Lecture_20_Game Theory :Solving Two Person and Zero - Sum Game

Game theory is a type of decision theory in which one’s choice of action is determined after
taking into account all possible alternatives available to an opponent playing the same game,
rather than just by the possibilities of several outcome results. Game theory does not insist on
how a game should be played but tells the procedure and principles by which action should be
selected. Thus it is a decision theory useful in competitive situations.
Game is defined as an activity between two or more persons according to a set of rules at the end
of which each person receives some benefit or suffers loss. The set of rules defines the game.
Going through the set of rules once by the participants defines a play.
20.2 Properties of a Gam e
1. There are finite numbers of competitors called ‘players’
2. Each player has a finite number of possible courses of action called ‘strategies’
3. All the strategies and their effects are known to the players but player does not know
which strategy is to be chosen.
4. A game is played when each player chooses one of his strategies. The strategies are
assumed to be made simultaneously with an outcome such that no player knows his
opponents strategy until he decides his own strategy.
5. The game is a combination of the strategies and in certain units which determines the
gain or loss.
6. The figures shown as the outcomes of strategies in a matrix form are called ‘pay-off
matrix’.
7. The player playing the game always tries to choose the best course of action which
results in optimal pay off called ‘optimal strategy’.
8. The expected pay off when all the players of the game follow their optimal strategies is
known as ‘value of the game’. The main objective of a problem of a game is to find the
value of the game.
9. The game is said to be ‘fair’ game if the value of the game is zero otherwise it s known as
‘unfair’.
20.3 Characteristics of Game Th eory
1. Competitive game
A competitive situation is called a competitive game if it has the following four properties
1. There are finite number of competitors such that n ? 2. In case n = 2, it is called a twoperson
game and in case n > 2, it is referred as n-person game.
2. Each player has a list of finite number of possible activities.
3. A play is said to occur when each player chooses one of his activities. The choices are
assumed to be made simultaneously i.e. no player knows the choice of the other until he
has decided on his own.