. They established the normal and extensive forms representation of a game which proved that solutions subsisted in every zero-sum game that involved two players. In this game the concerns of the players are directly opposed and the players do not have common interests at all. Later this model was advanced by Nash in 1950 who proposed what is currently called the Nash equilibrium which extended the theory to account for non-zero-sum games. Nash showed that set games usually have a point of equilibrium where all players decide what action is good for them considering the opponents choice. This is the main concept which has been used as a focal point for analysis from1950 to date. The theory applied to predicaments of war crisis and politics in the 1950s and 60s and in 1970 it was applied in social sciences such as Biology and Economics. Aumann (1985) argued that for the last three decades the theory has become one of economist’s major theoretical tools. The theory also led to an uprising in economic theories.
Rubinstein (1990) argued that the game theory revolutionized economics in the eighties. Nash was awarded a Nobel Prize in 1994 for advancing the theory.The Stanford Encyclopedia of Philosophy brings out the point that the Nash equilibrium has been mostly used in finding solutions since it was introduced in 1950. The Nash equilibrium is a type of non-cooperative game whereby a set of strategies stands for strategies with the best response in regard to other strategies. In Nash equilibrium, when every player is playing the strategies, they have no independent motivation to diverge because their strategy is the best taking into considering what the other players are doing. Utility of individual players is characterized by the payoffs of the game. In most modeling situation the payoffs is usually money which matches up to the utility of the individual.The game theory was applied in auctions by the mid nineties where well known game theorists designed auctions for apportioning rights of using electromagnetic spectrum bands to the mobile telecommunications industry which raised a lot of money in the US and Europe. Bianchi and Moulin (1991) argued that the application of the game theory to economic, political and social situations led to many statements which are testable. The game theory has foundation in mathematics and internal stability and thus it serves as a key tool for forming and devising decision making processes that are mechanized in interactive environments. The relevance of Game Theory in research has been the topic of many journal articles and conferences however in these applications there is call for making efficient choices and readiness against abuse constrains that the theory of the game attends to. For instance, Krivka and Ginevicus (2008) conducted a research on the application of the theory on duopoly market analysis. The game theory is strong and acts as a mathematical tool for most decision makers. The decision makers’ can clearly itemize players and their tactical options and to give consideration to choice and inclinations. The theory enables the decision makers to have clear and broad view of the situation. The game thus enables decision makers to make tactical choices.The Game theory is like other modes of economic theories because it is model based. The process of theorizing in economics constructs, analyzes, manipulate models and transfer the results of this to what happens in the real world. Economists mostly use these model as interpreted entities as proposed by Gibbard and Varian (1978). Models thus play a major role in the Game theory. Games such as prisoners, dilemma, the ultimatum and battle of the sexes are some of the games that most people are accustomed to.
Game theory of economics is all the composite elements with which most economists endeavor to explore and clarify phenomena of strategic interaction. There is the game model and theory proper in the theory and within these game models there is game structure and model narrative. The figure below shows the game structure.
This figure above shows a game matrix that represents a strategic form game. There is also a n extensive form game. R1 and R2 at the beginning of the row of the matrix signify the tactics or strategies of a player. The labels C1 and C2 at the top of each column represent those of another. The numbers in the cells show the playoffs for two players and usually called strategy profile. The first number shows the payoffs for the player whose strategies are shown in rows while the second number shows the payoffs for the player whose strategies are shown in columns.
A game tree strategy is made up of branches and nodes. The number at the end of each node shows the player who chooses a move at the particular node. The strategy tree combines all players’ tactics from the first node to the final branch. The numbers found at the end of every final branch usually show the payoff for every player for that particular strategy profile Game Theory. The Net website shows that the applet allows up to four players and up to fourteen periods. The website gives the four steps where a player first picks a model game tree, then he modify the tree to look like ones game, after which he adds payoffs and finally solves. In the second step, the player selects a node and drag it or select the add child option to insert a sub-node or remove node option to get rid of a node.
These game structures are units which beginners are introduced into the game theory. The learners are taught about the player, strategy and payoff function strategies. Their moves may be concurrent or follow a sequence. These matrices and trees comprise of what game theory is all about. These models present the content for game structures and these games structure are constricted by the game theory. This theory identifies the formal components of possible game structures and offers methods to decide the strategy equilibrium in some specific games. Though the game theory of economics works with models, it has a body of theory which does not comprise of models. This theoretical work betrays the theory as a mathematic discipline since it pays much attention to develop equilibrium concepts or existence proof which many game theorists focus on since it is the core of their discipline. Holt and Goree (2001) argued that game theory usually provided evidence for theories and that it was not for playing games.
The game theory application plays a central role and it often leads to empirical statements which are meaningful. The theory terms do not have an interpretation because it is mathematical and theorem proving in nature. It uses terms such as players, utility and strategies but they do not have any perceptive meaning. The theory is widely used in social sciences from population genetics to logic. Fudenberg and Tirole (1991) argued that the textbooks that taught the theory properly concentrated on introducing concepts with a lot of toy examples and general results than applications that are detailed. Most students learn the theory properly and learn a wide range of games. The theoretical part of the theory is the source and constrains game structures.The theory part determines the constituents of the game structures. For instance the theory demands that a game tree has one initial node. The theory thus is the kit from where constituents of the game structure are taken from and also the rules by which the elements are brought together. The theory offer solutions for game structures. Binmore (1991) argued that the theory clearly describes the Nash equilibrium concepts and sub-game perfection for extensive form games.
Game theory has been useful in studying behavior of humans and animals. When it was originally developed it was used to comprehend economic behavior. This has changed and the theory is being used in social sciences such as Political Science, Psychology and Sociology. The theory is important in application in economic situations according to Gibbons (1992). The application depends on the nature of a particular situation. Scholars use the theory in understanding virtues or vices. Don (2008) argued that theoretic arguments date back to Plato’s time. The theory is used in a wide range of economics situations, for instance it has been used in auctions for more than twenty years. The theory is also used to determine the voting systems, duopolies and oligopolies among others.