# Game Theory

## Game Theory

**Game Theory**, or **Theory of Games**, is a branch of mathematical and economic analysis developed to study decision making in conflict situations. Game theory analyzes strategic interactions in which the outcome of one's choices depends upon the choices of others.

A conflict situation exists when two or more decision makers who have different objectives act on the same system or share the same resources.

#### Game theory: Chess

Chess and checkers are two examples of combinatorial game theory. Two players have perfect knowledge of rules, there is no chance element, and players take turns. Strategic decisions of one player depend on moves of the other player.

In classical game theory, players move, bet, or strategize simultaneously. Both hidden information and chance elements are frequent features in this type of game theory.

#### Difference between game theory and decision analysis

Game theory assumes that the agent has opponents that are adjusting their strategies according to what they believe everybody else is doing.

In a situation where we do not consider actions of other players, the problem becomes one of standard decision analysis. For example, a company that reduces prices to increase sales and therefore increase profit may lose money if other players respond with price cuts.

On the other hand, the main purpose of game theory is to consider situations where agents are not making decisions as reactions to exogenous factors, but their decisions are strategic reactions to other agents actions.

An agent is faced with a set of moves he can play and will form a strategy, a best response to his environment, which he will play by.

#### Elements of a game

Each game has a number elements that can be summarized as follows:

- Players: The decision makers in the game.
- Actions: Choices available to a player.
- Information: Knowledge that a player has when making a decision.
- Strategies: Rules that tell a player which action to take at each point of the game.
- Outcomes: The results that unfold, such as a war, peace, etc.
- Payoffs: The positive wealth that each player realizes for a particular outcome.
- Equilibria: An equilibrium is a stable result. Equilibria are not necessarily good outcomes, a fact that is illustrated by the prisoner's dilemma.

#### Game theory in real business

Game theory, or game-playing, while sounding whimsical, is becomming a serious business these days. Governments use it to model behavior of economies.

Managers frequently play "games" both within the firm and outside it. Businesses are trying to model behavior of their competitors, customers, regulators, and even capital markets.

Developing game theory models for business use often calls for the use of heavy computational power and IT solutions. A network of agents is built where each agent performs its function, and the network as a whole is being observed.

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