Game Theory Lecture

A two person zerosum game is of the form 〈{1, 2}, S1, S2, u1,−u1〉. Note that when a player tries to maximize her payoff, she is also simultaneously minimizing payoff of the other player. For this reason, these games are also called strictly competitive games. Player 1 is usually called the row player and player 2 is called the column player . Let S1 = {s11, s12, . . . , s1m} and S2 = {s21, s22, . . . , s2n}. Without any confusion, we will assume from now on that S1 = {1, 2, . . . ,m} and S2 = {1, 2, . . . , n}. Since the payoffs in a finite two person zerosum game can be completely described by a single matrix, namely the matrix that represents u1(i, j) ∀i ∀j, such a game is aptly called a matrix game. Since the payoffs of one player are just the negative of the payoffs of the other player, these games can be represented by a matrix with m rows and n columns. For this reason, these games are also called matrix games.