At its most basic, game theory is the study of how individuals, businesses, or nations (referred to as "agents or players") select strategies in various scenarios in the face of conflicting plans enacted by other agents or players. Game theory presupposes that actors always make rational decisions. That is, they will choose strategies that maximize their own benefits while minimizing their costs.

Game theorists analyze situations using three elements: agents, actions, and outcomes. An agent is any player or entity capable of action. Examples include companies, countries, and individuals. Actions are choices that agents can make within the context of a game. These could be strategic (e.g., attack or defend) or tactical (e.g., hide or seek). Outcomes are what happens to agents after they take actions. These could be positive (e.g., win) or negative (e.g., lose). Agents try to find ways to increase their chances of achieving **preferred outcomes**. Game theorists use mathematics to help them understand these relationships and develop strategies for action.

Game theory has **many applications**. It is used by economists to explain why some markets work well while others do not; by **political scientists** to understand why some countries or organizations are strong while others are not; and by **military planners** to know how to best protect themselves from attack.

In conclusion, game theory is the study of agents choosing strategies in order to achieve preferred outcomes.

The study of mathematical models of strategic interaction among rational decision-makers is known as game theory. It is used in all branches of social science, as well as logic, systems science, and computer science. Game theorists work with abstract models that capture important features of real-world games without being too restrictive.

In economics, a market model is any of several simple economic models that attempt to explain certain observed regularities in the prices and quantities demanded and supplied by markets. They are usually based on the assumption that consumers and producers act rationally within the limits imposed by reality. The most common example is the demand curve analysis which attempts to describe how much people want to buy a particular product at different prices. Other examples include cost-based price analysis, where the marginal cost of producing an additional unit of the good in question is taken as its price; and revenue-based price analysis, where the marginal cost of selling the product is used instead.

In sociology, psychology, and anthropology, game theories models have been applied to understand **such phenomena** as cooperation between individuals in groups, conflict resolution, altruism, punishment, and rights. These applications are discussed in **more detail** under **each topic** listed above.

In mathematics, a game theory is a field of research that studies **mathematical models** of conflict and cooperation between intelligent agents (i.e., players).

Strategy emerges from competition in any of **its numerous forms**. Game theory is an area of applied mathematics that is used to develop an optimal strategy for success in competitive circumstances characterized by uncertainty and partial knowledge (like most real-life scenarios). The theories of **game theorists** provide a framework for determining how players should act so as to achieve **some degree** of success in such situations.

Game theory was first developed by mathematicians during the 20th century. It started with two separate but related efforts: one led by Carl von Weizsäcker and the other by John Forbes Nash, Jr.. Both men were members of the Institute for Advanced Study in Princeton, New Jersey. They were also colleagues at Princeton University at the time. However, they had no contact with each other until 1955, when they both received Nobel prizes for their work.

Weizsäcker's work focused on mathematical models of conflict and cooperation between nations. He showed how the results of such games could be analyzed mathematically using concepts from **linear algebra** and function theory.

Nash worked on a different approach to analyzing competition and cooperation. He realized that games played by individuals are actually combinations of two types of games: coordination games and bargaining games. A coordination game requires players to make joint decisions about how to play the game, while bargaining involves only one player deciding how to play against a fixed situation.

John von Neumann (1903–1957), a Hungarian-born mathematician and economist, was the first to apply game theory to economics. In a nutshell, game theory is the study of how individuals (or organizations) use strategy to attain a favorable outcome, i.e. a pay-off. Game theorists classify strategies into **two types**: pure and mixed. A pure strategy is one in which an individual can only choose one option from among several alternatives. For example, if there are three options available to a player - call them A, B, and C - then they could choose option A, B, or C. If all other things are equal, then choosing one option over another would be purely a matter of personal preference. However, in some cases, certain choices may be dictated by necessity. For example, if going back to school causes you pain when it's time to play football, then you should probably avoid doing so. The only option left after avoiding pain is to sit out football.

Mixed strategies, on the other hand, give players more choice than just those between pure strategies. With mixed strategies, players can choose any number of options from among several alternatives. For example, if there are three options available to a player - call them A, B, and C - then they could choose option A with probability p or C with probability 1 - p. It does not matter **which option** they pick as long as they do so randomly.

Economists utilize "game theory" to study economic competition and phenomena such as bargaining, mechanism design, auctions, voting theory, experimental economics, political economy, behavioral economics, and so on. In the corporate realm, game theory is used to identify various tactics. For example, a company might label its competitors with different prices to see which one wins most sales.

Game theorists also use their knowledge to create software that plays games against human opponents or the computer. This software is then tested to determine how well it performs compared to people who play against it.

Finally, game theory is applied in psychology to understand why we act the way we do. Economists and psychologists have used games to learn about judgment and decision-making, respectively. Games allow researchers to control **many variables** at once, which allows them to draw conclusions about **what role** each factor played in determining **our actions**.

In conclusion, game theory is used by economists to explain **competitive markets**, by psychologists to understand behavior, and by software developers to create effective programs.