Bimatrix game

Bimatrix games are a particular instance of strategic form games, the two player, general sum case. The Prisoner's dilemma, one of the best known problems in game theory, is an example of such a game.

For a strategic form game X,Y,A,B, the Bimatrix representation is a matrix whose entries are ordered pairs (a_ij,b_ij) of elements of the payoff matrices A and B:

(a11,b11) . . . (a1n,b1n)
    .   .          .
    .       .      .
    .          .   .
(am1,bm1) . . . (amn,bmn)

For a concrete example, consider the game of Two finger morra, which has the following Bimatrix form:

                                         
                                    +--------------+--------------+
                                    |              |              |
                                    |   -2  , 2    |   3  ,  -3   |
                                    |              |              |
                                    +--------------+--------------+
                                    |              |              |
                                    |   3  , -3    |   -4 ,  4    |
                                    |              |              |
                                    +--------------+--------------+

Part of A survey of game theory- see project homenode for details and links to the print version.