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# Games Theory

Is a set of concepts aimed at decision making in situations of competitions or conflicts (as well as of co-operation and interdependence) under specified rules. It is a decision theory which is applicable to competitive situations.

COMPETITIVE GAME: this is the competitive situations which occur between two or more persons.

PROPERTIES OF A COMPETITIVE GAME

• The number of participants is stated or finite.
• Each action of operations of individuals is certain
• The choices of players are made simultaneously, in other for the participants choices to be personal to the others until he makes his decision.
• The players of the games must know all the courses of actions available to but must not know which of these courses will be chosen.      TYPES OF GAMES
• One-person games
• Two-person games
• Two-person zero sum games
• N-person games.

ONE-PERSON GAMES

This is a game that consists of one player. There is no competition or conflicts in this, because the interest of the only player is at stake. i.e. solitaire game.

TWO-PERSON GAMES

This involves two players who have conflicting interest. Each players has several possible choices open to them at each play of the game. E.g. checkers, chess etc.

N-PERSON GAMES

This involves unspecified numbers of players. E.G. POKER (board and card games), monopoly game etc.

PAYOFF (OUTCOME) MATRIX This is an expression of the first law of decision science. Each row represents one action that the decision maker might or might not freely choose to perform while each column represents a possible state of nature.

PLAYOFF MATRIX OF B

MAXIMINI AND MINIMAXI PRINCIPLES.

THE MAXIMIN PRINCIPLE: This is a decision rule used in game theory to maximize the minimum guaranteed gains of player A

The maximum of these minimum gains is called the MAXIMIN VALUE and the corresponding alternative course of action is called the MAXIMIN STRATEGY.

MINIMAX PRINCIPLE

This is a decision rule in game theory that is used to minimize the maximum losses.

The minimum of these maximum losses is called the MINIMAX VALUE and the corresponding alternative course of action is called MINIMAX STRATEGY.

SADDLE POINT. This is when the maximin value is equal to the minimax in a game.