Maxmin Versus Minmax
In this chapter we will consider games where one player or the other is compelled to make the first move, with the other player having the privilege of examining it before making his own choice. A game is usually represented as a rectangular matrix of payoffs (utilities) to player 1. The rows and columns will be referred to as “strategies”. In any play of the game, the payoff is at the intersection of the row chosen by player 1 and the column chosen by player 2. Player 1 makes his choice in the hope of making the payoff as large as possible, so he will be referred to as the maximizer. Since the game is zero-sum, player 2 has the opposite motivation, and will therefore be referred to as the minimizer. There is no need to develop an explicit notation for player 2’s payoff, but there is a need to remember the convention that “payoff” invariably means “payoff to player 1”. The matrix format is the game’s “normal” form.