GAME THEORY: In the field of mathematics game theory describes itself as a main feature. It gives output of complex problem related to rational entities where demands are strictly fulfills to produce the result. The main part of application of game theory are science, arts, medical, engineering, computer science etc. etc. it directly addresses the outcome on the basics of decision makers.
So what is game theory? In the broadest terms, game theory analyses how groups of people interact in social and economic situations. There are two main branches of game theory: co-operative and non-co-operative game theory. Most of the research in game theory is in the field of non-co-operative games, which analyses how intelligent (or rational) people interact
Decision variables. In a linear program, the variables are a set of quantities to be determined for solving the problem; i.e., the problem is solved when the best values of the variables have been identified. The variables are sometimes called decision variables because the problem is to decide what value each variable should take. Usually, the variables represent the amount of a resource to use or the level of some activity. For instance, a variable might represent the number of acres to cut from a particular part of the forest during a given period.
Game theory is the science of strategy. It attempts to determine mathematically and logically the actions that “players” should take to secure the best outcomes for themselves in a wide array of “games.” The games it studies range from chess to child rearing and from tennis to takeovers. But the games all share the common feature of interdependence. That is, the outcome for each participant depends on the choices (strategies) of all. In so-called zero-sum games the interests of the players conflict totally, so that one person’s gain always is another’s loss.
Throughout history, dating back to 3600 BC, games of chance and gambling have existed ("Introduction- Gambling and Probability"). Since their invention, people have tried to decipher ways to predict the outcome of such games, thus a need to determine the likelihood of winning in games such as these evolved. The method created to suit this need is known as probability theory. Probability theory has been developed over hundreds of years, and is used to predict possible outcomes and assist in daily life. Probability has been developed and studied over time, and has been formed into formulas and theories that allow it to be used in a myriad of applications.
The tennis prediction model is developed to evaluate the chance of winning match that the players will face. When a game is played, the result depends on many factors including the playing environment, player’s skill and past match results. Many approaches such as statistical data evaluation have been used so far. But predicting the theoretical outcome of tennis matches is a challenging task and has been a keen interest for many researchers. Indeed, enough scope is there for making significant improvement in the quality of prediction and the interpretation of results.
A game in which players assume the roles of characters in a fictional setting. 5- Dice Games. Are games that use or incorporate one or more dice as their sole or central component, usually as a random device. 6- Strategy games. It’s a game where player make a plan to know the limits of the game and to determine how to win it, Like Chess.
Game Theory By Trevor Chow Introduction Game theory is a branch of mathematics, which uses mathematics and mathematical models to study strategy and decisions between logical decision-makers who need to make competing choices in a strategic game. A strategic game is a term to describe a situation where several logical decision makers face different choices of action, whereby they may win or lose depending on their choice and other’s choices. These strategic games are often situations of uncertainty, as the decision makers do not know what choices the other decision makers choose to make. There are many types of strategic games, for example • Two-person zero-sum game: one’s gain will mean another’s loss (used for military strategy) • Many-person
But other fields which are complex to understand and have many variables, we cannot design theories to explain it. The reason being a lot of facts need to be collected to actually test the theory. Suppose we were trying to predict the score of ball game then we would need to know the all the rules of the game and the mental and physical state of the players at the exact time the game was being played and their individual level of skills precisely at every moment. In reality we cannot possible know the exact facts. But a theory could be created to ascertain the score with the information available to us but the exact score cannot be predicted because all the necessary facts cannot be acquired.
Game Theory and the Prisoners’ Dilemma Strategic Rationality In this chapter, Daniel Little indicates that under circumstances of uncertainty and risks, decision-makers attempt to maximize utility through collecting information of the utility and analyzing the probability of each feasible choice. Finally the maximum expected payoff of outcomes is given to the decision-maker since all other decision makers also made the rational decisions. Also strategic rationality is embodied on interactive social behavior that these individual decision-makers make choices regard to predictions about the other decision-makers’ next move in performance, the choices that other agents made lead to the level of outcomes that individual decision-maker would receive. Generally speaking, individual choices are made from strategic interaction and under circumstances of uncertainty.