## GAME THEORY ( OVER-VIEW / BASICS) :-

### OBJECTIVES OF THIS ARTICLE :-

➤Understand Basics terminologies used in game theory.

➤Familiarize the various methods for solving games.

➤Analyze limitation of game in competitive situation.

### TERMINOLOGY :-

➤The participants to the game who act as decision-makers are called players. In a game Two or more participants in the conflict.

➤The former of these is called a

**Two person game**and the latter one is known as a**Person Game**.
➤A finite or infinite number of possible course of action available to a player are called

**Strategies**.**(1) PLAY :-**

A play occurs when each player select one of his available strategies. Two basic assumptions in a play are :-

**(a)**The choice of course of action by player are made simultaneously.

**(b)**No player known the choice of his opponents until he has decided his own.

**(2) OUTCOME :-**

Every combination of strategies of player determined an outcome called pay-off , where pay-off is nothing but a gain to a player A loss is considered as a negative gain.

**(3) Value of the game :-**

The value of the game is the "Excepted gain to a player", if he and his opponent use their best strategies.

**(4) Saddle Point :-**

A saddle point in a pay-off matrix corresponds to that element of the matrix which represents the

**"Maximin"**value of a player &

**"Minimax"**value of his opponent.

➤For this we find maximum element of each row and column & then find

**minimum**value of the column maxima known as**MINIMAX**.
➤Similarly , we identify

**minimum**element of each row and then find**Maximum**of those entries known as**MAXIMIN**.
➤If, Minimax = Maximin , --Saddle point exist. And value of the game is = Minimax / Maximin.

➤If, Minimax ⇏ Maximin , -- No saddle point.

➤If, Minimax = Maximin , -- Optimum strategies.

➤If, Minimax = Maximin =0, Game is Fair.

➤If, Minimax = Maximin , Game is strictly determinable.

➤Usually Maximin ≤ Value of game ≤ Mnimax.

**(5) PAY-OFF Matrix.(Game Theory) :-**

➤The gains resulting from a game is presented in the form of a table called " Pay-Off Matrix ". It comprises of n-rows & m-column is the number of strategies for player 1 & player 2. The pay off of each combinations of the strategies of player are placed as element of matrix.

➤A positive element shows the gain to the first player (i.e. payment from 2 to 1 ) and negative entries indicates the loss to the player 1 (i.e. payment from 1 to 2 ).

In a game with two players, if the gain of one player is equal to the loss of another player , then that game is called two-person zero sum game.

**(6) Two person zero sum game :-**In a game with two players, if the gain of one player is equal to the loss of another player , then that game is called two-person zero sum game.

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