Theory Of Games

Description of game : (cont.)

4.All players act rationally and intelligently.

5.Each player is interested in maximizing his gains or minimizing his losses. The winner, i.e. the player on the left side of the matrix always tries to maximize his gains and is known as Maximin player. He is interested in maximizing his minimum gains. Similarly, the player B, who is at the top of the matrix, a loser always tries to minimize his losses and is known as Minimax player - i.e. who tries to minimize his maximum losses.

6.Each player makes individual decisions without direct communication between the players.

7.It is assumed that each player knows complete relevant information. Game theory models can be classified in a number of ways, depending on such factors as the:

a.       Number of players,

b.      Algebraic sum of gains and losses

c.       Number of strategies of each player, which decides the size of matrix.

Number of players:

a)      If number of players is two it is known as Two-person game.

b)      If the number of players is ‘n’ (where n ≥ 3) it is known as n- person game.

c)       In real world two person games are more popular.

d)      If the number of players is ‘n’, it has to be reduced to two person game by two constant collations, and then we have to solve the game, this is because, the method of solving n- person games are not yet fully developed.

Algebraic sum of gains and losses:

a)      A game in which the gains of one player are the losses of other player or the algebraic sum of gains of both players is equal to zero, the game is known as Zero sum game (ZSG).

b)      In a zero sum game the algebraic sum of the gains of all players after play is bound to be zero. i.e. If g i as the pay of to a player in a n-person game, then the game will be a zero sum game if sum of all g i is equal to zero.

c)       In game theory, the resulting gains can easily be represented in the form of a matrix called pay - off matrix or gain matrix as A pay - off matrix is a table, which showshow payments should be made at end of a play or the game. Zero sum game is also known as constant sum game.

d)      Conversely, if the sum of gains and losses does not equal to zero, the game is a nonzero -sum game.

e)      A game where two persons are playing the game and the sum of gains and losses is equalto zero, the game is known as Two-Person Zero-Sum Game (TPZSG).

f)       A good example of two persongame is the game of chess. A good example of n- person game is the situation when several