Bimatrix game
In game theory, a bimatrix game is a simultaneous game for two players in which each player has a finite number of possible actions. The name comes from the fact that the normal form of such a game can be described by two matrixes - matrix A describing the payoffs of player 1 and matrix B describing the payoffs of player 2.
Player 1 is often called the "row player" and player 2 the "column player". If player 1 has m possible actions and player 2 n possible actions, then each of the two matrixes has m rows by n columns. when the row player selects the -th action and the column player selects the -th action, the payoff to the row player is and the payoff to the column player is .
![A[i,j]](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1a9bfca6057f52b4e5c3844ecd704962b7e426c)
![{\displaystyle B[i,j]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c807f9e5a23d9752f73987e37eb84f6c24701b10)
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Wikipedia