 Mechprof.com is The platform to learn Designing, Digital Manufacturing , manufacturing, simulation , CAM , CAD design, operation research, industrial engineering, mechanical tools, design, AutoCAD , Ansys, solidworks.

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

➤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.

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 ).

(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.

Thank You.